The Null Factor Law
Fill in the blanks.
$6\times$
$=0$
$\times7=0$
$\left(-3\right)\times$
$=0$
$\times\left(-5\right)=0$
$a\times$
$=0$
$\times b=0$
If $a\times b=0$, then $a=$
or $b=$
or both.
Fill in the blanks.
$6\times \left(\square-5\right) =0$
$\left(-3\right) \left(\square +4\right) =0$
$a\times \left(\square -p\right) =0$
$\left(\square +9\right) \times 7=0$
$\left(\square -\frac{1}{2}\right) \left(-5\right)=0$
$\left(\square -q\right) \times b=0$
Solve for $x$. If there are multiple answers, separate them with commas.
$\left(x-2\right)\left(x-1\right)=0\qquad \qquad x=$
$\left(x-7\right)\left(x+7\right)=0\qquad \qquad x=$
$\left(x-4\right)^2=0\qquad \qquad x=$
$x\left(x+8\right)=0\qquad \qquad x=$
$3\left(x-5\right)\left(x+4\right)=0\qquad \qquad x=$
$-2x\left(x+6\right)^2=0\qquad \qquad x=$
$\left(x-3\right)\left(2x-1\right)=0\qquad \qquad x=$
$-\left(x+5\right)\left(3x+4\right)=0\qquad \qquad x=$
$2\left(4x+1\right)^2=0\qquad \qquad x=$
$\left(2x-5\right)\left(5x+2\right)=0\qquad \qquad x=$
Solve for $x$. If there are multiple answers, separate them with commas.
$\left(x-1\right)\left(x-2\right)\left(x-3\right)=0\qquad \qquad x=$
$\left(x-7\right)\left(x+7\right)^2=0\qquad \qquad x=$
$\left(x-5\right)^3=0\qquad \qquad x=$
$x^2\left(x+8\right)\left(x-\frac{1}{2}\right)=0\qquad \qquad x=$
$-\left(x+2\right)\left(x-3\right)^2\left(x+1\right)^3=0\qquad \qquad x=$
Solving by Factorizing
Fully factorize. $\qquad x^2-3x+2=$
Solve for $x$.$\qquad x^2-3x+2=0\qquad \qquad x=$
Fully factorize. $\qquad x^2-49=$
Solve for $x$.$\qquad x^2-49=0\qquad \qquad x=$
Fully factorize. $\qquad x^2-8x+16=$
Solve for $x$.$\qquad x^2-8x+16=0\qquad \qquad x=$
Fully factorize. $\qquad x^2+8x=$
Solve for $x$.$\qquad x^2+8x=0\qquad \qquad x=$
Fully factorize. $\qquad 3x^2-3x-60=$
Solve for $x$.$\qquad 3x^2-3x-60=0\qquad \qquad x=$
Fully factorize. $\qquad -2x^2-24x-72=$
Solve for $x$.$\qquad -2x^2-24x-72=0\qquad \qquad x=$
Solve for $x$. If there are multiple answers, separate them with commas.
$x^2-3x=-2\qquad \qquad x=$
$x^2=49\qquad \qquad x=$
$x^2+16=8x\qquad \qquad x=$
$8x=-x^2\qquad \qquad x=$
$3\left(x^2-20\right)=3x\qquad \qquad x=$
$-72=2x\left(x+12\right)\qquad \qquad x=$
Solve for $𝑥$. If there are multiple answers, separate them with commas.
$x^2-9x=0\qquad x=$
$x^2-2x=0\qquad x=$
Solve for $𝑥$. If there are multiple answers, separate them with commas.
$x^2=7x\qquad x=$
$x^2=8x\qquad x=$
Solve for $𝑥$. If there are multiple answers, separate them with commas.
$-3x^2+4x=0\qquad x=$
$4x^2-7x=0\qquad x=$
Solve for $𝑥$. If there are multiple answers, separate them with commas.
$7x^2=-4x\qquad x=$
$9x^2=-2x\qquad x=$