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:
$2x^2+7x+6$

$2x^2+5x+3$

$3x^2-11x+6$

$3x^2-13x+12$

$3x^2+13x-56$

$2x^2+19x+42$

$8x^2+13x-6$

$4x^2-17x+4$

$x^2-1$

$x^2-4$

$25x^2-64$

$25x^2-36$

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

$3x^2+7x+4=0 \qquad x=$

$3x^2+10x+8=0 \qquad x=$

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

$2x^2-11x+12=0 \qquad x=$

$3x^2-26x+35=0 \qquad x=$

$2x^2+11x-63=0 \qquad x=$

$8x^2+27x+9=0 \qquad x=$

$4x^2-3x-1=0 \qquad x=$

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

$15x^2-7x-2=0 \qquad x=$

$9x^2+36x+35=0 \qquad x=$

$9x^2+6x-35=0 \qquad x=$