Question

How do you factor `4x^2-15x+9`?

Answer 1

You need to "play with multiples of 4 (1x4, 2x2, 4x1) and multiples of 9 (1x9, 3x3, 9x1) to give:

`(4x - 3)(x - 3)`

Answer 2

`(4x-3)(1x-3)`

Explanation:

When you want to find the factors of a quadratic trinomial, there is a lot of information in the quadratic itself.

`ax^2 +bx + c` describes a quadratic trinomial.

`4x^2 -15x+9`

Find factors of `a` and `c`
Find factors of `4 and 9` which combine and ADD [because of PLUS 9.] to give 15

The signs in the brackets will be the SAME (because of PLUS 9).
they will BOTH be NEGATIVE (because of negative 15.)

`" "4 " and "9" "larr` find factors and cross multiply
`" "darr" "darr`
`" "4 " " 3 rarr 1 xx 3 = 3`
`" "1 " " 3 rarr 4 xx 3 = ul12`
`color(white)(....................... ...................)15" "larr 3+12`

The top row gives the one bracket, the second row gives the other bracket.

This gives `(4x-3)(1x-3)`

Multiplying out the brackets will give the original trinomial.

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Note: There is a clue in the fact that 15 is odd. An odd number is formed from an odd + even. This tells us that 4 is not split as 2 x 2, because then both products would be even. Even + even = even

Therefore 4 has to be used as `4xx1`
Once you know that there are only 3 possibilities to try for 9:

`9 xx 1, 1 xx 9 and 3 xx3`