ediculeN

## Answered question

2020-10-28

Need to calculate:The factorization of the polynomial ${a}^{2}+ac+a+c$

### Answer & Explanation

curwyrm

Skilled2020-10-29Added 87 answers

Formula used:
The factors of a polynomial can be found by taking a common factor and this method is called factor by grouping,
$ab+ac+bd+cd=a\left(b+c\right)+d\left(b+c\right)$
$=\left(a+d\right)\left(b+c\right)$
Or,
$ab-ac+bd-cd=a\left(b-c\right)+d\left(b-c\right)$
$=\left(a+d\right)\left(b-c\right)$
Calculation:
Consider the polynomial ${a}^{2}+ac+a+c$.
This is a four term polynomial, factorization of this polynomial can be find by factor by grouping as,
${a}^{2}+ac+a+c=\left({a}^{2}+ac\right)+\left(a+c\right)$
$=a\left(a+c\right)+\left(a+c\right)$
As, $\left(a+c\right)$ is the common factor of the polynomial factor it out as follows:
${a}^{2}+ac+a+c=a\left(a+c\right)+\left(a+c\right)$
$=\left(a+c\right)\left(a+1\right)$
The factorization of the polynomial ${a}^{2}+ac+a+c$ is $\left(a+c\right)\left(a+1\right)$.
Check the result as follows:
$\left(a+c\right)\left(a+1\right)=a\ast a+a\ast 1+c\ast a+c\ast 1$
$={a}^{2}+ac+a+c$
Thus, the factorization of the polynomial ${a}^{2}+ac+a+c$  is $\left(a+c\right)\left(a+1\right)$.

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