How do you factor the equation y = -2x^2 +3x +5 into the form y = (x-p)(x-q)?

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Answer 1 · 2018-05-23T02:26:30

$y=(x+1)(-2x+5)$

$y=-2x^2 +3x +5$

you need to factor this by grouping:

$y=ax^2 + bx +c$

we need to find factors of $a*c$ that add up to $b$ :

$a*c=-2*5$ and $-2+5 = 3$ so let's split the parts, we split the $bx$ term into $h+k=b$

$y=-2x+5x = 3x$

Now replace the $3x$ in our quadratic equation:

$y=-2x^2 -2x+5x +5$

now group:

$y=(-2x^2 -2x)+(5x +5)$

use the distributive property:

$y=-2x(x +1)+5(x +1)$

factor out $(x+1)$

$y=(x+1)(-2x+5)$

Answer 2 · 2018-05-23T02:34:11

$(-2x+5)(x+1)$

We can start by factoring by grouping. Here, we'll split up the $b$ term into two terms so we can factor them separately.

We can rewrite $3x$ as $-2x$ and $5x$ . Thus, we have

$color(blue)(-2x^2-2x)+color(purple)(5x+5)$

We can factor out a $-2$ out of the blue term and a $5$ out of the purple term. Doing this, we get

$-2x(x+1)+5(x+1)$

Both terms have an $(x+1)$ in common, so we can factor that out. We get

$(-2x+5)(x+1)$

as our final answer.

Hope this helps!