MATH SOLVE

3 months ago

Q:
# Drag the tiles to the correct boxes to complete the pairs.Match each polynomial function with one of its factors.f(x) = x3 − 3x2 − 13x + 15f(x) = x4 + 3x3 − 8x2 + 5x − 25f(x) = x3 − 2x2 − x + 2f(x) = -x3 + 13x − 12x − 2arrowRightx + 3arrowRightx + 4arrowRightx + 5arrowRight

Accepted Solution

A:

Answer:f(x) = x3 − 3x2 − 13x + 15 Factor: x+3f(x) = x4 + 3x3 − 8x2 + 5x − 25 Factor: x+5f(x) = x3 − 2x2 − x + 2 Factor: x-2f(x) = -x3 + 13x − 12 Factor: x+4Step-by-step explanation:f(x) = x^3 − 3x^2 − 13x + 15 Solving:We will use rational root theorem: -1 is the root of x^3 − 3x^2 − 13x + 15 so, factor out x+1x^3 − 3x^2 − 13x + 15 / x+1 = x^2-2x-15Factor: x^2-2x-15 =(x+3)(x-5)So, factors are: (x+1)(x+3)(x-5)Factor: (x+5)f(x) = x^4 + 3x^3 − 8x^2 + 5x − 25Solving:We will use rational root theorem: -5 is the root of x^4 + 3x^3 − 8x^2 + 5x − 25, so factour out (x+5)x^4 + 3x^3 − 8x^2 + 5x − 25 / x+5 = x^3-2x^2 +2x -5So, factors are (x+5) (x^3-2x^2 +2x -5) Factor: x+5f(x) = x^3 − 2x^2 − x + 2 Solving:x^2(x-2)-1(x-2)(x-2)(x^2-1)(x-2) (x-1) (x+1) Factor: x-2f(x) = -x^3 + 13x − 12 Solving: -(x^3 + 13x -12)We will use rational root theorem:The 1 is a root of (x^3 + 13x -12) so, factor out x-1Now solving (x^3 + 13x -12)/x-1 we get (x-3)(x+4)So, roots are: - (x-1)(x-3)(x+4)Factor (x+4)