John Landry

Answered

2022-07-26

Solve by factoring.
1. ${x}^{2}-2x-15=0$
2. $2{x}^{2}+5x-3=0$
3. ${x}^{2}=10x$
4. ${x}^{3}+2{x}^{2}-8x=0$
V: Solving Cubic Equations, V: Factoring cubes.

Answer & Explanation

autosmut6p

Expert

2022-07-27Added 8 answers

Step 1
1) ${x}^{2}-2x-15=0$
${x}^{2}-5x+3x-15=0$
$x\left(x-5\right)+3\left(x-5\right)=0$
$\left(x+3\right)\left(x-5\right)=0$
$x=3,x=5$
Step 2
2) $2{x}^{2}+5x-3=0$
$2{x}^{2}+6x-x-3=0$
$2x\left(x+3\right)-1\left(x+3\right)=0$
$\left(2x-1\right)\left(x+3\right)=0$
$x=\frac{1}{2},x=-3$
3) ${x}^{2}-10x=0$
$x\left(x-10\right)=0$
$x=0,x=10$
4) ${x}^{3}+2{x}^{2}-8x=0$
$x\left({x}^{2}+2x-8\right)=0$
$x\left({x}^{2}+4x-2x-8\right)=0$
$x\left[x\left(x+4\right)-2\left(x+4\right)\right]=0$
$\left(x\right)\left(x-2\right)\left(x+4\right)=0$
$x=0,x=2,x=-4$

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