itomath.com

Quadratic Equations $ax^2+bx+c=0$

Factorizing $ax^2+bx+c$

Expand $\left(\color{#0275d8}{2x}+\color{#d9534f}{3}\right)\left(\color{#d9534f}{x}+\color{#0275d8}{1}\right)=$ $x^2+$ $\color{#0275d8}{x}+$ $\color{#d9534f}{x}+$

$=$ $x^2+$ $x+$

So, to factorize $2x^2+5x+3$
$\color{#0275d8}{x}$ ╳
$\color{#d9534f}{1x}$
where if you cross multiply and add, you get the middle term $5x$

Therefore, $2x^2+5x+3=\left(2x+3\right)\left(x+1\right)$

Practice
Factorize $3x^2+16x+5$
$x$ ╳
$x$
Therefore, $3x^2+16x+5=$

Factorize $6x^2+13x+6$
╳ $3$
Therefore, $6x^2+13x+6=$

Factorize $8x^2+2x-15$
╳ $3$
Therefore, $8x^2+2x-15=$

Factorize $-4x^2+19x-12$
╳
$x$
Therefore, $-4x^2+19x-12=$
Factorize:
$3x^2+7x+4$

$3x^2+11x+6$

$2x^2+5x-12$

$2x^2-5x+3$

$3x^2+19x-40$

$3x^2-32x+45$

$7x^2+24x-16$

$8x^2-11x+3$

$x^2-36$

$x^2-49$

$16x^2-1$

$49x^2-25$

Solve for $x$. If there are multiple answers, separate them with commas. Give answers as simplified fractions and not decimals.

$2x^2+9x+9=0 \qquad x=$

$2x^2+7x+6=0 \qquad x=$

$3x^2+5x-12=0 \qquad x=$

$3x^2-8x+4=0 \qquad x=$

$3x^2-32x+45=0 \qquad x=$

$2x^2-9x-35=0 \qquad x=$

$8x^2-29x-12=0 \qquad x=$

$4x^2+x-3=0 \qquad x=$

$15x^2+17x+4=0 \qquad x=$

$9x^2+18x+8=0 \qquad x=$

$20x^2-x-63=0 \qquad x=$

$6x^2+17x-45=0 \qquad x=$