Factorising quadratics

The Maths Habit

A rectangle has an area of 24 cm2.
Its sides are whole numbers of cm.
What could its perimeter be?

50, 28, 22 or 20 cm

Find two numbers

  1. Multiply to 12, add to 8

    2 and 6

  2. Multiply to 10, add to 7

    2 and 5

  3. Multiply to 10, add to −7

    −2 and −5

  4. Multiply to −12, add to 1

    −3 and 4

Factorise
Put the brackets back in.
Factor pair
Two numbers that multiply to make a number.

x2 + 5x + 6

Multiply to 6Add to 5?

Factorise x2 + 8x + 12

Multiply to 12Add to 8?
1 × 1213
2 × 68 ✓
3 × 47
×x+6
xx2+6x
+2+2x+12
Answer(x + 2)(x + 6)

Factorise x2 + 9x + 18

Multiply to 18Add to 9?
1 × 1819
2 × 911
3 × 69 ✓
×x+6
xx2+6x
+3+3x+18
Answer(x + 3)(x + 6)

x2 − 6x + 8

Multiply to 8Add to −6?

Factorise x2 + 8x + 12

Multiply to 12Add to 8?
1 × 1213
2 × 68 ✓
3 × 47
×x+6
xx2+6x
+2+2x+12
Answer(x + 2)(x + 6)

Factorise x2 + 4x − 21

Multiply to −21Add to 4?
1 × −21−20
−1 × 2120
3 × −7−4
−3 × 74 ✓
×x+7
xx2+7x
−3−3x−21
Answer(x − 3)(x + 7)

Factorise x2 + 8x + 12

Multiply to 12Add to 8?
1 × 1213
2 × 68 ✓
3 × 47
×x+6
xx2+6x
+2+2x+12
Answer(x + 2)(x + 6)

Factorise x2 − 7x + 10

Multiply to 10Add to −7?
−1 × −10−11
−2 × −5−7 ✓
×x−5
xx2−5x
−2−2x+10
Answer(x − 2)(x − 5)

Factorise x2 + 8x + 12

Multiply to 12Add to 8?
1 × 1213
2 × 68 ✓
3 × 47
×x+6
xx2+6x
+2+2x+12
Answer(x + 2)(x + 6)

Factorise x2 + 11x + 24

Multiply to 24Add to 11?
1 × 2425
2 × 1214
3 × 811 ✓
4 × 610
×x+8
xx2+8x
+3+3x+24
Answer(x + 3)(x + 8)

Factorise x2 + 8x + 12

Multiply to 12Add to 8?
1 × 1213
2 × 68 ✓
3 × 47
×x+6
xx2+6x
+2+2x+12
Answer(x + 2)(x + 6)

Factorise x2 − 5x − 14

Multiply to −14Add to −5?
1 × −14−13
−1 × 1413
2 × −7−5 ✓
−2 × 75
×x−7
xx2−7x
+2+2x−14
Answer(x + 2)(x − 7)

Factorising quadratics worksheet, page 1

Factorising quadratics worksheet, page 2

Answer sheet

  1. x2 + bx + 12 factorises. Find every value that b could be.

    13, 8, 7, −7, −8, −13

  2. Factorise x2 − 49

    (x + 7)(x − 7)

  1. Factorise x2 + 9x + 14

    (x + 2)(x + 7)

  2. Factorise x2 − 2x − 24

    (x + 4)(x − 6)

  3. Jay says x2 − 8x + 15 = (x + 3)(x + 5). Find the right answer.

    (x − 3)(x − 5)
Exit tickets to print