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How do you factor the equation 2w^2 + 3w - 90?

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chocolate975 | Student, Undergraduate | eNoter

Posted May 3, 2010 at 7:14 AM via web

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How do you factor the equation 2w^2 + 3w - 90?

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neela | High School Teacher | Valedictorian

Posted May 3, 2010 at 9:37 AM (Answer #1)

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To factor 2w^2+3w-90.

Solution:

The first term is 2w^2 and the last term is -90. Their product is 2w^2(-90) = -180w^2.. The factors of -180w^2 in such way that the sum of the factors is middle term,3w of the given quadratic is. -180w^2 = (15w)(-12w). And  (15w)+(-12w)=3w.

Now we can can group the given quadratic splitting the middle term into 15w and -12w as below:

2w^2+15w-12w-90

=w(2w+15)-6(2w+15)

=(2.w+15)(w-6)

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krishna-agrawala | College Teacher | Valedictorian

Posted May 3, 2010 at 11:24 AM (Answer #2)

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The given expression is:

2w^2 + 3w - 90

(Please note that it is just an expression, not an equation)

We can find factors of this expression by modifying it in equivalent expression in following steps:

2w^2 - 12w + 15w - 90

2w(w - 6) + 15(w - 6)

(w - 6)(2w + 15)

Answer:

Factors of the given expression are (w - 6) and (2w + 15).

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atyourservice | Student, Grade 10 | Valedictorian

Posted June 26, 2014 at 4:01 AM (Answer #3)

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2w^2 + 3w - 90

 a          b      c

multiply a by c

2 x -90 = -180

find factors of -180 that subtract to 3  (15 and -12)

now plug in those numbers are the b

2w^2 - 12w + 15w - 90

group

(2w^2 - 12w ) (+ 15w - 90)

now factor the parentheses:

2w ( w - 6 ) + 15 (w - 6)

nwo put the numbers outside of the parentheses together:

(w - 6) (2w + 15)

you can go further and find out the solutions by setting the parentheses = 0

w - 6 = 0

w = 6

2w + 15 =0

2w = -15

w = 7.5

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