Chapter 8.8, Problem 39PPE

To determine

To write: A four-term polynomial that can be factored by grouping and factor that polynomial.

Answer to Problem 39PPE

A factored of four-term polynomial is $3x^2+5x+25+15x=\left(3x+5\right)\left(x+5\right)$ .

Explanation of Solution

Given information:

A four-term polynomial that can be factored by grouping and to factor the polynomial.

Formula used:

The polynomial $a{x}^2+bx+b^2+abx$ is a four − term polynomial that can be factorized by grouping and then using distributive property.

Calculations:

A four − term polynomial may be given as $3x^2+5x+25+15x$ .

The polynomial can be factorized by grouping and then using distributive property as:

  $3x^2+5x+25+15x=3x^2+5x+15x+25$

Grouping of terms

  $\Rightarrow 3x^2+5x+25+15x=x\left(3x+5\right)+5\left(3x+5\right)$

  $\Rightarrow 3x^2+5x+25+15x=\left(3x+5\right)\left(x+5\right)$

Distributive property of multiplication over addition

Thus, a factored of four-term polynomial is $3x^2+5x+25+15x=\left(3x+5\right)\left(x+5\right)$ .

Conclusion:

A factored of four-term polynomial is $3x^2+5x+25+15x=\left(3x+5\right)\left(x+5\right)$ .