Exhibit 5.1

June 7, 2018

Blucora, Inc.

6333 State Highway 161, 4th Floor

Irving, Texas 75038

Re: Blucora, Inc. Post-Effective Amendments to Registration Statements on Form S-8 (File Nos. 333-169691, 333-198645, 333-211625 and 333-204585)

Ladies and Gentlemen:

We have acted as counsel to Blucora, Inc., a Delaware corporation (the “Company”), with respect to certain legal matters in connection with the preparation of the Company’s Post-Effective Amendment No. 4 to the Registration Statement on Form S-8 (File No. 333-169691), Post-Effective Amendment No. 2 to the Registration Statement on Form S-8 (File No. 333-198645), Post-Effective Amendment No. 1 to the Registration Statement on Form S-8 (File No. 333-211625) and Post-Effective Amendment No. 1 to the Registration Statement on Form S-8 (File No. 333-204585) (collectively, the “Current Post-Effective Amendments”) under the Securities Act of 1933, as amended (the “Securities Act”), filed with the Securities and Exchange Commission on the date hereof.

On September 30, 2010, the Company filed a Registration Statement on Form S-8 (File No. 333-169691) (the “2010 Form S-8”) with the Securities and Exchange Commission (the “SEC”), as amended by Post-Effective Amendment No. 1 to Registration Statement on Form S-8, filed on May 29, 2015 (the “2010 S-8 Post-Effective Amendment No. 1”), Post-Effective Amendment No. 2 to Registration Statement on Form S-8, filed on May 25, 2016 (the “2010 S-8 Post-Effective Amendment No. 2”), and Post-Effective Amendment No. 3 to Registration Statement on Form S-8, filed on October 27, 2017 (the “2010 S-8 Post-Effective Amendment No. 3,” and collectively with the 2010 Form S-8, the 2010 S-8 Post-Effective Amendment No. 1 and the 2010 S-8 Post-Effective Amendment No. 2, the “Amended 2010 Form S-8”) for the purpose of registering 9,651,091 shares of common stock, par value $0.0001 per share (“Common Stock”) that could be issued to participants under the Blucora, Inc. Restated 1996 Flexible Stock Incentive Plan (the “1996 Plan”). In addition, on September 8, 2014, the Company filed a Registration Statement on Form S-8 (File No. 333-198645) for the purpose of registering an additional 1,804,432 shares of Common Stock that could be issued to participants under the 1996 Plan (the “2014 Form S-8”), as amended by Post-Effective Amendment No. 1 to Registration Statement on Form S-8, filed on October 27, 2017 (the “2014 S-8 Post-Effective Amendment No. 1,” and together with the 2014 Form S-8, the “Amended 2014 Form S-8”).

On May 28, 2015, the Company’s stockholders approved the Blucora, Inc. 2015 Incentive Plan, which was subsequently amended and restated on May 24, 2016 (the “2015 Plan”) and, in connection therewith, no further awards were permitted to be made under the 1996 Plan. The maximum number of shares of Common Stock reserved for issuance under the 2015 Plan included (i) all of the shares of Common Stock that were reserved for issuance under the 1996 Plan but unissued as of May 28, 2015 and (ii) all of the shares of Common Stock that were subject to awards under the 1996 Plan as of May 28, 2015 that subsequently ceased to be subject to such awards, such as by expiration, cancellation or forfeiture of the awards. As a result, the Company subsequently filed (i) the 2010 S-8 Post-Effective Amendment No. 1 for the purpose of deregistering 1,252,940 shares of Common Stock that remained available for issuance under the 1996 Plan that were not subject to awards at the time of adoption of the 2015 Plan (the “Unissued 1996 Plan Shares”) and (ii) the 2010 S-8 Post-Effective Amendment No. 2 for the purpose of deregistering 756,136 shares of Common Stock that ceased to be subject to outstanding awards under the 1996 Plan by expiration, cancellation or forfeiture of such awards (the “Cancelled 1996 Plan Shares”).

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On May 28, 2015, the Company filed a Registration Statement on Form S-8 (File No. 333-204585) for the purpose of registering 6,252,940 shares of Common Stock issuable pursuant to awards under the 2015 Plan, including the Unissued 1996 Plan Shares (the “2015 Form S-8”). On May 25, 2016, the Company filed a Registration Statement on Form S-8 (File No. 333-211625) for the purpose of registering 4,156,136 additional shares of Common Stock issuable pursuant to awards under the 2015 Plan, including the Cancelled 1996 Plan Shares (the “2016 Form S-8”).

On October 27, 2017, pursuant to guidance from the staff of the SEC in Compliance and Disclosure Interpretation 126.43 of the Securities Act Forms (“C&DI 126.43”), the Company filed the 2010 S-8 Post-Effective Amendment No. 3 and the 2014 S-8 Post-Effective Amendment No. 1 to reflect that (i) 538,122 shares of Common Stock that were subject to outstanding awards under the 1996 Plan and that remained registered on the 2010 Form S-8 and the 2014 Form S-8 may become issuable under the 2015 Plan as a result of expiration, cancellation or forfeiture and (ii) 769,623 shares of Common Stock that were originally subject to outstanding awards under the 1996 Plan and that remained registered on the 2010 Form S-8 and the 2014 Form S-8 had expired, been cancelled or were forfeited and had become issuable under the 2015 Plan.

On June 7, 2018, the Company’s stockholders approved the the Blucora, Inc. 2018 Long-Term Incentive Plan (the “2018 Plan”) and the 2018 Plan became effective. Pursuant to the terms of the 2018 Plan, the maximum number of shares of the Company’s Common Stock, issuable under the 2018 Plan shall include (i) 2,600,000 newly authorized shares of Common Stock, (ii) 2,963,134 shares of Common Stock that were reserved for issuance under the 2015 Plan but remained unissued as of April 2, 2018 (the “Unissued 2015 Plan Shares”) and (iii) the total number of shares subject to outstanding awards under the 2015 Plan and the 1996 Plan as of the effective date of the 2018 Plan and that subsequently cease to be subject to such awards, such as by expiration, cancellation or forfeiture of the awards.

The purpose of the Current Post-Effective Amendments is to amend the Amended 2010 Form S-8, the Amended 2014 Form S-8, the 2015 Form S-8 and the 2016 Form S-8 to reflect that the following shares of Common Stock may be issued pursuant to the 2018 Plan:

(i) the Unissued 2015 Plan Shares, which remain registered on the 2015 Form S-8 and the 2016 Form S-8;

(ii) an aggregate of 3,238,694 shares of Common Stock that were subject to outstanding awards under the 2015 Plan as of June 6, 2018 but may become issuable under the 2018 Plan as a result of expiration, cancellation or forfeiture and which remain registered on the 2015 Form S-8 and 2016 Form S-8; and

(iii) an aggregate of 113,563 shares of Common Stock that were subject to outstanding awards under the 1996 Plan as of June 6, 2018 but may become issuable under the 2018 Plan as a result of expiration, cancellation or forfeiture and which remain registered on the Amended 2010 Form S-8 and the Amended 2014 Form S-8 (the shares described in clauses (i), (ii) and (iii), the “Carryover Shares”).

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As a result of the Current Post-Effective Amendments, any shares of Common Stock that are subject to outstanding awards under the 1996 Plan and that would have become issuable under the 2015 Plan upon the expiration, forfeiture or cancellation of such awards pursuant to the 2010 S-8 Post-Effective Amendment No. 3 and the 2014 S-8 Post-Effective Amendment No. 1 will instead become issuable under the 2018 Plan. In connection with the potential issuance of the Carryover Shares under the 2018 Plan, we have provided the opinion set forth below.

This opinion is being furnished in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act.

The opinion expressed herein is limited exclusively to the General Corporation Law of the State of Delaware, as currently in effect, and we have not considered, and express no opinion on, any other laws.

In rendering the opinion set forth herein, we have examined originals or copies, certified or otherwise identified to our satisfaction, of: (i) the Certificate of Incorporation of the Company, as amended through June 1, 2017, and the Amended and Restated Bylaws of the Company, dated February 28, 2017; (ii) certain resolutions of the Board related to the filing of the Current Post-Effective Amendments and the issuance of the Carryover Shares under the 2018 Plan; (iii) the 2018 Plan; (iv) each of the Amended 2010 Form S-8, the Amended 2014 Form S-8, the 2015 Form S-8 and the 2016 Form S-8 and all exhibits thereto; (v) the Current Post-Effective Amendments and all exhibits thereto; (vi) the specimen Common Stock certificate; (vii) a certificate executed by an officer of the Company, dated as of the date hereof; and (viii) such other records, documents and instruments as we considered appropriate for purposes of the opinion stated herein.

In making the foregoing examinations, we have assumed the genuineness of all signatures, the legal capacity of all natural persons, the authenticity of all documents submitted to us as originals, the conformity to original documents submitted to us as certified, conformed or photostatic copies thereof and the authenticity of the originals of such latter documents. As to all questions of fact material to the opinion stated herein, we have, without independent third party verification of their accuracy, relied in part, to the extent we deemed reasonably necessary or appropriate, upon the representations and warranties of the Company contained in such documents, records, certificates, instruments or representations furnished or made available to us by the Company.

In rendering the opinion set forth below, we have assumed that, at the time of the issuance of the Carryover Shares: (i) the resolutions of the Company referred to above will not have been modified or rescinded; (ii) there will not have occurred any change in the law affecting the authorization, execution, delivery, validity or fully paid status of the Common Stock; and (iii) the Company will receive consideration for the issuance of the Carryover Shares required by the 2018 Plan and that is at least equal to the par value of the Common Stock.

Based on the foregoing, and subject to the assumptions, qualifications, limitations, and exceptions set forth herein, we are of the opinion that upon the issuance of the Carryover Shares in accordance with the terms of the 2018 Plan, the Carryover Shares will be validly issued, fully paid and non-assessable.

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We hereby consent to the filing of this opinion as an exhibit to the Registration Statements and to all references to us in the Registration Statements. In giving this consent, we do not admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act and the rules and regulations thereunder. This opinion is given as of the date hereof and we assume no obligation to update or supplement such opinion after the date hereof to reflect any facts or circumstances that may thereafter come to our attention or any changes that may thereafter occur.

Very truly yours,

/s/ Haynes and Boone, LLP

Haynes and Boone, LLP

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