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

Question
Polynomial factorization
asked 2020-10-28
Need to calculate:The factorization of the polynomial \(a^{2}+ac+a+c\)

Answers (1)

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 \((a+c)(a+1)\).
0

Relevant Questions

asked 2021-02-22
Need to calculate:The factorization of the polynomial, \(2x^{4}+6x^{2}+5x^{2}+15\).
asked 2020-11-08
Need to calculate:The factorization of the polynomial, \(3x^{2}-2x+3x-2\).
asked 2021-03-06
Need to calculate: The factorization of the polynomial \(ax^{2}+ay+bx^{2}+by\).
asked 2020-11-23
Need to calculate:The factorization of \(2x^{3}-8x^{2}-9x+36\).
asked 2020-11-12
Need to calculate:The factorization of \(3p^{3}-2p^{2}-9p+6\).
asked 2021-02-14
Need to calculate:The factorization of \(6z^{3}+3z^{2}+2z+1\).
asked 2021-01-06
Need to calculate:The factorization of \(x^{3}+8x^{2}-3x-24\).
asked 2021-02-16
Need to calculate:The factorization of \(8x^{3}+20x^{2}+2x+5\).
asked 2021-01-07
Need to calculate:The factorization of \(3x^{3}+2x^{2}+3x+2\).
asked 2021-01-10
Need to calculate:The factorization of \(x^{3}-7x^{2}+4x-28\).
...