quads

Factor
k²+7x+10

• (k+2)(k+5)

• (k-2)(k-5)

• (k+10)(k+4)

• (k+2)(k-5)

Answer explanation

To factor k² + 7k + 10, we look for two numbers that multiply to 10 and add to 7. The numbers 2 and 5 fit this, so we can write it as (k + 2)(k + 5). Thus, the correct choice is (k + 2)(k + 5).

Factor
r² -16r + 60

• (r - 15)(r + 4)

• (r - 6)(r + 10)

• (r - 6)(r - 10)

• (r +30)(r - 2)

Answer explanation

To factor r² - 16r + 60, we look for two numbers that multiply to 60 and add to -16. The numbers -6 and -10 fit this, so the expression factors to (r - 6)(r - 10). Thus, the correct choice is (r - 6)(r - 10).

Factor
k² -2k - 24

• (k+4)(k-6)

• (k+4)(k+6)

• (k+6)(k-1)

• (k-4)(k+6)

Answer explanation

To factor k² - 2k - 24, we look for two numbers that multiply to -24 and add to -2. The numbers 4 and -6 fit this, leading to the factors (k + 4)(k - 6). Thus, the correct choice is (k + 4)(k - 6).

Factor
x² + x - 6

• (x + 2)(x + 3)

• (x + 6)(x -1)

• (x + 3)(x - 2)

• (x +1)(x - 6)

Answer explanation

To factor x² + x - 6, we look for two numbers that multiply to -6 and add to 1. The numbers 3 and -2 fit this, so we can write it as (x + 3)(x - 2). Thus, the correct answer is (x + 3)(x - 2).

Factor
x²+4x-32

• (x+8)(x-4)

• (x-8)(x-4)

• (x-8)(x+4)

• (x+8)(x+4)

Answer explanation

To factor the quadratic x² + 4x - 32, we look for two numbers that multiply to -32 and add to 4. The numbers 8 and -4 fit this, leading to the factors (x + 8)(x - 4). Thus, the correct answer is (x + 8)(x - 4).

Factor
x² - 36

• (x + 9)(x - 4)

• (x - 6)(x - 6)

• (x - 9)(x + 4)

• (x + 6)(x - 6)

Answer explanation

To factor x² - 36, recognize it as a difference of squares: (x + 6)(x - 6). This matches the correct choice, as it simplifies to x² - 36.

Factor
x² + 4x + 3

• (x - 1)(x - 3)

• (x + 1)(x + 3)

• (x - 1)(x + 3)

• (x + 1)(x - 3)

Answer explanation

To factor x² + 4x + 3, we look for two numbers that multiply to 3 and add to 4. The numbers 1 and 3 fit this, so we can write it as (x + 1)(x + 3). Thus, the correct answer is (x + 1)(x + 3).

Factor
x² + 5x + 4

• (x + 4)(x + 1)

• (x + 2)(x + 2)

• (x + 4)(x - 1)

• (x + 5)(x + 1)

Answer explanation

To factor x² + 5x + 4, we look for two numbers that multiply to 4 and add to 5. The numbers 4 and 1 fit this, so we can write the expression as (x + 4)(x + 1). Thus, the correct choice is (x + 4)(x + 1).

Factor x² + 4x - 12

• (x - 6) (x + 2)

• (x + 4) (x - 3)

• (x + 6) (x - 2)

• (x + 3) (x + 4)

Answer explanation

To factor x² + 4x - 12, we look for two numbers that multiply to -12 and add to 4. The numbers 6 and -2 work. Thus, the expression factors to (x + 6)(x - 2), which is the correct choice.

• -100

• 100

• -25

• 25

Answer explanation

To complete the square for x^2 + 10x, take half of 10 (which is 5) and square it (5^2 = 25). Thus, the number that should replace the question mark is 25.