Answer:
The pair of numbers are -7 and 4
The factored form is given by
[tex](x-1)(7x+4)[/tex]
Step-by-step explanation:
The given trinomial is [tex]7x^2-3x-4[/tex]
Comparing, with the equation [tex]y=ax^2+bx+c[/tex]
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
[tex]7x^2-7x+4x-4[/tex]
Factor out GCF
[tex]7x(x-1)+4(x-1)[/tex]
Factored out the common term
[tex](x-1)(7x+4)[/tex]
Hence, the factored form is given by
[tex](x-1)(7x+4)[/tex]
