Question

Which binomial expressions are factors of 4x3+9x2−x−6? Select each correct answer.

Answer 1

 (x + 1)   ,  (4x - 3)    & (x + 2)  are Factors of 4x³ + 9x² - x - 6

Step-by-step explanation:

4x³ + 9x² - x - 6

= (x + 1) ( 4x² + 5x - 6)

= (x + 1) ( 4x² + 8x - 3x - 6)

= (x + 1) ( 4x(x + 2) - 3(x + 2))

= (x + 1) (4x - 3)(x + 2)

Factors of 4x³ + 9x² - x - 6

 (x + 1)   ,  (4x - 3)    & (x + 2)

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Answer 2

Answer:

Factors are (x + 1), (4x - 3) and (x + 2)

Step-by-step explanation:

Given expression,

$4x^3+9x^2-x-6$

Since, for x = -1,

$4(-1)^3+9(-1)^2-(-1)-6=-4+9+1-6 = 6-6=0$

Thus, x+ 1 is one of the factors of $4x^3+9x^2-x-6$,

By dividing $4x^3+9x^2-x-6$ by (x+1) we get, ( shown below ),

Quotient = $4x^2+5x-6$

So,

$4x^3+9x^2-x-6=(x+1)(4x^2+5x-6)$

Now, by middle term splitting,

$4x^2 + 5x - 6 = 4x^2 + 8x - 3x - 6 = 4x(x+2)-3(x+2) = (4x-3)(x+2)$

$\implies 4x^3+9x^2-x-6 = (x+1)(4x-3)(x+2)$

Hence, the factors of $4x^3+9x^2-x-6$ are x + 1, 4x - 3 and x + 2

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