7.3 A factorising trinomials

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• Leerjaar 2

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You are able to factorise trinomials using the product-sum method.

Find two numbers of which the product is 15 and the sum 8.

Find two numbers of which the product is -20 and the sum 8.

Expand the brackets:

(x+2)(x+7)

We've just seen that

Can you find a relation between 2, 7 and 9, 14?

This relation is always there.

We can use this relation to factorise trinomials.

(x+2)(x+7)=x​2​​+9x+14

To factorise

we need two numbers which give +30 when multiplied and +13 when added.

Which two numbers do we need?

There's always just one solution.

x​2​​+13x+30

To factorise

we need two numbers which give +30 when multiplied and +13 when added.

It's 3 and 10, so

x​2​​+13x+30

x​2​​+13x+30=(x+3)(x+10)

Three more examples:

x​2​​−5x−50

x​2​​+x−6

x​2​​+3x−4

Three more examples:

x​2​​−5x−50

x​2​​+x−6

x​2​​+3x−4=(x+4)(x−1)

Three more examples:

x​2​​−5x−50

x​2​​+x−6=(x+3)(x−2)

x​2​​+3x−4=(x+4)(x−1)

Three more examples:

x​2​​−5x−50=(x−10)(x+5)

x​2​​+x−6=(x+3)(x−2)

x​2​​+3x−4=(x+4)(x−1)

Factorise:

x​2​​+6x−27

1. (x + 3)(x + 9)
2. (x - 9)(x + 3)
3. (x - 3)(x + 9)
4. (x + 9)(x - 3)

Factorise:

x​2​​+11x+10

Factorise:

x​2​​+2x+1