7.3 A factorising trinomials

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• Middelbare school
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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:

$$x^2+2x+1$$