Q 56E

In the following exercises, factor.

$5 x^{3} - 3 x^{2} + 5 x - 3$ .

Verified

Answer

The factors for the expression $5 x^{3} - 3 x^{2} + 5 x - 3$ are, $(5 x - 3) (x^{2} + 1)$ .

1Step 1 Given expression is,

$5 x^{3} - 3 x^{2} + 5 x - 3$ .

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

2Step 2 First group each term with the common factors.

$5 x^{3} - 3 x^{2} + 5 x - 3 = (5 x^{3} - 3 x^{2}) + (5 x - 3)$

Now factor out the common terms.

$5 x^{3} - 3 x^{2} + 5 x - 3 = x^{2} (5 x - 3) + 1 (5 x - 3) = (x^{2} + 1) (5 x - 3)$

The obtained factors are, $(x^{2} + 1) (5 x - 3)$ .

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

$(5 x - 3) (x^{2} + 1) = 5 x^{3} + 5 x - 3 x^{2} - 3 = 5 x^{3} - 3 x^{2} + 5 x - 3$

which is true.