Examkin

Question

Difficulty: MediumFactoring Polynomials

An architect is designing a rectangular layout where the area is represented by the algebraic expression 4y2+12y−404y^2 + 12y - 40. To determine the possible dimensions of the layout in terms of yy, the architect needs to rewrite this expression in its completely factored form. Which of the following represents the completely factored expression?

  1. 4(y+5)(y−2)4(y + 5)(y - 2)Answer
  2. B
    4(y−5)(y+2)4(y - 5)(y + 2)
  3. C
    (4y−8)(y+5)(4y - 8)(y + 5)
  4. D
    4(y+5)(y+2)4(y + 5)(y + 2)

Answer

The completely factored expression is 4(y+5)(y−2)4(y + 5)(y - 2).
The correct answer completely factors out the GCF of 4 from all terms and correctly factors the remaining trinomial y2+3y−10y^2 + 3y - 10 into (y+5)(y−2)(y + 5)(y - 2).

Step-by-Step Solution

1
Identify and extract the greatest common factor (GCF) from all terms in the expression 4y2+12y−404y^2 + 12y - 40.
4(y2+3y−10)4(y^2 + 3y - 10)
Factoring out the GCF simplifies the polynomial and makes the remaining trinomial easier to factor.
2
Find two integers that multiply to the constant term (-10) and add to the coefficient of the middle term (3).
The correct integers are 5 and -2.
These integers are required to construct the binomial factors of the simplified trinomial y2+3y−10y^2 + 3y - 10.
3
Write the trinomial as a product of two binomials using the integers found, and combine them with the GCF.
4(y+5)(y−2)4(y + 5)(y - 2)
This represents the original expression fully broken down into its prime polynomial factors.

Key Concept

Factoring Polynomials by Extracting the GCF and Grouping
Rate this question

Topics

Factoring Polynomials

More questions from this topic