Factor the expression by grouping terms. 5x^{3}+x^{2}+5x+1

kloseyq

kloseyq

Answered question

2021-12-20

Factor the expression by grouping terms.
5x3+x2+5x+1

Answer & Explanation

Jacob Homer

Jacob Homer

Beginner2021-12-21Added 41 answers

Step 1
We have to factor the following expression:
5x3+x2+5x+1
Step 2
Taking x2 as common factor from first two terms and 1 as common factor from last two terms and grouping them we get,
5x3+x2+5x+1
=x2(5x+1)+1(5x+1)
=(5x+1)(x2+1)
Hence is the required factorization.
Annie Gonzalez

Annie Gonzalez

Beginner2021-12-22Added 41 answers

Consider the expression 5x3+x2+5x+1
Need to factor the expression by grouping terms
Grouping first two terms as one group last two terms as another group
5x3+x2+5x+1
=(5x3+x2)+(5x+1)
=x2(5x+1)+1(5x+1) (Taking x2 as common in first two terms and taking 1 as common in next two terms)
=(5x+1)(x2+1) Taking 5x+1 as common
=(x2+1)(5x+1)
Thus the required factors for the given expression are (x2+1)(5x+1).

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