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:

The pair of binomials are;

[tex](x+1)(3x+8)[/tex]

and

[tex](x-1)(3x-8)[/tex]

Step-by-step explanation:

The given expression is  [tex]3x^2+tx+8[/tex].

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

By comparing to [tex]ax^2+bx+c[/tex], we have [tex]a=3,b=t,c=8[/tex]

We find [tex]ac=3\times8=24[/tex]

We also know that; [tex]-3\times -8=24[/tex]

This implies that;

[tex]t=8+3=11[/tex] or [tex]t=-3-8=-11[/tex]

When t=11;

[tex]3x^2+11x+8[/tex]

When we factor this we obtain;

[tex](x+1)(3x+8)[/tex]

When t=-11;

[tex]3x^2-11x+8[/tex]

When we factor this we obtain;

[tex](x-1)(3x-8)[/tex]