Question

How do you factor `2x^2-5x+2`?

Answer 1

`=(2x-1)(x-2)`

Explanation:

Ok, we are just going to factor this one out!

`=2x^2-5x+2`

Break it into groups

`=(2x^2-x)+(-4x+2)`

At this point we can factor out x and -2 respectively

`=x(2x-1)-2(2x-1)`

Then factor out the common term

`=(2x-1)(x-2)`

Hope this helped!
~Chandler Dowd

Answer 2

`(2x-1)(x-2)`

Explanation:

`"the factors of + 4 which sum to - 5 are - 4 and - 1"`

`"splitting the middle term"`

`2x^2-4x-x+2larrcolor(blue)"factor by grouping"`

`=color(red)(2x)(x-2)color(red)(-1)(x-2)`

`"take out "color(blue)"common factor "(x-2)`

`=(x-2)(color(red)(2x-1))`

`rArr2x^2-5x+2=(x-2)(2x-1)`

Answer 3

`(2x -1)(x-2)`

Explanation:

`color(magenta)(2)x^2 -color(blue)(5)x color(red)(+)color(lime)(2)`

All the information is in the trinomial.

Find the factors of `color(magenta)(2) and color(lime)(2)` which `color(red)("ADD")` to make `color(blue)(5)`

The `color(red)(+)` sign gives two clues:

• ADD the factors to get the middle number
• the sign in the brackets will be the SAME.

Note that `2 xx 2=4" " and 1xx1 =1`

Now `4+1=5`, so `2 and 2` are the factors.
As `2` is a prime number there are only two ways of combining the factors.

SO know we know:

`(2x" "1)(x" "2)`

We also know the signs will be the SAME.

The sign of the middle term `color(blue)(-5)` shows they will be negative.

`(2x -1)(x-2)`

Check by multiplying:

`=2x^2 -4x-1x+2`

`=2x^2 -5x+2`