HW #44 Factoring Special Cases (honors)

Answer explanation

The trinomial x^2 + 6x + 9 can be factored by recognizing it as a perfect square. It can be expressed as (x + 3)(x + 3), which simplifies to (x + 3)^2. Thus, the correct factorization is (x + 3)^2.

Tags

CCSS.HSA.APR.C.4

Answer explanation

The expression 4x^2 - 25 is a difference of squares, which factors as (2x + 5)(2x - 5). The other options do not correctly represent the factorization of the given expression.

Tags

CCSS.HSA.APR.C.4

Answer explanation

The trinomial y^2 - 10y + 25 is a perfect square because it can be expressed as (y - 5)(y - 5) or (y - 5)^2. Thus, the correct factorization is (y - 5)^2.

Tags

CCSS.HSA.APR.C.4

Which of the following expressions is a difference of squares?

Answer explanation

The expression x^2 - 16 is a difference of squares because it can be factored as (x + 4)(x - 4). The other options do not fit this form.

Tags

CCSS.HSA.APR.C.4

Answer explanation

The expression 9a^2 - 1 is a difference of squares, which factors as (3a + 1)(3a - 1). The other options do not correctly represent this factorization.

Tags

CCSS.HSA.APR.C.4

Answer explanation

To factor the trinomial m^2 + 12m + 36, we look for two identical factors that add to 12 and multiply to 36. The correct factorization is (m + 6)(m + 6), which simplifies to (m + 6)^2.

Tags

CCSS.HSA.APR.C.4

Answer explanation

The expression x^2 - 49 is a difference of squares, which factors as (x + 7)(x - 7). This is the correct factorization, as it represents the product of two binomials that yield the original expression.

Tags

CCSS.HSA.APR.C.4

Answer explanation

To factor the trinomial 4y^2 - 20y + 25, recognize it as a perfect square. It can be expressed as (2y - 5)(2y - 5), which simplifies to (2y - 5)^2. Thus, the correct answer is (2y - 5)^2.

Tags

CCSS.HSA.APR.C.4

Answer explanation

The expression x^2 - 2x + 1 can be factored as (x - 1)(x - 1), which simplifies to (x - 1)^2. This shows that the correct factorization is (x - 1)^2.

Tags

CCSS.HSA.APR.C.4

• 4z

Answer explanation

To factor \(16z^2 - 81\), recognize it as a difference of squares: \((4z)^2 - (9)^2\). This factors to \((4z - 9)(4z + 9)\). Thus, one of the factors is \((4z + 9)\).

Tags

CCSS.HSA.APR.C.4