Q. 19

Question

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

$5 x^{3} - 15 x^{2} + 20 x$

Step-by-Step Solution

Verified

Answer

The factored form is $\begin{array}{rcl} 5 x (x^{2} - 3 x + 4) \end{array}$ .

1Step 1. Given Information

The given polynomial is $5 x^{3} - 15 x^{2} + 20 x$ .

2Step 2. Find the GCF of the terms

Factor each of the terms in the given expression.

$\begin{array}{rcl} 5 x^{3} & = & 5 \cdot x \cdot x \cdot x \\ 15 x^{2} & = & 5 \cdot 3 \cdot x \cdot x \\ 20 x & = & 2 \cdot 2 \cdot 5 \cdot x \end{array}$

From the obtained factors, it is observed that the common factors are $5, x$ .
Multiply the common factors.

$5 \cdot x = 5 x$

So, the GCF of the terms of the given expression is $5 x$ .

3Step 3. Rewrite the given expression

Express each of the term of the given expression as a product of GCF, $5 x$ .

$5 x \cdot x^{2} - 5 x \cdot 3 x + 5 x \cdot 4$

Use the reverse distributive property, $a b + a c = a (b + c)$ to rewrite the obtained expression.

$5 x \cdot x^{2} - 5 x \cdot 3 x + 5 x \cdot 4 = 5 x (x^{2} - 3 x + 4)$

4Step 4. Check

Multiply the obtained factors.

$\begin{array}{rcl} 5 x (x^{2} - 3 x + 4) & = & 5 x \cdot x^{2} - 5 x \cdot 3 x + 5 x \cdot 4 \\ = & 5 x^{3} - 15 x^{2} + 20 x \end{array}$

Since the obtained expression is the same as the given expression, the obtained factors are verified.

Q. 18

Q. 20

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Q. 21

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