How the quadratic may be factored by grouping 5x^2 + 17x – 40 = 0?

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atyourservice's profile pic

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

Posted on

`5x^2+17x-40 = 0 `

`A=5`  `b=17`   `c=-40`

Multiply `axxc` and find factors of that number that minus to b

`-40xx5=-200`    factors of -200 that minus to 17 are 25, -8    plug these numbers into the problem

`5x^2+25x-8x–40` now factor by grouping

`(5x^2+25x)(-8x–40)`

Find the greatest number the numbers in the parenthesis have in common and factor them out

`5x(x+5) -8(x+5)`

(5x-8) (x+5)

and the answers are  (5x-8) (x+5)

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll re-write the middle terms as 17x = 25x – 8x.

We'll re-write the equivalent equation:
5x^2 – 8x + 25x – 40 = 0

We'll create pairs of terms:
(5x^2 – 8x) + (25x – 40) = 0

We'll factorize each pair:
x(5x – 8) + 5(5x – 8) = 0

We'll notice the common factor (5x – 8):
(5x – 8)(x+5) = 0

The factor quadratic is: 5x^2 + 17x – 40 = (5x – 8)(x+5)

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