Factorising quadratics: harder

The Maths Habit

Two whole numbers add to 9.
What could they multiply to?

8, 14, 18 or 20

Find two numbers

  1. Multiply to 12, add to 7

    3 and 4

  2. Multiply to 6, add to 7

    6 and 1

  3. Multiply to −6, add to −5

    −6 and 1

  4. Multiply to −24, add to 5

    8 and −3

Expand and simplify

(2x + 1)(x + 3) 2x2 + 7x + 3

Factorise 2x2 + 9x + 4

the first number times the last
2 × 4 =8
multiply to make that, add to make 9
8and1
split the middle term in the grid, then find the headings
×x+4
2x2x2+8x
+1+x+4
Answer(2x + 1)(x + 4)

Factorise 3x2 + 11x + 6

the first number times the last
3 × 6 =18
multiply to make that, add to make 11
9and2
split the middle term in the grid, then find the headings
×x+3
3x3x2+9x
+2+2x+6
Answer(3x + 2)(x + 3)

Factorise 2x2 + 9x + 4

the first number times the last
2 × 4 =8
multiply to make that, add to make 9
8and1
split the middle term in the grid, then find the headings
×x+4
2x2x2+8x
+1+x+4
Answer(2x + 1)(x + 4)

Factorise 2x2 − 3x − 5

the first number times the last
2 × −5 =−10
multiply to make that, add to make −3
2and−5
split the middle term in the grid, then find the headings
×x+1
2x2x2+2x
−5−5x−5
Answer(2x − 5)(x + 1)

Factorising quadratics: harder worksheet, page 1

Answer sheet

  1. Solve 2x2 + 7x + 3 = 0

    x = −12 or x = −3

  2. Factorise 6x2 + 7x + 2

    (2x + 1)(3x + 2)

  3. Factorise fully 9x2 + 21x + 6

    3(3x2 + 7x + 2) = 3(3x + 1)(x + 2)

  1. Factorise 2x2 + 11x + 12

    (2x + 3)(x + 4)

  2. Factorise 3x2 − 4x − 4

    (3x + 2)(x − 2)

  3. Factorise fully 4x2 + 10x + 4

    2(2x + 1)(x + 2)
Exit tickets to print