How do you find the zeros by rewriting the function g(x)=3x^2+24x+21 in intercept form?

Dec 6, 2017

$x = - 1 , x = - 7$

Explanation:

$\text{factorise g(x)}$

$g \left(x\right) = 3 \left({x}^{2} + 8 x + 7\right) \leftarrow \textcolor{b l u e}{\text{common factor of 3}}$

$\text{the factors of + 7 which sum to + 8 are + 1 and + 7}$

$\Rightarrow g \left(x\right) = 3 \left(x + 1\right) \left(x + 7\right) \leftarrow \textcolor{b l u e}{\text{in intercept form}}$

$\text{equate each of the factors to zero and solve for x}$

$x + 1 = 0 \Rightarrow x = - 1$

$x + 7 = 0 \Rightarrow x = - 7$