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Factor theorem polynomial coefficient

CMAT 2018 · Quantitative Techniques & Data Interpretation · Easy · Algebra

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If (x+4)(x + 4) is a factor of x3+2x2+bx+68x^3 + 2x^2 + bx + 68, what is the value of b?

  1. A.

    -9

  2. B.

    9

  3. C.

    8

  4. D.

    -8

Answer

B

Explanation

By the Factor Theorem, if (x+4)(x + 4) is a factor, then f(−4)=0f(-4) = 0. f(−4)=(−4)3+2(−4)2+b(−4)+68=0f(-4) = (-4)^3 + 2(-4)^2 + b(-4) + 68 = 0 −64+32−4b+68=0  ⟹  36−4b=0  ⟹  b=9-64 + 32 - 4b + 68 = 0 \implies 36 - 4b = 0 \implies b = 9.

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