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

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

Clarification:

1) The expression is -7x^3 + 21x^2 + 3x - 9

2) Separate the first two terms from the last two:

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

3) Factor out -7x^2 from the first pair and 3 from the second:

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

4) Factor out the common term x - 3

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

Using the commutative property, this can also be expressed as (3 - 7x^2) (x - 3)

The right option is (3–7x²<span>)(x–3). The justification follows:
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By using the distributive property on (</span>3–7x²)(x–3), you arrive at:
<span>
3x-9-</span>7x²(x)+21x²
3x-9-7x³+21x²

After reorganizing the expression, it becomes:

-7x³+21x²+3x-9

Therefore, the result is (3–7x²)(x–3)