Question

Find all solutions to the equation (x² + 5x + 6)(x² − 3x − 4) = 0.

Answer 1

Answer:

The solutions are:

$x=-2,\:x=-3,\:x=-1,\:x=4$

Step-by-step explanation:

To find the solutions to the equation $\left(x^2+5x+6\right)\left(x^2-3x-4\right)=0$ you need to:

• Factor $\left(x^2+5x+6\right)$

Break the expression into groups

$x^2+5x+6=\left(x^2+2x\right)+\left(3x+6\right)$

Factor out $x$ from $(x^2+2x)$

$x^2+2x=x\left(x+2\right)$

Factor out 3 from $3x+6$

$3x+6=3\left(x+2\right)$

$x^2+5x+6=x\left(x+2\right)+3\left(x+2\right)\\\\\mathrm{Factor\:out\:common\:term\:}x+2\\\\x^2+5x+6=\left(x+2\right)\left(x+3\right)$

• Factor $\left(x^2-3x-4\right)$

$x^2-3x-4=\left(x^2+x\right)+\left(-4x-4\right)\\\\x^2-3x-4=x\left(x+1\right)-4\left(x+1\right)\\\\x^2-3x-4=\left(x+1\right)\left(x-4\right)$

Therefore

$\left(x^2+5x+6\right)\left(x^2-3x-4\right)=\left(x+2\right)\left(x+3\right)\left(x+1\right)\left(x-4\right)=0$

Using the Zero Factor Theorem: