Solve 4x2 + x - 14 by factoring?

Question

Solve 4x2 + x - 14 by factoring?

Answer 1

(4x + 2)(x - 7)

therefore,

4x + 2 = 0

4x = -2

x = -1/2

and

x - 7 = 0

x = 7

Answer 2

4x^2 + 8x - 7x - 14

= 4x(x+2) -7(x+2)

= (4x-7)(x+2)

Answer 3

(4x-7)(x+2)

Answer 4

I would be happy to explain and provide online resources for factoring, but need some more information.

Is your question:

"Four (times) x (times) two (plus) x (minus) 14" ?

Or, is your equation "Four (times) x (squared)" ?

Answer 5

alright to solve this the first step is to take the coefficient of the leading term (4x^2) and multiply it by the last tern (-14) this gives you -56

next step is to find 2 numbers that when multiplied = -56 and when you add them they = the coefficient of the middle term

so in this example your numbers are 8 and -7 because 8*-7 equals -56 and 8+-7 equals 1

then you rewrite the trinomial with those numbers with the variable of the middle term like so...

4x^2 + 8x - 7x - 14

next you factor by grouping:

you can take 4x out of the first set of terms giving you

4x(x+2) - 7x - 14

you can take -7 out of the second set of terms giving you

4x(x+2) - 7(x+2)

at this point you have your factors...what is common to both terms is a factor (x+2) and what is left is a factor (4x-7) is a factor so....

the solution is (x+2)(4x-7)

to check if it is correct you just FOIL the 2 binomials, if it results in the original trinomial your answer is correct