how do you work out x2-8x+15

Question

factoring vs quadratics

 

Answer 1

So what you want to do is find factors of 15 which will add to 8.

 

The factors of 15 are 1,3,5,and 15. 3 and 5 will add to 8.

But it is negative 8, so (-3) and (-5) are the factors we are looking for. But let's double check.

(-3)+(-5) = (-8) AND (-3)(-5) = 15.

 

F   First

O  Outside

I   Inside

L   Last

 

Now we know x(x) = $x^{2}$ 

So that will give us (x    )(x   )

 

F = (x)(x)  = $x^{2}$

 

Now the Last needs to multiply to 15 and the middle terms need to add to (-8)

so, based off the factors we got (-3) and (-5), we can see it is:

 

(x-5)(x-3)

 

Now we want to find a way to FOIL everything to check  the answer

 

F    = $x(x)$   = $x^{2}$

O   = $x(-3)$  = $-3x$

I    = $x(-5)$  = $-5x$

L    = $(-3)(-5)$  = $15$

 

And now we add the terms:

$x^{2} - 3x - 5x +15$

= $x^{2} -8x +15$

 

which matches our original answer, therefore your answer is:

(x-3)(x-5)  OR  (x-5)(x-3) since multiplication is commutative