Q. 347

In the following exercises, factor the greatest common factor from each polynomial.

$- 3 x^{3} + 27 x^{2} - 12 x$

Verified

Answer

The factored form of the polynomial is,

$3 x (- x^{2} + 9 x - 4)$

1Step 1. Given Information

We are given a polynomial,

$- 3 x^{3} + 27 x^{2} - 12 x$

2Step 2. Finding the greatest common factor

Factoring the polynomial,

$3 x^{3} = = 3 \times x \times x \times x 27 x^{2} = 3 \times 3 \times 3 \times x \times x 12 x = 2 \times 2 \times 3 \times x$

The greatest common factor is $3 x$ , so

$- 3 x^{3} + 27 x^{2} - 12 x = - 3 x \times x^{2} + 3 x \times 9 x - 3 x \times 4 - 3 x^{3} + 27 x^{2} - 12 x = 3 x (- x^{2} + 9 x - 4)$

3Step 3. Checking the factorization

Multiplying the factors,

$3 x (- x^{2} + 9 x - 4) = - 3 x^{3} + 27 x^{2} - 12 x - 3 x^{3} + 27 x^{2} - 12 x = - 3 x^{3} + 27 x^{2} - 12 x L H S = R H S$

Hence the factorization is correct.