Answer:
[tex](2t+5)(8t-1)[/tex]
Step-by-step explanation:
We can factor the quadratic expression:
[tex]16t^2+38t-5[/tex]
by grouping (also called the ac method).
First, we need to multiply the squared term's coefficient by the constant term:
[tex]16 \cdot (-5) = -80[/tex]
Next, we list out the factor pairs of the product:
- (-1, 80)
- (-2, 40)
- (-4, 20)
- etc.
And we select the pair whose factors add to the middle term's coefficient:
So, we can split the middle term, using these two factors as coefficients:
[tex]16t^2-2t + 40t-5[/tex]
Then, we can undistribute (factor out) the GCF between the first two and last two terms:
[tex]2t(8t-1) + 5(8t-1)[/tex]
Finally, we can rewrite the expression by combining like terms (treating [tex]8t-1[/tex] like a variable:
[tex]\boxed{(2t+5)(8t-1)}[/tex]
