Question

For what values of t can 3(x^2) + tx + 8 be written as the product of two binomials and what are the pairs of binomials?

Answer 1

Answer:

The pair of binomials are;


`(x+1)(3x+8)`

and


`(x-1)(3x-8)`

Explanation:

The given expression is
`3x^2+tx+8`.

If the given quadratic trinomial can be factored as two binomials, then,

By comparing to
`ax^2+bx+c`, we have
`a=3,b=t,c=8`

We find
`ac=3*8=24`

We also know that;
`-3* -8=24`

This implies that;


`t=8+3=11` or
`t=-3-8=-11`

When t=11;


`3x^2+11x+8`

When we factor this we obtain;


`(x+1)(3x+8)`

When t=-11;


`3x^2-11x+8`

When we factor this we obtain;


`(x-1)(3x-8)`