Question

6.4 trinomials where a does not equal 1: problem 13 (1 point) factor the expression 4z² + 8z − 12. simplify your answer as much as possible, and put the greatest common factor in the first answer box. ( ( )( ) ) help (formulas) note: you can earn partial credit on this problem. preview my answers submit answers you have attempted this problem 0 times. you have unlimited attempts remaining. email instructor page generated december 1, 2023, 2:24 am cdt webwork © 1996-2024 | theme: math4 | ww_version: 2.19 | pg_version: 2.19 the webwork project

Explanation:

Step1: Factor out the greatest common factor

The greatest common factor of \(4z^{2}\), \(8z\), and \(- 12\) is \(4\).

$$4z^{2}+8z - 12=4(z^{2}+2z - 3)$$

Step2: Factor the quadratic trinomial

We need to find two numbers \(m\) and \(n\) such that \(m + n=2\) and \(m\times n=-3\). The numbers are \(m = 3\) and \(n=-1\).

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

Answer:

\(4(z + 3)(z - 1)\)