Divide x^4 -16x^3 + 4x^2 + 10x -11
by x - 2
.
Divide x^4 -16x^3 + 4x^2 + 10x -11
by x +4
.
Divide x^4 -16x^3 + 4x^2 + 10x -11
by x -1
.
Are any of the binomials below factors of x^4 -16x^3 +4x^2 +10x -11
? Explain.
x- 2
x+ 4
x-1
State the degree of the quotient for each of the following division statements, if possible.
(x^4 - 15x^3 + 2x^2 + 12x -10) \div (x^2 -4)
State the degree of the quotient for each of the following division statements, if possible.
(5x^3 -4x^2 + 3x -4) \div ( x +3)
State the degree of the quotient for each of the following division statements, if possible.
(x^4 - 7x^3 + 2x^2 + 9x)\div (x^3 -x^2 + 2x + 1)
State the degree of the quotient for each of the following division statements, if possible.
(2x^2 +5x -4)\div (x^4 + 3x^3 - 5x^2 +4x - 2)
Complete the divisions
(x^4 -15x^3 + 2x^3 + 12x -10) \div (x^2 -4)
Complete the divisions
(5x^3 -4x^2 + 3x -4) \div ( x +3)
Complete the divisions
(x^4 - 7x^3 + 2x^2 + 9x)\div (x^3 -x^2 + 2x + 1)
Is this expression solvable? Explain.
(2x^2 +5x -4)\div (x^4 + 3x^3 - 5x^2 +4x - 2)
Complete the following table.
a) Given P(x) = 2x^3 -5x^2 + 8x + 4, D(x) = x+ 3, Q(x) =2x^2 -11x + 41
, find R(x)
.
b) Given D(x) = 2x + 4, Q(x) =3x^2 -5x + 8, R(x) = -3
, find P(x)
.
c) Given P(x) = 6x^4 + 2x^3 + 3x^2 -11x - 9, Q(x) =2x^3 + x -4, R(x) = -5
, find D(x)
.
a) Given P(x) = 3x^3 + x^2 -6x + 16, D(x) = x +2, R(x) =8
, find Q(x)
.
Calculate each of the following using long division.
(x^3 - 2x + 1)\div (x - 4)
Calculate each of the following using long division.
(x^3 + 2x^2 - 6x + 1) \div ( x +2)
Calculate each of the following using long division.
(2x^3 + 5x^2 - 4x -5)\div (2x + 1)
Calculate each of the following using long division.
(x^4 + 3x^3 - 2x^2 + 5x - 1)\div (x^2 + 7)
Calculate each of the following using long division.
(x^4 + 6x^3 - 8x +12)\div (x^3 -x^2 -x + 1)
Calculate each of the following using synthetic division.
(x^3 -7x - 6)\div(x - 3)
Calculate each of the following using synthetic division.
(2x^3 - 7x^2 -7x + 19)\div(x - 1)
Calculate each of the following using synthetic division.
(6x^4 + 13x^3 - 34x^2 - 47x + 28)\div(x + 3)
Calculate each of the following using synthetic division.
(2x^3 +x^2 -22x + 20)\div(2x -3)
Calculate each of the following using synthetic division.
(12x^4 - 56x^3 + 59x^2 + 9x -18)\div(2x + 1)
Each divisor was divided into another polynomial, resulting in the given quotient and remainder. Find the other polynomial (the dividend).
divisor: x+ 10
, quotient: x^2 - 6x + 9
, remainder: -1
Each divisor was divided into another polynomial, resulting in the given quotient and remainder. Find the other polynomial (the dividend).
divisor: 5x + 2
, quotient: x^3 + 4x^2 -5x + 6
, remainder: x - 2
Determine the remainder, r
, to make each multiplication statement true.
(2x -3)(3x +5) + r = 6x^2 +x + 5
Determine the remainder, r
, to make each multiplication statement true.
(x+ 3)(x +5) + r = x^2 + 9x - 7
Determine the remainder, r
, to make each multiplication statement true.
(x+ 3)(x^2 - 1) + r =x^3 + 3x^2 -x - 3
Determine the remainder, r
, to make each multiplication statement true.
(x^2 + 1)(2x^3 -1) + r = 2x^5 + 2x^3 + x^2 + 1
Each dividend was divided by another polynomial, resulting in the given quotient and remainder. Find the other polynomial (the divisor).
Dividend: 5x^3 + x^2 +3
, quotient: 5x^2 -14x + 42
, remainder: -124
Each dividend was divided by another polynomial, resulting in the given quotient and remainder. Find the other polynomial (the divisor).
Dividend: 10x^4 -x^2 + 20x -2
, quotient: 10x^3 -100x^2 + 999x - 9970
, remainder: 99 698
Each dividend was divided by another polynomial, resulting in the given quotient and remainder. Find the other polynomial (the divisor).
Dividend: x^4 + x^3 - 10x^2 -1
, quotient: x^3 - 3x^2 + 2x - 8
, remainder: 31
Each dividend was divided by another polynomial, resulting in the given quotient and remainder. Find the other polynomial (the divisor).
Dividend: x^3 + x^2 + 7x - 7
, quotient: x^2 + 3x +13
, remainder: 19
Find a binomial that is a factor of the given polynomial.
x^3 + 6x^2 -x - 30
Find a binomial that is a factor of the given polynomial.
x^4 - 5x^2 +4
Determine whether each binomial is a factor of the given polynomial.
x^4 - 5x^2 + 6
A. x^2-3
B. x+3
C. x+1
D. x^2+1
Find a binomial that is a factor of the given polynomial.
2x^4 -x^3 -4x^2 + 2x + 1
Determine whether each binomial is a factor of the given polynomial.
3x + 5, 3x^6+ 5x^5+9x^2+ 17x - 1
Determine whether each binomial is a factor of the given polynomial.
5x -1, 5x^4 - x^3 + 10x -10
The volume of a rectangular box is (x^3 + 6x^2 + 11x +6)cm^3
. The
A box is (x + 3)
cm long and (x + 2)
cm wide. How high is the box?
8x^3 + 10x^2 - px -5
is divisible by 2x + 1
. There is no remainder. Find the value of p
.
When x^6 + x^4 -2x^2 + k
is divided by 1 + x^2
, the remainder is 5
. Find the value of k
.
The polynomial x^3 + px^2 -x -2, p\in \mathbb{R}
, has x -1
as a factor. What is the value of p
?
Let f(x) =x^n -1
, where n
is an integer and n \geq 1
. Name a factor that makes f(x)
always divisible by it? Explain.
If the divisor of a polynomial, f(x)
, is x - 4
, then the quotient is
x^2 + x -6
and the remainder is 7.
f(x)
using your results in part b).The volume of a cylindrical can is (4\pi x^3 + 28 \pi x^3 + 65 \pi x + 50\pi)cm^3
. The can is (x + 2)
cm high. What is the radius?
Divide.
(x^4 + x^3y -xy^3 - y^4)\div(x^2 - y^2)
Divide.
(x^4 -2 x^3y + 2x^2y^2 - 2xy^3 + y^4)\div(x^2 + y^2)
Find a factor for x^3 - y^3
.
Is f(x) = (x + 5)q(x) + (x + 3)
, what is the first multiple of (x + 5)
that greater than f(x)
.
The Division Algorithm
Long Division Ex1
Long Division Ex2 Converting Rational Expression to Mixed Form
Long Division Ex3 Dividing with Quotient of Degree 2
Introduction to Synthetic Division
Synthetic Division Example