Chapter 6: Q 56E (page 573)

In the following exercises, factor.
$5 x^{3} - 3 x^{2} + 5 x - 3$ .

Short Answer

Expert verified

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

Step by step solution

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.

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

Step 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.

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In the following exercises, factor.
$5 x^{3} - 3 x^{2} + 5 x - 3$ .

Short Answer

Step by step solution

Given expression is,

First group each term with the common factors.

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

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In the following exercises, factor.5x3-3x2+5x−3.

Short Answer

Step by step solution

Given expression is,

First group each term with the common factors.

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Discrete Mathematics

Decision Maths

Statistics

Geometry

Probability and Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises, factor.
$5 x^{3} - 3 x^{2} + 5 x - 3$ .