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]
