Factoring Trinomials of the Type x² + bx + c

Factor the expression: d² + 6d + 5

• (d + 1)(d + 5)

• (d + 2)(d + 3)

• (d + 1)(d + 6)

• (d + 5)(d + 5)

Answer explanation

To factor d² + 6d + 5, we look for two numbers that multiply to 5 and add to 6. The numbers 1 and 5 fit this, so we can write the expression as (d + 1)(d + 5). Thus, the correct choice is (d + 1)(d + 5).

Factor the expression: b² + 9b + 14

• (b + 2)(b + 7)

• (b + 1)(b + 14)

• (b + 3)(b + 6)

• (b + 4)(b + 5)

Answer explanation

To factor b² + 9b + 14, we look for two numbers that multiply to 14 and add to 9. The numbers 2 and 7 fit this, so the expression factors to (b + 2)(b + 7). Thus, the correct choice is (b + 2)(b + 7).

Factor the expression: x² + 7x + 18

• (x + 3)(x + 6)

• (x + 2)(x + 9)

• (x + 1)(x + 18)

• (x + 4)(x + 5)

Answer explanation

To factor x² + 7x + 18, we look for two numbers that multiply to 18 and add to 7. The numbers 3 and 6 fit this, so the expression factors to (x + 3)(x + 6). Thus, the correct choice is (x + 3)(x + 6).

Factor the expression: x² + 7x + 10

• (x + 2)(x + 5)

• (x + 1)(x + 10)

• (x + 3)(x + 4)

• (x + 2)(x + 4)

Answer explanation

To factor x² + 7x + 10, we look for two numbers that multiply to 10 and add to 7. The numbers 2 and 5 fit this, so the expression factors to (x + 2)(x + 5), which is the correct choice.

Factor the expression: x² - 2x - 24

• (x - 6)(x + 4)

• (x + 6)(x - 4)

• (x - 4)(x - 6)

• (x + 4)(x + 6)

Answer explanation

To factor x² - 2x - 24, we look for two numbers that multiply to -24 and add to -2. The numbers -6 and 4 fit this, so the expression factors to (x - 6)(x + 4). Thus, the correct choice is (x - 6)(x + 4).

Factor the expression: x² - 2x - 15

• (x - 5)(x + 3)

• (x + 5)(x - 3)

• (x + 3)(x + 5)

• (x - 3)(x - 5)

Answer explanation

To factor x² - 2x - 15, we look for two numbers that multiply to -15 and add to -2. The numbers -5 and 3 fit this, so the expression factors to (x - 5)(x + 3). Thus, the correct choice is (x - 5)(x + 3).

Factor the expression: a² - 4a - 21

• (a - 7)(a + 3)

• (a - 3)(a + 7)

• (a + 7)(a + 3)

• (a - 1)(a - 21)

Answer explanation

To factor a² - 4a - 21, we look for two numbers that multiply to -21 and add to -4. The numbers -7 and 3 fit this, so the expression factors to (a - 7)(a + 3). Thus, the correct choice is (a - 7)(a + 3).

Factor the expression: x² - 6x - 27

• (x - 9)(x + 3)

• (x - 9)(x - 3)

• (x - 3)(x + 9)

• (x + 3)(x + 9)

Answer explanation

To factor x² - 6x - 27, we look for two numbers that multiply to -27 and add to -6. The numbers -9 and 3 fit this, so the expression factors to (x - 9)(x + 3), which is the correct choice.

Factor the expression: x² + 7x + 12

• (x + 3)(x + 4)

• (x + 2)(x + 6)

• (x + 1)(x + 12)

• (x + 5)(x + 2)

Answer explanation

To factor x² + 7x + 12, we look for two numbers that multiply to 12 and add to 7. The numbers 3 and 4 fit this, so the expression factors to (x + 3)(x + 4). Thus, the correct choice is (x + 3)(x + 4).