Need to calculate:The factorization of the polynomial a2+ac+a+c

Question

curwyrm · Accepted Answer

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

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

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