Factorising Expressions

Question 1

What is factorising the opposite of?

Answer 1

Expanding.

Question 2

What is the factor in this expression ax+bx?

Answer 2

x

Question 3

What is the factor in this expression ax+ay?

Answer 3

a

Question 4

How can you find a factor in a simple expression?

Answer 4

You can look for common multipliers in the different terms and bring them outside brackets.

Question 5

How can you factorise a quadratic expression of the form a(x^2)+bx?

Answer 5

You can factorise x outside the brackets to get x(ax+b).

Question 6

How can you factorise a quadratic expression of the form a(x^2)-c?

Answer 6

You can use the difference of squares rule (a^2)-(b^2)=(a+b)(a-b). This can be used to factorise the expression into ((a^(1/2))x+(c^(1/2)))((a^(1/2))x-(c^(1/2))).

Question 7

How can you factorise a quadratic expression of the form a(x^2)+bx+c?

Answer 7

You need to find factors (fx+d)(gx+e). de must equal c, fe+gd must equal b and fg must equal a. You can then work the values out using trial and error.