To calculate: The factorization of the polynomial a2+ac+a+c.

Question

Nancy Johnson · 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,
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} + 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 \cdot a + a \cdot 1 + c \cdot a + c \cdot 1 = a^{2} + a c + a + c

Thus, the factorization of the polynomial

a^{2} + a c + a + c

is (a+c)(a+1).

To calculate: The factorization of the polynomial a^{2}+ac+a+c.

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