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How do you find the product #[(t^2+3t-8)-(t^2-2t+6)](t-4)#?

Answer 1

Isaiah Anthony

#[(t^2+3t-8)-(t^2-2t+6)] (t-4) = 5t^2-34t+56#

# [(cancel(t^2)+3t-8)-(cancel(t^2)-2t+6)] (t-4)#

# = (5t-14)(t-4)#

We have the first term: #t^2+3t-8-t^2+2t+6=5t-14# so we get # [(cancel(t^2)+3t-8)-(cancel(t^2)-2t+6)] (t-4)#

# = (5t-14)(t-4)#

#(5t-14)(t-4)=5t^2-14t-20t+56# Combining like terms, we get: #5t^2-34t+56#

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Answer 2

Kennedy Adams

To find the product of (t^2+3t-8)-(t^2-2t+6), first simplify the expression inside the brackets by subtracting the second polynomial from the first. Then distribute the resulting expression by multiplying it by (t-4).

(t^2+3t-8)-(t^2-2t+6) simplifies to 5t-14.

Now, multiply 5t-14 by (t-4):

(5t-14)(t-4) = 5t^2 - 20t - 14t + 56

Combine like terms:

5t^2 - 34t + 56

So, the product is 5t^2 - 34t + 56.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.