Hi, I have a career link question from gr.12 advanced functions and intro. calculus. The equations is:

R(t) = 5(t⁴ - 4t³ + 19/4 t² - 3/2 t)

The question is to apply the factor theorem and quadratic formula to determine the times it crosses the t axis. The only method i know of for using the factor theorem is when the last number does not have a variable beside it so i'm not sure how you would even use the factor theorem for this? We haven't dealt with any that have 0 as the last number with no variable so i'm a little confused! please help!

Thank you
LisaMarie

Hi LisaMarie,

What you need to see is that t is a common factor in the expression for R(t). You can take it out as a common factor to get

R(t) = 5t(t³ - 4 t² + ¹⁹/₄ t -  ³/₂)

To use the factor theorem you want all the coefficients to be integers so put the expression inside the parentheses over a common denominator of 4 to get

R(t) = ⁵/₄ t(4 t³ - 16 t² + 19 t -  6)

Now apply the factor theorem.

Penny

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