Factor each polynomial completely. If the polynomial cannot be factored,

Josh Sizemore

Josh Sizemore

Answered question

2021-12-14

Factor each polynomial completely. If the polynomial cannot be factored, say it is prime.
8x2+88x+80

Answer & Explanation

Bukvald5z

Bukvald5z

Beginner2021-12-15Added 33 answers

Step 1
We have to factorize the polynomial:
8x2+88x+80
Factorizing the polynomial by middle term splitting method
Here,
80×8
For middle term,
80+8=88
Step 2
Therefore,
8x2+88x+80=8x2+80x+8x+80
=8x(x+10)+8(x+10)
=(x+10)(8x+8)
=(x+10)×8(x+1)
=8(x+1)(x+10)
Hence, factorized form of the expression is 8(x+1)(x+10).
Jenny Bolton

Jenny Bolton

Beginner2021-12-16Added 32 answers

There are many ways of factorize a polynomial. Key point is to find out the common factor from whole polynomial. Sometimes it is easy to form groups of terms in such a way that there is always one factor common in several groups. Then with the help of distributive property common factor can be factored out of each group. This technique of factorization is called factor by grouping. Sometimes there is no common factor coefficient in middle term. In such case, it is known as prime polynomial.
Objective is factor the polynomial 8x2+88x+80. It cannot be factored, then it is prime polynomial.
It is obviously seen first common factor is 8 in the polynomial. Take it as common factor then solve it further as given below:
8x2+88x+80=8(x2+11x+10)
=8(x2+10x+x+10)
=8(x(x+10)+1(x+10))
=8(x+10)(x+1)
Hence, the factor of 8x2+88x+80 polynomial is 8(x+10)(x+1). Since it has three factors, since. The is not a prime polynomial.

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