Examkin

Question

Difficulty: EasyFactoring Polynomials

Pair each algebraic expression with its completely factored equivalent.

  • 4y2−16y4y^2 - 16y4y(y−4)4y(y - 4)
  • y2−16y^2 - 16(y−4)(y+4)(y - 4)(y + 4)
  • y2−8y+16y^2 - 8y + 16(y−4)2(y - 4)^2
  • 4y+164y + 164(y+4)4(y + 4)

Answer

The correct pairings are: 4y2−16y4y^2 - 16y matches with 4y(y−4)4y(y - 4); y2−16y^2 - 16 matches with (y−4)(y+4)(y - 4)(y + 4); y2−8y+16y^2 - 8y + 16 matches with (y−4)2(y - 4)^2; and 4y+164y + 16 matches with 4(y+4)4(y + 4).
Each polynomial requires a distinct factoring method. Identifying the correct structure—such as GCF, difference of squares, or perfect square trinomial—leads directly to the completely factored form.

Step-by-Step Solution

1
Factor 4y2−16y4y^2 - 16y
4y(y−4)4y(y - 4)
The terms share a greatest common factor of 4y4y.
2
Factor y2−16y^2 - 16
(y−4)(y+4)(y - 4)(y + 4)
It follows the difference of squares pattern a2−b2=(a−b)(a+b)a^2 - b^2 = (a - b)(a + b).
3
Factor y2−8y+16y^2 - 8y + 16
(y−4)2(y - 4)^2
It is a perfect square trinomial, as (−4)×(−4)=16(-4) \times (-4) = 16 and (−4)+(−4)=−8(-4) + (-4) = -8.
4
Factor 4y+164y + 16
4(y+4)4(y + 4)
The terms share a greatest common factor of 44.

Key Concept

Factoring polynomials using greatest common factors, difference of squares, and perfect square trinomial patterns.
Rate this question

Topics

Factoring Polynomials

More questions from this topic