Quadratic Equations

Question 1

How do you factor x² + 11x + 18?

Answer 1

Find a factor pair of 18 that sums to 11:
(x + 9)(x + 2)
9 + 2 = 11, 9 × 2 = 18

Question 2

How do you factor x² – 8x + 12?

Answer 2

Find a factor pair of 12 that sums to 8, then make both numbers negative:
(x – 6)(x – 2)
(–6) + (–2) = –8, (–6) × (–2) = 12

Question 3

How do you factor x² + 6x – 16?

Answer 3

Find a factor pair of 16 that differs by 6, then make the bigger number positive:
(x + 8)(x – 2)
8 + (–2) = 6, 8 × (–2) = –16

Question 4

How do you factor x² – 5x – 14?

Answer 4

Find a factor pair of 14 that differs by 5, then make the bigger number negative:
(x – 7)(x + 2)
(–7) + 2 = –5, (–7) × 2 = –14

Question 5

How do you factor –2x² + 16x – 24?

Answer 5

Factor out –2 from all terms first, then factor the quadratic expression:
–2x² + 16x – 24 = –2(x² – 8x + 12) = –2(x – 6)(x – 2)