Divide the expression.
Simplify the expression.
Divide using polynomial long division.
(x2 + 7x – 5) (x – 12)
(4x4 + 9) (x2 – 1)
Divide.
Perform he division.
Divide using synthetic division:
(x3 – 5x – 6) (x – 2)
(3x2 + 7x – 3) (x + 2)
Perform synthetic division.
Find the remainder of the polynomial using synthetic division:
Evaluate the function using the remainder theorem:
f(x) =x2 + 3x + 7 at x = – 4
f(x) = 2x2 – 3x + x + 2 at x = 2
Use synthetic substitution to find f(1) and f(–2) for a function.
f(x) = 2x2 –7x + 5
Use synthetic substitution to find f(2) and f(–1) for a function.
f(x) = x3 – 12x2 – 4x + 3
Factor the polynomial given that f(k) = 0.
f(x) = x3 – 6x2 – 7x + 60, k = – 3
f(x) = x3 – 16x2 + 43x + 60, k = 12
f(x) = x3 – 2x2 – 32x + 96, k = – 6
One of the zeroes of the function f(x) = x3 – x2 – 12x is at x = –3. Determine the other zeroes.
Given a polynomial and one of its factors, find the remaining factors of the polynomial.
81x5 – 243x4 – 256x + 768, x – 3
Given one zero of the polynomial function, determine the other zeros.
f(x) = 7x3 + 15x2 – 19x – 3, –3
f(x) = 3x3 + 7x2 – 43x – 15, 3
Find polynomial Q(x) and constant R in 2x3 + 3x2 + 1 = Q(x)(x + 2) + R.
Find polynomial Q(z) and constant R in 2z3 – 3z2 + 2z – 1 = Q(z)(z+ i) +R.
You are given an expression for the volume of the rectangular prism. Determine an expression for the missing dimension.
V = 4x3 + 5x2 – 32x – 33 and the dimensions are (x + 1) and (x + 3).
f(x) = x2 + 3x + 7 at x = – 4
Find polynomial Q(z) and constant R in 2z3 – 3z2 + 2z – 1 = Q(z)(z+ i) + R.
