Chapter 4.3, Problem 30PPS

To determine

To calculate: The factors of the polynomial $4x^2+29x+30$ .

Answer to Problem 30PPS

The polynomial is factored as $\left(x+6\right)\left(4x+5\right)$ .

Explanation of Solution

Given information:

The polynomial $4x^2+29x+30$ .

Formula used:

To factor a polynomial split the middle term in such a way that sum of two numbers is the middle term and product of two numbers is same is product of first and last term.

Calculation:

Consider the polynomial $4x^2+29x+30$ .

Recall that to factor a polynomial split the middle term in such a way that sum of two numbers is the middle term and product of two numbers is same is product of first and last term.

For the above polynomial $5$ and $24$ are two numbers such that their sum is $29$ and product is $120$ .

Apply it, first the group the similar terms,

  $\begin{array}{c}4x^2+29x+30=4x^2+24x+5x+30\\ =4x\left(x+6\right)+5\left(x+6\right)\\ =\left(x+6\right)\left(4x+5\right)\end{array}$

Thus, the polynomial is factored as $\left(x+6\right)\left(4x+5\right)$ .