Q 53E

In the following exercises, factor.

$3 x^{3} - 7 x^{2} + 6 x - 14$ .

Verified

Answer

The obtained factor for the expression $3 x^{3} - 7 x^{2} + 6 x - 14$ is, $(3 x - 7) (x^{2} + 2)$ .

1Step 1 Given expression is,

$3 x^{3} - 7 x^{2} + 6 x - 14$ .

The objective is, we need to find the factor for this expression.

2Step 2 First group the terms with the common factors.

$3 x^{3} - 7 x^{2} + 6 x - 14 = (3 x^{3} - 7 x^{2}) + (6 x - 14)$

Now factor out the common factors.

$3 x^{3} - 7 x^{2} + 6 x - 14 = x^{2} (3 x - 7) + 2 (3 x - 7) = (3 x - 7) (x^{2} + 2)$

The obtained factors are, $(3 x - 7) (x^{2} + 2)$

3Step 3 Let us check the answer by multiplying the factors.

$(3 x - 7) (x^{2} + 2) = 3 x^{3} + 6 x - 7 x^{2} - 14 = 3 x^{3} - 7 x^{2} + 6 x - 14$

which is true.