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

$(x-1)(3x-8)$

Step-by-step 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 $ac=3\times8=24$

We also know that; $-3\times -8=24$

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;

$(x-1)(3x-8)$