How do you factor these quadratic expressions?

Question

1) x^2-8x+15


2) 3x^2-17x+20

Answer 1

1)x^2-8x+15
Since -3 and -5 equal -8, you do this:
(x-3)(x-5)

2)3x^2-17x+20
(3x-5)(x-4)

Answer 2

The general rule of thumb when factoring goes as follows:
First, ask yourself what two values make the first (in #1, x^2 can be decomposed as x times x), and then you ask yourself what two values can you multiply to make the third and add to get the second?

Let's try that here.

x^2 - 8x + 15
This will factor into
(x + ?) (x + ?)
And it is up to you to find out the question marks.

What two numbers can you multiply to make 15 but add to make -8? Remember that adding two numbers to make a negative usually means negative numbers will be involved. In this case, the two numbers that multiply to make 15 and add to make -8 is (-3 + -5). That's what goes in the question marks.

(x - 3) (x - 5)

2. This one is slightly more complicated. Your first terms in the brackets will most likely be:

(3x + ?) (x + ?)

In this case, what you have to do is randomly plug in two numbers that multiply to make 20, and test the outer and inner of the FOIL. Let's try -5 and -4, and plugging them in the brackets.

(3x - 5) (x - 4)

Now from here, what you have to do is test the outer and test the inner, and see if they add up to the middle term (-17). The outer is equal to (-4 * 3x) = -12x and the inner is equal to (-5 * x) =-5x. Thus, they definitely add up to make the middle term, so that is the correct factorization.

Answer 3

Trial and error FOIL at first.

For the first one, factor 1 and 15. Make sure you include the positive and negative factors. Then, come up with a pair of factors for each one so that the cross terms add to -8.

1: 1,1; -1,-1
15: 1,15;3,5;-1,-15;-3,-5

A bit of trial and error'll show you that 1*-3+1*-5 will work, so your factors look like:
(1x-3)(1x-5)

Same thing for the other one.

Answer 4

(x-3)(x-5)=x^2-8x+15

(3x-5)(x-4)=3x^2-17x+20

Answer 5

1.)
x^2 - 8x + 15 = (x - 3)(x - 5)

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2.)
3x^2 - 17x + 20

x = (-b ± sqrt(b^2 - 4ac))/(2a)

x = (-(-17) ± sqrt((-17)^2 - 4(3)(20)))/(2(3))
x = (17 ± sqrt(289 - 240))/6
x = (17 ± sqrt(49))/6
x = (17 ± 7)/6
x = (10/6) or (24/6)
x = (5/3) or 4

ANS : (3x - 5)(x - 4)

Answer 6

1. (x-3)(x-5)
2. (3x-5)(x-4)