Β 
VIEW IN FULL SCREEN

Edexcel A-level Maths Factorising techniques

Factorising techniques

This page covers the following topics:

When solving linear equations we generally want to rearrange it, and make some variable the 'subject' of the formula. Something is the subject of the formula if it appears by itsel on one side of the equation. For example, if y = 2x + 3, then y is the subject. To solve an equation for y, we want to isolate it like that on one side, and then evaluate the terms on the other side with numbers we know.

Factorising linear equations

When given a quadratic such as (x + 1)(x + 2), we can multiply out the brackets using FOIL (meaning first, outside, inside, last), giving xΒ² + 2x + x + 2, which is just xΒ² + 3x + 2. However, for solving a quadratic it's more useful to do this process in reverse. Given some quadratic like xΒ² + 3x + 2, we want to find 2 values to fit in (x + _)(x + _). We know these values need to equal 2 when multiplied together, and when summed they need to equal 3. Once we spot the values 1 and 2 for this, we have (x + 1)(x + 2), and it's very easy to solve an equation like (x + 1)(x + 2) = 0, because this just gives our solutions x = –1 and –2.

Factorising quadratic equations

We have a quadratic equation of the form axΒ² + bx + c = 0, where a, b, and c are just coefficients. The solutions to the quadratic are given by the quadratic formula: x = (–b +– √(bΒ² – 4ac))/2a.

The quadratic equation

For a polynomial f(x), if f(a) = 0 then we know (x – a) is a factor of the polynomial. Likewise, is we know (x – a) is a factor then f(a) = 0. While not particularly useful for quadratics, this can prove helpful in factorising more difficult polynomials of order 3 or above.

Factor Theorem

1

βœ…

Suppose we have 5 + x = 1 + y. Rearrange the equation so that y is the subject.

Edexcel A-level Maths Factorising techniques Suppose we have 5 + x = 1 + y. Rearrange the equation so that y is the subject.
Image_edited.png

Did you know?

By simply logging in, you would be able to access 50% more questions.

2

βœ…

Solve s – 4 = b + 3 for b when s = 4.

Edexcel A-level Maths Factorising techniques Solve s – 4 = b + 3 for b when s = 4.
Image_edited.png

Did you know?

By simply logging in, you would be able to access 50% more questions.

3

βœ…

Factorise xΒ² + 5x + 6.

Edexcel A-level Maths Factorising techniques Factorise xΒ² + 5x + 6.
Image_edited.png

Did you know?

By simply logging in, you would be able to access 50% more questions.

4

βœ…

Solve xΒ² + 5x + 4 = 0.

Edexcel A-level Maths Factorising techniques Solve xΒ² + 5x + 4 = 0.
Image_edited.png

Did you know?

By simply logging in, you would be able to access 50% more questions.

5

βœ…

Solve xΒ² + 5x = 6.

Edexcel A-level Maths Factorising techniques Solve xΒ² + 5x = 6.
Image_edited.png

Did you know?

By simply logging in, you would be able to access 50% more questions.

6

βœ…

Solve xΒ² + 6x + 9 = 0 using the quadratic formula.

Edexcel A-level Maths Factorising techniques Solve xΒ² + 6x + 9 = 0 using the quadratic formula.
Image_edited.png

Did you know?

By simply logging in, you would be able to access 50% more questions.

7

βœ…

Solve 4xΒ² + 3x – 7 = 0 using the quadratic formula.

Edexcel A-level Maths Factorising techniques Solve 4xΒ² + 3x – 7 = 0 using the quadratic formula.
Image_edited.png

Did you know?

By simply logging in, you would be able to access 50% more questions.

8

βœ…

Solve 22x + xΒ² = –21.

Edexcel A-level Maths Factorising techniques Solve 22x + xΒ² = –21.
Image_edited.png

Did you know?

By simply logging in, you would be able to access 50% more questions.

9

βœ…

Identify a factor of f(x)= xΒ³ + xΒ² + x – 3.

Edexcel A-level Maths Factorising techniques Identify a factor of f(x)= xΒ³ + xΒ² + x – 3.
Image_edited.png

Did you know?

By simply logging in, you would be able to access 50% more questions.

10

βœ…

Factorise f(x) = xΒ³ – 3xΒ² + 2x as far as possible, just using the factor theorem.

Edexcel A-level Maths Factorising techniques Factorise f(x) = xΒ³ – 3xΒ² + 2x as far as possible, just using the factor theorem.
Image_edited.png

Did you know?

By simply logging in, you would be able to access 50% more questions.

Image.png

Have you found the questions useful?

Sign up to access 50% more of them for free πŸ˜€

End of page

Β