The given polynomial x^{2} - 22x + 72 and factors by multiplying.

The given polynomial ${x}^{2}-22x+72$ and factors by multiplying.
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Calculation: We have a quadrratic ${x}^{2}-22x+72.$
In order to factor the given quadratic we need to compare given quadratic with standard quadratic $a{x}^{2}+bx+c.$
Now, we need to get the values of a, b and c and product sum rule to factor the quadratic.
On comparing given quadratic ${x}^{2}-22x+72$ with standard quadratic
$a{x}^{2}+bx+c,$
we get $a=1,b=-22,c=72.$
Product of value of a and $c=1×72=72.$
Value of $b=-22.$
Now, we need to get two factors of 72 those add upto -22.
We could see $72=-18×\left(-4\right),-22=-4+\left(-18\right)$
So, split middle term $-22xinto-4x-18x$, we get
${x}^{2}-4x-18x+72$
Now, making it into two groups and factor out Greatest Common Factor (GCF) of each group $\left({x}^{2}-4x\right)+\left(-18x+72\right)$
Factor out Greates Common Factor $\left(GCF\right)xfrom\left({x}^{2}-4x\right)$
and -18 from $\left(-18x+72\right)$
$x\left(x-4\right)-18\left(x-4\right)$
Factor out the common parenthesis $\left(x-4\right)$
$\left(x-4\right)\left(x-18\right)$
Now, let us check its