Question

Factoring: Did I Do it Right?

4x^2-8x+3

4x^2+6x+8x+3

2x (2+3x) + 1 (2+3x)

(2x+1) (2+3x)

I think my signs are off, if they are how do I know what the correct ones are?

Answer 1

well I think you have a few issues...

Answer 2

You can always check your work by multiplying out (2x+1)(2+3x) to see if you got the original quadratic. In this, it's wrong.

Look at your second line. You replaced (-8x) with (+6x + 8x). These are not equal quantities.

Factoring is usually trial and error, but we can limit out options if we're clever.

The leading term has a coefficient of 4, and the constant term is 3. So our options for the factored quadratic will look like (4x 1)(x 3) or (4x 3)(x 1) or (2x 1)(2x 3), where the plus or minus signs have not been filled in yet.

We want the linear term's coefficient to add up to 8, and we see that any combination of 12x and 3x will not get us -8x. So it has to be of the form (2x 1)(2x 3).

We want the constant coefficient to be positive, so the choices for the signs are either + & +, or - & -. Two plus signs will get us 6x + 2x = 8x though, and we'd like -8x, so the solution is 4x^2 - 8x + 3 = (2x-1)(2x-3).

Answer 3

split -8x into -6x and -2x

so then grouping you get

\[(4x^2 - 6x) + (-2x + 3)\]

now factor both pairs

\[2x(2x - 3) -1(2x -3)\]

now you can finish it.

hope it makes sense

Answer 4

An alternate method you might want to show your teacher

for a quadratic \[ax^2 + bx + c = 0\]

multiply a and c

so in your question its 4 * 3 = 12

find the factors of 12 that add to -8... both factors are negative, so -6, -2

next write the factorisation as

(ax + factor 1)(ax + factor 2)
-------------------------
a

so you have

\[\frac{(4x - 6)(4x - 2)}{4}\]

factor the binomials in the numerator

\[\frac{2(2x -3)2(2 - 1)}{4}\]

the factors in the numerator cancel with the denominator so

\[\frac{2 \times 2\times(2x - 3)(2x -1)}{4} = (2x -3)(2x -1)\]

this method saves having to split the middle term.

hope it helps

Answer 5

~Thank you, so I tried another one...Do you mind checking it?~

4x^2+7x+3

4x^2+4x+3x+3

4x (1x+1) + 3(1x+ 1)

(1x+1) (4x+3)

Answer 6

that makes sense