Question

(x² + 6x − 16)(x − 2) = ax³ + bx² + cx + d

What is the value of
c/d
a.8
b.7
c.-7
d.-8

Answer 1

The value of c/d is -7/8

Solution:

Given that,

`(x^2 + 6x - 16)(x - 2) = ax^3 + bx^2 + cx + d`

We have to find the value of
`(c)/(d)`

Let us simplify the given expression

Simplify the left hand side of equation

`(x^2 + 6x - 16)(x - 2)\\\\Distribute\:parentheses\\\\x^2x+x^2\left(-2\right)+6xx+6x\left(-2\right)+\left(-16\right)x+\left(-16\right)\left(-2\right)\\\\Simplify\\\\x^2x-2x^2+6xx-6\cdot \:2x-16x+16\cdot \:2\\\\x^3+4x^2-12x-16x+32\\\\\mathrm{Add\:similar\:elements:}\\\\x^3+4x^2-28x+32`

Therefore,

`x^3 + 4x^2 - 28x + 32 = ax^3 + bx^2 + cx + d`

On comparing both sides we get,

c = -28

d = 32

Therefore,

`(c)/(d) = (-28)/(32) = (-7)/(8)`

Thus value of c/d is -7/8