AlgebraGCSE Higher

Factorising quadratics - in the form

Factor out a negative sign, then factorise the quadratic inside the bracket.

  • Start by taking out . Every sign inside the bracket changes.
  • For the quadratic inside, find two numbers that multiply to the constant and add to the coefficient of .
  • Keep the negative sign outside both factors in the final answer.

Example 1

Factorise fully.

Factor out first. Reverse every sign inside the bracket.

For the quadratic inside the bracket, compare with .

Find two numbers that multiply to make and add to make .

A negative product means one number is positive and one is negative.

Selected factor-pair trials, their products and their sums. The chosen pair is circled. Vertical dots indicate other factor pairs that are not shown.
NumbersProductSum
Chosen pair

Use and in the two brackets.

Example 2

Factorise fully.

Factor out first. Reverse every sign inside the bracket.

For the quadratic inside the bracket, compare with .

Find two numbers that multiply to make and add to make .

A negative product means one number is positive and one is negative.

Selected factor-pair trials, their products and their sums. The chosen pair is circled. Vertical dots indicate other factor pairs that are not shown.
NumbersProductSum
Chosen pair

Use and in the two brackets.

Remember
For example, . The minus sign changes all three terms.

Your turn

Question 1

Factorise fully.

Check answer

Factor out first. Reverse every sign inside the bracket.

For the quadratic inside the bracket, compare with .

Find two numbers that multiply to make and add to make .

A negative product means one number is positive and one is negative.

Selected factor-pair trials, their products and their sums. The chosen pair is circled. Vertical dots indicate other factor pairs that are not shown.
NumbersProductSum
Chosen pair

Use and in the two brackets.

Question 2

Factorise fully.

Check answer

Factor out first. Reverse every sign inside the bracket.

For the quadratic inside the bracket, compare with .

Find two numbers that multiply to make and add to make .

A negative product means one number is positive and one is negative.

Selected factor-pair trials, their products and their sums. The chosen pair is circled. Vertical dots indicate other factor pairs that are not shown.
NumbersProductSum
Chosen pair

Use and in the two brackets.

Question 3

Factorise fully.

Check answer

Factor out first. Reverse every sign inside the bracket.

For the quadratic inside the bracket, compare with .

Find two numbers that multiply to make and add to make .

A negative product means one number is positive and one is negative.

Selected factor-pair trials, their products and their sums. The chosen pair is circled.
NumbersProductSum
Chosen pair

Use and in the two brackets.

Question 4

Factorise fully.

Check answer

Factor out first. Reverse every sign inside the bracket.

For the quadratic inside the bracket, compare with .

Find two numbers that multiply to make and add to make .

A negative product means one number is positive and one is negative.

Selected factor-pair trials, their products and their sums. The chosen pair is circled. Vertical dots indicate other factor pairs that are not shown.
NumbersProductSum
Chosen pair

Use and in the two brackets.

Question 5

Factorise fully.

Check answer

Factor out first. Reverse every sign inside the bracket.

For the quadratic inside the bracket, compare with .

Find two numbers that multiply to make and add to make .

A negative product means one number is positive and one is negative.

Selected factor-pair trials, their products and their sums. The chosen pair is circled. Vertical dots indicate other factor pairs that are not shown.
NumbersProductSum
Chosen pair

Use and in the two brackets.

← All Algebra cardsReport a mistake

Related cards

Factorising quadratics in the form x²+bx+cFactorising quadratics in the form ax²+bx+c