Factorise x^2+7x+10 to find the roots of the equatino x^2+7x+10=0

When we are asked to solve a quadratic, we can use the formula, but we are here specifically asked to use factorisation.

First of all, we need to know the format of factorisation: usually, it's (x+)(x+), and we have to fill in those blanks, so that when we multiply out, we get the equation we're given.

When we don't have any number in front of x^2, there's a quick trick - try to find a pair of numbers which ADD to the number in front of x (here 7), and MULTIPLY to give the number without any x terms (here 10). Knowing this, we can quickly spot 5 & 2: 5+2=7, and 5*2=10.

Now, we can easily throw 5 & 2 into the format we mentioned above, so it would read (x+5)(x+2). Note, (x+2)(x+5) has exactly the same outcome. To check this, we multiply out, and can see we get x^2+10+2x+5x, which simplifies to x^2+7x+10.

We've been asked to find the roots (these are the two x values that our equation would have when it crosses the x-axis), and this is a step lots of people forget; 5 & 2 aren't the roots. We need to take the negative of the numbers we put inside the brackets, so our roots are -5 & -2. If we had put a negative number into the brackets, that would become positive.

x=-2 x=-5