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Consider the polynomial p(x)=8x3+12x2+2x+3.

Part A: What is the correct factorization of p(x)=8x3+12x2+2x+3 over the integers?

Part B: What method is used to factor p(x)=8x3+12x2+2x+3?

Select one answer for Part A and select one answer for Part B.

B: perfect-square trinomial
B: grouping
A: (2x+3)(4x+1)
B: sum of cubes
A: (4x2+1)(2x+3)
A: (2x+3)(4x2+6x+1)

Answer :

absor201

A: [tex](4x^2+1)(2x+3)[/tex]

B: grouping

Step-by-step explanation:

We are given the polynomial: [tex]p(x)=8x^3+12x^2+2x+3[/tex]

Part A: What is the correct factorization of [tex]p(x)=8x^3+12x^2+2x+3[/tex] over the integers?

We need to factorize the term [tex]p(x)=8x^3+12x^2+2x+3[/tex]

Factorizing by grouping:

[tex]p(x)=8x^3+12x^2+2x+3[/tex]

[tex]p(x)=(8x^3+12x^2)+(2x+3)[/tex]

[tex]p(x)=4x^2(2x+3)+1(2x+3)[/tex]

[tex]p(x)=(4x^2+1)(2x+3)[/tex]

So, factors of the term [tex]p(x)=8x^3+12x^2+2x+3[/tex] are [tex]p(x)=(4x^2+1)(2x+3)[/tex]

Part B: What method is used to factor p(x)=8x3+12x2+2x+3?

The method used to factor the given polynomial is grouping.

We group the terms and then find the common terms in that specific group

So, the answers are:

A: [tex](4x^2+1)(2x+3)[/tex]

B: grouping

Keywords: Finding Factors

Learn more about finding factors at:

  • brainly.com/question/1414350
  • brainly.com/question/1464739
  • brainly.com/question/2568692

#learnwithBrainly

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