Deer Valley Unified School District



GUIDED NOTES – Lesson 3-7 The Factor & Remainder Theorem Name: ______________________ Period: ___ Objective: I can use synthetic division to evaluate functions and to prove factors exist for specific functions.THE REMAINDER THEOREM: If you want to evaluate a function at a given x value, make that x value the divisor and the remainder is the answer.Remember that ‘evaluate’ is terminology that typically means ______________.EXAMPLES:Evaluate f(x) = x4 – 10x2 – 2x + 4 at x = -3If g(x) = (2x3 – 3x2 + 7), find g(3)If h(x) = (8x4 – 4x2 + x + 4), find h(-?)The Factor Theorem: States that if there is no remainder after dividing the function by k, the polynomial (x - k) is a factor. EXAMPLES:Given (x – 2) is a factor of p(x) = x3 + 6x2 – x – 30, factor the entire function completely.We know that (x – 2) and (x + 3) are factors of m(x) = 2x4 + 7x3 – 4x2 – 27x – 18Factor them out, then find the remaining factors. ................
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