Taking out a common factor before factorising a quadratic
Take out the common factor, then factorise the quadratic that remains.
- Check for a common factor before searching for a quadratic factor pair.
- Factorise the quadratic inside the bracket using its new coefficients.
- Keep the original common factor outside the two final brackets.
Example 1
Factorise fully.
Take out the highest common factor,
For the quadratic inside the bracket, 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.
Take out the highest common factor,
For the quadratic inside the bracket, 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
For example,
Your turn
Factorise fully.
Check answer
Take out the highest common factor,
For the quadratic inside the bracket, 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
Take out the highest common factor,
For the quadratic inside the bracket, 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
Take out the highest common factor,
For the quadratic inside the bracket, 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
Take out the highest common factor,
For the quadratic inside the bracket, 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
Take out the highest common factor,
For the quadratic inside the bracket, 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.
Take out the highest common factor,
For the quadratic inside the bracket, 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.
Take out the highest common factor,
For the quadratic inside the bracket, 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.
Take out the highest common factor,
For the quadratic inside the bracket, 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.
Take out the highest common factor,
For the quadratic inside the bracket, 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.
Take out the highest common factor,
For the quadratic inside the bracket, 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