Algebra 2 How do you Factor 4x^2-7x+3?

4x^2 - 7x + 3 ......... format: ax^2 + bx + c

Note: Try to find two integers whose product is = 4*3 = 12 and sum = -7

................... what about -3 and -4? product = 12, sum = -7

Transform the equation in to:

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

= 4x(x -1) - 3 (x-1)

= (x-1)(4x-3)

............................... done

A big part of math is pattern recognition, and a lot of homework is just fighting with stuff so you will remember the pattern when you see it again. The pattern here is (x + a) * (x + b) = x^2 + (a + b)x + ab

I notice that 4 = 2^2 but that does not lead to anything useful so I try 4x. I see we have +3 but -7. that tells me there are two minuses, so I try (4x - 3) * (x - 1). then I go to wolfie to check my answer.

https://www.wolframalpha.com/input/?i=4x%5E2-7x%2B...

I usually try to figure out the first and last numbers first. The only answers that would make 4x^2 are (2x)(2x) or (4x)(x). Obviously 3 would have to be (3)(1) and since it is a positive 3 and the 7x is negative, it's a pretty good bet that that your signs are negative and negative.

So, our options are (2x-1)(2x-3), (4x-1)(x-3), or (4x-3)(x-1). It's just a matter of crunching it out to figure out which one gives you back the original equation.

You know how to do FOIL right? To get variables out of (ax-b)(x-c) form? Just in case FOIL stands for First, Inside, Outside, Last.

Example using (ax-b)(x-c):

First- (ax)(x)

Outside- (ax)(c)

Inside- (b)(x)

Last-(b)(c)

Correct Answer

(4x-3)(x-1)

4x^2-7x+3

exponents first so we do 4x^2 = 16x because 4x4=16

so so far its 16x-7x+3 combine like terms 16x-7x = 9x because 16-7=9

so the answer is 9x + 3 you cant finish it cuz the 3 doesnt have an x behind it so 9x+3 is the answer hope i helped

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