STAAR Practice A.10E 3C

• f(x) = (x - 6)(x - 3)

• f(x) = (x - 6)(x + 3)

• f(x) = (x + 6)(x + 3)

• f(x) = (x + 6)(x - 3)

Answer explanation

To find the equivalent function, we can factor the quadratic. The expression f(x) = x^2 + 3x - 18 factors to (x + 6)(x - 3). Thus, the correct choice is f(x) = (x + 6)(x - 3).

• -4x - 1

• x + 1

• -x - 1

• -4x + 1

Answer explanation

To find a factor of the equation -8x^2 = 10x + 3, we can rearrange it to -8x^2 - 10x - 3 = 0. Factoring gives us (-4x + 1)(2x + 3) = 0. Thus, -4x + 1 is a factor.

• (x - 16)(x - 4)

• There are no real factors.

Answer explanation

The expression x^2 + 8x + 64 can be rewritten as (x + 4)^2 + 48, which has no real roots. Therefore, it cannot be factored into real linear factors, making 'There are no real factors' the correct choice.

The trinomial 4x^2 - 20x + 25 is factorable. Which of these is the correct factorization?

• (2x + 5)(2x - 5)

• (x - 5)(4x - 5)

Answer explanation

The trinomial 4x^2 - 20x + 25 can be rewritten as (2x - 5)(2x - 5), which is (2x - 5)^2. This shows that the correct factorization is (2x - 5)^2.

• (22x - 3) units by (x + 2) units

• (11x - 2) units by (2x + 3) units

• (22x + 3) units by (x - 2) units

• (11x + 2) units by (2x - 3) units

Answer explanation

To find the dimensions, we factor the area expression. The correct factorization of 22x^2 + 29x - 6 is (11x - 2)(2x + 3), matching the choice (11x - 2) units by (2x + 3) units.

• x - 3

• 2x - 6

• 12 + 2x

• 2x - 12

Answer explanation

To find the base of the triangle, use the area formula: Area = 1/2 * base * height. Given Area = x^2 + 3x - 18 and height = x + 6, we can solve for base, yielding base = 2x - 6.

• (3x + 8)(3x + 2)

• (x - 4)(9x - 4)

Answer explanation

To factor the trinomial 9x^2 - 24x + 16, we look for two identical binomials. The expression (3x - 4)(3x - 4) simplifies to (3x - 4)^2, matching the original trinomial. Thus, the area is represented by (3x - 4)^2.

The trinomial -6d^2 + 8d - 6 can be factored: Which of these shows the correct factors?

• 6 and (d^2 - 2d + 1)

• -2 and (3d^2 - 4)

Answer explanation

To factor -6d^2 + 8d - 6, we can factor out -2, resulting in -2(3d^2 - 4d + 3). This matches the correct choice, confirming that -2 and (3d^2 - 4d + 3) are the correct factors.

For 3x² - 3x - 18, what is the complete factorization?

• 3(x - 2)(x - 3)

• 3(x + 3)(x - 2)

• 3(x² - x - 6)

• 3(x + 2)(x - 3)

Answer explanation

To factor 3x² - 3x - 18, first factor out 3: 3(x² - x - 6). Then, factor x² - x - 6 into (x + 2)(x - 3). Thus, the complete factorization is 3(x + 2)(x - 3).

For the trinomial 9x + 6 - 15x², what is the complete factorization?

• -3(5x - 2)(x - 1)

• -3(x - 1)(5x + 2)

• 3(-5x² + 3x + 2)

• None of these

Answer explanation

To factor the trinomial 9x + 6 - 15x², first rewrite it as -15x² + 9x + 6. Factoring out -3 gives -3(5x² - 3x - 2). This factors to -3(x - 1)(5x + 2), making the correct choice -3(x - 1)(5x + 2).