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

Answer:

The pair of numbers are -7 and 4

The factored form is given by

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

Step-by-step 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

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