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

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

2020-10-29
Formula used:
The factors of a polynomial can be found by taking a common factor and this method is called factor by grouping,
$$ab+ac+bd+cd=a(b+c)+d(b+c)$$
$$=(a+d)(b+c)$$
Or,
$$ab-ac+bd-cd=a(b-c)+d(b-c)$$
$$=(a+d)(b-c)$$
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,
$$a^{2}+ac+a+c=(a^{2}+ac)+(a+c)$$
$$=a(a+c)+(a+c)$$
As, $$(a + c)$$ is the common factor of the polynomial factor it out as follows:
$$a^{2}+ac+a+c=a(a+c)+(a+c)$$
$$=(a+c)(a+1)$$
The factorization of the polynomial $$a^{2}+ac+a+c$$ is $$(a+c)(a+ 1)$$.
Check the result as follows:
$$(a+c)(a+1)=a*a+a*1+c*a+c*1$$
$$=a^{2}+ac+a+c$$
Thus, the factorization of the polynomial $$a^{2}+ac+a+c$$ is $$(a+c)(a+1)$$.

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