Question

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

Answer 1

Hey!!


Let p ( x ) = 0

Factor ( x + 4 ) = 0


x = - 4 is a factor of x^3 + 2x^2 + bx + 68


$p(x) = x {}^{3} + 2x {}^{2} + bx + 68$

Put x = - 4

$p( - 4) = ( - 4) {}^{3} + 2( - 4) {}^{2} + b( - 4) + 68 \\ \\ = > 0 = - 64 + 2 \times 16 - 4b + 68 \\ \\ = > 0 = - 64 + 32 - 4b + 68 \\ \\ = > 0 = 100 - 64 - 4b \\ \\ = > 0 = 36 - 4b \\ \\ = > 4b = 36 \\ \\ = > b = \frac{36}{4} \\ \\ = > b = 9.$


Therefore the value of b is 9.



Hope it helps!