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

neela | High School Teacher | (Level 3) Valedictorian

Posted on

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)

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

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

krishna-agrawala | College Teacher | (Level 3) Valedictorian

Posted on

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)