Question

Factor –7x3 + 21x2 + 3x – 9 by grouping. What is the resulting expression? (3 – 7x)(x2 – 3) (7x – 3)(3 + x2) (3 – 7x2)(x – 3) (7x2 – 3)(3 + x)

Answer 1

Answer: (3 - 7x^2) (x - 3)

Explanation:

1) Given: -7x^3 + 21x^2 + 3x - 9

2) Group the first two terms and the second two terms:

[-7x^3 + 21x^2] + [3x - 9]

3) Extract common factor -7x^2 from the first group and common factor 3 from the second group:

-7x^2 [x - 3] + 3[x - 3]

4) Take common factor x - 3

(x - 3) (3 - 7x^2)

By commutative property that is equal to (3 - 7x^2) (x - 3)

Answer 2

The correct answer is the option (3–7x²)(x–3). The reasons are shown below:

 If you apply the distributive property in (3–7x²)(x–3), you obtain:

 3x-9-7x²(x)+21x²
 3x-9-7x³+21x²
 
 When you order the expression, you have:

 -7x³+21x²+3x-9
 
 Then, the answer is (3–7x²)(x–3)