how do factor this: 4x^2 +7x-15?

Answer 1

The behind this is to split 7 {the co-efficient of term with x} into two nos. such that the sum of the two nos is 7 {the co-efficient of term with x} and the product of those two nos is equal to the product of 4 and -15 {coeeficient of term with x^2 and constant term}

Here the two nos should add up to +ive7 and have a product of -ive60 {-60 is derived from -15 * 4}.

Two such nos are. + 12 and -5 {by trial and error}

Hence 4x^2 + 7x - 15 = 4x^2 + 12x - 5x - 15

= 4x*(x+3) - 5*(x+3) {taking 4x common from first two terms and -5 common from last two terms}
= (4x-5) * (x+3) {taking (x+3) common}



Alternatively the roots(solutions of x) of the eqn ax^2 + bx + c = 0 is [ -b (+or-) sqrt(b^2 - 4ac) ] : 2a

Here a = 4 ; b = 7 ; c = -15
Substituting we get....
Roots = [-7 +/- sqrt(7^2 - 4*4*-15) ] : 2*4
= [-7 +/- sqrt(289)] : 8.
= [-7 +/- 17] : 8

1st sol = (-7 + 17) : 8 = 5/4
2nd sol = (-7 - 17) : 8 = -3

Hence the factors are ( x - 1st Sol) * (x - 2nd Sol)
= (x-5/4) * (x+3)


This can be realted to the answer from alternative 1 as
(x - 5/4)*(x+3) = 0 => [(4x-5)/4]*(x+3) = 0
(4x-5)*(x+3) = 0 { as when the 4 in Dr is taken to the other side and multiplied with 0 it becomes 0

Answer 2

You could always do the quadratic formula:

(-b +- sqrt(b^2 - 4ac)) / 2a

(-7 +- sqrt(49 + 16*15)) / 8
(-7 +- sqrt(289)) / 8
(-7 +- 17) / 8
(10 / 8) and (-34 / 8)
(5 / 4) and (-17 / 4)

(x - 5/4)(x + 17/4)

Answer 3

Quadratic formula is best for this, except that it isnt -34 / 8, its -24 / 8, or -3

(x - 5/4)(x + 3)

Answer 4

well 4x times 2 = 8x, so 8x +7x = 15x, and 15x-15 is the answer

just do it step by step

hope i helped

Answer 5

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