Exhibit 5.1

October 27, 2017

Blucora, Inc.

6333 State Highway 161, 6th Floor

Irving, Texas 75038

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

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. 3 to the Registration Statement on Form S-8 (File No. 333-169691) and Post-Effective Amendment No. 1 to the Registration Statement on Form S-8 (File No. 333-198645) (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 “Original 2010 Form S-8”) as amended by Post-Effective Amendment No. 1 to Registration Statement on Form S-8, filed on May 29, 2015 (“Post-Effective Amendment No. 1”), and Post-Effective Amendment No. 2 to Registration Statement on Form S-8, filed on May 25, 2016 (“Post-Effective Amendment No. 2,” and collectively with the Original 2010 Form S-8 and Post-Effective Amendment No. 1, 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 may 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 may be issued to participants under the 1996 Plan (the “2014 Form S-8”).

On May 28, 2015, the Company’s stockholders approved the Company’s 2015 Incentive Plan, which was subsequently amended and restated on May 24, 2016 (the “2015 Plan”) and, in connection therewith, no further awards will be made under the 1996 Plan. The maximum number of shares of Common Stock reserved for issuance under the 2015 Plan includes (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 cease to be subject to such awards, such as by expiration, cancellation or forfeiture of the awards. As a result, the Company subsequently filed (i) 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) 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”).

On May 28, 2015, the Company filed a Registration Statement on Form S-8 (File No. 333-204585) for the purpose of, among other things, registering 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, among other things, registering additional shares of Common Stock issuable pursuant to awards under the 2015 Plan, including the Cancelled 1996 Plan Shares (the “2016 Form S-8”).

The purpose of the Current Post-Effective Amendments is to update the Amended 2010 Form S-8 and the 2014 Form S-8 to reflect that 538,122 shares of Common Stock that are subject to outstanding awards under the 1996 Plan may become issuable under the 2015 Plan and 769,623 shares of Common Stock that have expired, been cancelled or were forfeited have become issuable under the 2015 Plan, for an aggregate of 1,307,745 shares of Common Stock (the "Carryover Shares"), and remain registered on the Amended 2010 Form S-8 and the 2014 Form S-8, in each case not including the Unissued 1996 Plan Shares or Cancelled 1996 Plan Shares. In connection with the potential issuance of the Carryover Shares under the 2015 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 and the Amended and Restated Bylaws of the Company, each as amended and/or restated as of the date hereof; (ii) certain resolutions of the board of directors of the Company related to the filing of the Post-Effective Amendments and the issuance of the Carryover Shares under the 2015 Plan; (iii) the 2015 Plan; (iv) each of the Amended 2010 Form S-8, the 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 2015 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 2015 Plan, the Carryover Shares will be validly issued, fully paid and non-assessable.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to all references to us in the Registration Statement. 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