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

1 Answer

4 votes

Answer:

The solutions are:


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

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:

User Karan Alang
by
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