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Zorluk: KolayFactoring 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)

Cevap

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.

Adım Adım Çözüm

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.

Anahtar Kavram

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

Factoring Polynomials

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