Algebra Demystified 2nd Ed

158 algebra De mystif ieD

x^2 + 11x + 24: 3 ⋅ 8 = 24 and 3 + 8 = 11 x^2 + 11x + 24 = (x + 3)(x + 8)

x^2 – 9x + 18: 3 ⋅ 6 = 18 and 3 + 6 = 9 x^2 – 9x + 18 = (x – 3)(x – 6)

x^2 + 9x – 36: 3 ⋅ 12 = 36 and 12 – 3 = 9 x^2 + 9x – 36 = (x + 12)(x – 3)

x^2 – 2x – 8: 2 ⋅ 4 = 8 and 4 – 2 = 2 x^2 – 2x – 8 = (x + 2)(x – 4)

PRACTICE

Factor the quadratic polynomial.

1. x^2 − 6x + 9 =


2. x^2 − x − 12 =


3. x^2 + 9x − 22 =


4. x^2 + x − 20 =


5. x^2 + 13x + 36 =


6. x^2 − 19x + 34 =


7. x^2 − 18 x + 17 =


8. x^2 + 24x − 25 =


9. x^2 − 14x + 48 =


10. x^2 + 16x + 64 =


11. x^2 − 49 =
    (Hint: x^2 − 49 = x^2 + 0x − 49)

✔SOLUTIONS

1. x^2 − 6x + 9 = (x − 3)(x − 3) = (x − 3)^2


2. x^2 − x − 12 = (x − 4)(x + 3)


3. x^2 + 9x − 22 = (x + 11)(x − 2)


4. x^2 + x − 20 = (x + 5)(x − 4)


5. x^2 + 13x + 36 = (x + 4)(x + 9)


6. x^2 − 19x + 34 = (x − 2)(x − 17)


7. x^2 − 18x + 17 = (x − 1)(x − 17)


8. x^2 + 24x − 25 = (x + 25)(x − 1)


9. x^2 − 14x + 48 = (x − 6)(x − 8)


10. x^2 + 16x + 64 = (x + 8)(x + 8) = (x + 8)^2


11. x^2 − 49 = (x − 7)(x + 7)

PRACTICE

Factor the quadratic polynomial.