How do you factor $7x^2 + 11x - 30 = 0$ ?

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Answer 1 · 2016-05-04T20:20:55

Note that the integer factors of $-30$ could be:

$6$ and $-5$

$10$ and $-3$

$15$ and $-2$

$-6$ and $5$

$-10$ and $3$

$-15$ and $2$

Remember "FOIL"? It implies that you will be multiplying the following:

$(7x pm A)(x pm B)$

$= 7x^2 pm stackrel("Useful Hint")overbrace(color(green)(7Bx pm Ax)) pm AB$

We will need to account for the following relationship:

$color(green)(7x*B + 1x*A = 11x)$ ,

which is the middle term based on the operation of the outer and inner terms in $(7x pm A)(x pm B)$ . It looks like this works:

$7x*color(green)(3) + 1x*color(green)((-10)) = 11x$

Compare and see:

$7x*B + 1x*A" "" " = 11x$
$7x*3 + 1x*(-10) = 11x$

This means $B = 3$ and $A = -10$ . So, the answer would be:

$= color(blue)((7x - 10)(x + 3))$

How do you factor 7x^2 + 11x - 30 = 07x^2 + 11x - 30 = 0?