Question

Factor the trinomial 7x2 – 3x – 4. Which pair of numbers has a product of ac and a sum of b? What is the factored form of the trinomial?

Answer 1

-7 and 4

(7x+4)(x-1)

Explanation:

Edgy

Answer 2

The pair of numbers are -7 and 4

The factored form is given by

`(x-1)(7x+4)`

Explanation:

The given trinomial is
`7x^2-3x-4`

Comparing, with the equation
`y=ax^2+bx+c`

a = 7

b = -3

c = -4

In order to write in factored form, we use AC method.

In AC method, first of all we find the product of A and C.

ac = 7×(-4)

ac = -28

Now, we find the factor pairs of 28 such that the product is equal to ac and the sum/difference is equal to b.

-28 = 1×(-28), (-28)×(1), 7×(-4) , (-7)×(4)

Among these factors pairs, (-7)×(4) is the correct choice because

(-7)×(4) = -28

-7 +4 = -3

Hence, the numbers are -7 and 4

Now, we write the middle term -3x as -7x+4x

`7x^2-7x+4x-4`

Factor out GCF

`7x(x-1)+4(x-1)`

Factored out the common term

`(x-1)(7x+4)`

Hence, the factored form is given by

`(x-1)(7x+4)`