Factor completely: 2x2 + 9x + 4

What are two numbers that multiply to 4*2 or 8 AND add to 9.

2 * 4 = 8 factors of 8 that add to 9? 8 and 1 (2+1)(2+8) all over 2 (2+1)2(1+4) all over 2 the 2's cancel out we have (2x + 1)(x+4)

@johnweldon1993 This technique of factoring: (2+1)(2+8) all over 2 (2+1)2(1+4) all over 2 the 2's cancel out What is the mathematical basis for it?

2x^2 + 9x + 4 = 2 x² + 8x + 1x + 4

2 x² + 8x + 1x + 4 = 2x (x + 4) + 1 ( x + 4)

2x (x + 4) + 1 ( x + 4) = (x + 4) ( 2x + 1)

just another way of looking at it....@jim_thompson5910 actually showed it to me...and I found i like it...it works a lot easier when there is a coefficient in front, a lot of people get thrown off by it and this method makes that easier

I get that. I have seen many people use the technique but so far nobody has been able to give the mathematical basis for why it seemingly works. If you look at the factoring by grouping that I did, I can justify every step with known mathematics principles. Can you support your work in the same way, maintaining equality throughout the steps? Tricks and shortcuts are great but if they cannot be explained, then how do you teach them to someone else? @johnweldon1993

@Directrix i see your point....i didn't really think about it....I'm going to look more into it...If i find a good basis for it, I'll definitely let you know!

@johnweldon1993 Would you factor the following expression completely using the "slide and divide" a.k.a. "upside-down" factoring technique. Thanks. 12x^2+16x-35

well lets see 12 times -35 = -420 factors of -420 that add to 16 420, 1 210,2 105,4 84,5 70,6 60, 7 42,10 35,12 30,14 (would be it) gets monotonous i see what you mean so we have (12x + 30)(12x - 14) all over 12 6 factors out , 2 factors out 6(2x + 5)2(6x - 7) all over 12 12(2x + 5)(6x - 7) all over 12 12's cancel out have (2x + 5)(6x - 7) check it equals 12x^2+16x-35 12x² - 14x + 30x - 35 12x² + 16x - 35 yes i see your reasoning behind that, the factors of big numbers DO get monotonous

@johnweldon1993 Thanks.

@Directrix was that your reasoning behind that?

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