Factorising quadratics - in the form
Factorise a quadratic by finding the required factor pair.
- Compare the expression with
: is the coefficient of , the coefficient of , and the constant. - Find two numbers that multiply to
and add to . - Use the chosen numbers in two brackets.
Example 1
Factorise fully.
Compare with
Find two numbers that multiply to make
The product and sum are both positive, so both numbers must be positive.
| Numbers | Product | Sum |
|---|---|---|
Use
Example 2
Factorise fully.
Compare with
Find two numbers that multiply to make
A negative product means one number is positive and one is negative.
| Numbers | Product | Sum |
|---|---|---|
Use
Remember
Some quadratics do not factorise into brackets with integer coefficients.
Your turn
Factorise fully.
Check answer
Compare with
Find two numbers that multiply to make
The product and sum are both positive, so both numbers must be positive.
| Numbers | Product | Sum |
|---|---|---|
Use
Factorise fully.
Check answer
Compare with
Find two numbers that multiply to make
A positive product means matching signs. The negative sum tells us both numbers must be negative.
| Numbers | Product | Sum |
|---|---|---|
Use
Factorise fully.
Check answer
Compare with
Find two numbers that multiply to make
A negative product means one number is positive and one is negative.
| Numbers | Product | Sum |
|---|---|---|
Use
Factorise fully.
Check answer
Compare with
Find two numbers that multiply to make
A negative product means one number is positive and one is negative.
| Numbers | Product | Sum |
|---|---|---|
Use
Factorise fully.
Check answer
Compare with
Find two numbers that multiply to make
A positive product means matching signs. The negative sum tells us both numbers must be negative.
| Numbers | Product | Sum |
|---|---|---|
Use
Factorise fully.
Compare with
Find two numbers that multiply to make
The product and sum are both positive, so both numbers must be positive.
| Numbers | Product | Sum |
|---|---|---|
Use
Factorise fully.
Compare with
Find two numbers that multiply to make
A positive product means matching signs. The negative sum tells us both numbers must be negative.
| Numbers | Product | Sum |
|---|---|---|
Use
Factorise fully.
Compare with
Find two numbers that multiply to make
A negative product means one number is positive and one is negative.
| Numbers | Product | Sum |
|---|---|---|
Use
Factorise fully.
Compare with
Find two numbers that multiply to make
A negative product means one number is positive and one is negative.
| Numbers | Product | Sum |
|---|---|---|
Use
Factorise fully.
Compare with
Find two numbers that multiply to make
A positive product means matching signs. The negative sum tells us both numbers must be negative.
| Numbers | Product | Sum |
|---|---|---|
Use