Function Factors f(x) = x^4 - 7x^3 + 5x^2 + 31x - 30 (x - 3), (x + 2) (a) Verify the given factors of f(x). (x - 3) 3 | 1 -7 5 31 -30 3 -12 -21 30 1 -4 -7 10 0 (x + 2) -2 | 1 -7 5 31 -30 -2 18 -46 30 1 -9 23 -15 0 (b) Find the remaining factor(s) of f(x). (Enter your answers as a comma-separate
Added by Gregory J.
Close
Step 1
We have: f(3) = 3 - Z(3) + S(3)^2 + 31(3)^30 = 3 - 3Z + 9S + 31(3)^30 We don't know the values of Z and S, but we can use the fact that (x - 3) is a factor to write f(x) as: f(x) = (x - 3)(ax^2 + bx + c) where a, b, and c are constants. We can expand this Show more…
Show all steps
Your feedback will help us improve your experience
Gregory Higby and 73 other Precalculus educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
(a) verify the given factors of $f(x),($ b) find the remaining factor(s) of $f(x),($ c) use your results to write the complete factorization of $f(x),(d)$ list all real zeros of $f,$ and (e) confirm your results by using a graphing utility to graph the function. $f(x)=10 x^{3}-11 x^{2}-72 x+45 \quad(2 x+5),(5 x-3)$
Polynomial and Rational Functions
Polynomial and Synthetic Division
Use the factor theorem to determine if the factors given are factors of $f(x)$. $f(x)=x^{3}-6 x^{2}+3 x+10$ a. $(x+2)$ b. $(x-5)$
Synthetic Division; the Remainder and Factor Theorems
Use the factor theorem to determine if the factors given are factors of $f(x)$. $f(x)=x^{3}-3 x^{2}-13 x+15$ a. $(x+3)$ b. $(x-5)$
Recommended Textbooks
Precalculus with Limits
Precalculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD