College Algebra
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Simplify by completely dividing the following expression. (a4 + 13a2 + 5a + 12)/(a2 + 6)
Simplify by completely dividing the following expression. (20b3 + 22b2 - 4b + 3)/(2b + 3)
Simplify by completely dividing the following expression. (5a3 - a + 9)/(a - 2)
Simplify by completely dividing the following expression. (5t3 - 11t2 + 4)/(t - 1)
Simplify by completely dividing the following expression. (2k3 + 3k2 -39k - 13)/(2k + 5)
Simplify by completely dividing the following expression. (v2 + 3v + 25)/(v + 5)
Simplify by completely dividing the following expression. (a2 + 6a + 13)/(a + 5)
Solve the polynomial equation x4 - 5x3 - 49x2 + 125x + 600 = 0 to see if 8 is a solution using synthetic division.
From there, solve the resulting equation to complete the values of x.
Find the polynomial, if 3x2 + 11x + 4 yields a quotient of 3x - 1 and a remainder of 8 when divided by this polynomial.
Work out the value of k that makes 9x + 1 a factor of 18x3 + 74x2 - 145x + k.
A rectangle has an area of 0.7x3 - 0.695x2 - 0.02x + 0.015 and a length of x + 0.15 units. Solve for the polynomial that describes its width.
Find the quotient of the following polynomials by using synthetic division.
(8x5 - 4x4 + 2x3 - 3x2 + 6x - 5) ÷ (x + 1)
(x4 - 1296) ÷ (x - 6)
(2x7 + 3x5 - 5x3 + 4) ÷ (x + 1)
(x5 + 3x3 - 6) ÷ (x - 3)
(8x2 - 4x - 2x3 + 3x4) ÷ (2 + x)
(x5 + 8x4 - 4x2 + 5x + 1) ÷ (x - 1)
(7x5 - 3x3 + x2 - 5x + 2) ÷ (x - 5)
(5x3 - 2x2 + 2x - 4) ÷ (x - 2)
(7x2 + 16x + 9) ÷ (x - 1)
(4x2 - 24x - 64) ÷ (x - 8)
Find the quotient and indicate the remainder, r(x), if long division would be performed on the following.
(4x5 + 2x3 + 8x2) ÷ (5x2 + 3)
(x4 + 13x3 + 37x2 - 26x - 40) ÷ (x2 + 7x - 9)
(36x3 + 67x2 + 124x + 13) ÷ (4x2 + 7x + 13)
(9x4 - 3x2 + 6x) ÷ (x - 6)
(4x2 - 3x + 8) ÷ (x - 1)
(3x3 + 31x2 + 43x + 58) ÷ (x + 9)
If 5/3 is a root of 12x3 -35x2 +28x -5 = 0, solve the equation.
If it is given that 4 is a zero of f(x)=2x3 +7x2 -38x -88, then solve the equation 2x3 +7x2 -38x -88 =0.
Use the result of the synthetic division of f(x)=x3−15x2+71x -105 by x-5 to determine all zeros of f.
Determine f(-1/3) using synthetic division and the remainder theorem. f(x) = 3x4 -2x3 - 10x2 +6x +2
Determine f(-3/4) using synthetic division and the remainder theorem. f(x) = 4x4 -x3 - 7x2 +5x +2
Determine f(-1) using synthetic division and the remainder theorem.
f(x)= -3x4-x3-5x2+8x+3
Determine f(-5) using synthetic division and the remainder theorem. f(x) = x3 -5x2 +8x +3
Determine f(2) using synthetic division and the remainder theorem. Where f(x) = 3x3 -14x2 +2x -1
(10x2 + 3x + 1) ÷ (5x - 1)
(8x3 + 22x2 + 7x + 5) ÷ (2x + 5)
(x3 + 10x2 + 27x + 10) ÷ (x + 5)
(x2 + 12x + 35) ÷ (x + 7)
What is the quotient if you divide 915 by 19? Indicate the quotient in the form of whole number + remainder/divisor.
For the given polynomial expression: 8x4 - 17x3 - 12x2 + 9x + 4, find f(5) using the Remainder Theorem.
Using long division, divide the following polynomials. (7x4 - 21x3 + 6x2 - x + 3) ÷ (x2 + 4)
Using long division, divide the following polynomials. (5x4 - 13x3 - 13x2 + 22x - 2) ÷ (x - 3)
For the given polynomial function, perform synthetic division to test if k = 9 is a zero. In case it's not, just evaluate f(k).
f(x) = x2 - 4x - 45
f(x) = x3 - 18x2 + 90x - 81
For the given polynomial function, perform synthetic division to test if k = 4 is a zero. In case it's not, just evaluate f(k).
f(x) = 3x3 - 18x2 - 25x + 28
For the given polynomial function, perform synthetic division to test if k = 0 is a zero. In case it's not, just evaluate f(k).
f(x) = x3 + 14x2 + 33x
Simplify by completely dividing the following expression. (21h2 + 35h - 9)/(7h)
Simplify by completely dividing the following expression. (21h3 + 35h2 + 84h)/(7h3)
Simplify by completely dividing the following expression. (- 55h12 - 22h9 + 88h6 - 44h3)/(- 11h3)
Simplify by completely dividing the following expression. (- 6g2h3 - 9gh3 + 12gh2)/(- 15g2h3)
Simplify by completely dividing the following expression. (12j2g2h3 + 5j2g3h2 + 15j3g2h2)/(3j2g3h2)
Simplify by completely dividing the following expression. (d2 + 3d - 108)/(d - 9)
Simplify by completely dividing the following expression. (2d2 + 13d + 20)/(2d + 5)
For the given polynomial function, use the remainder theorem to find f(-4). Write the coordinates of the respective point on the graph of the function f(x).
f(x) = x3 - 4x2 - 3x + 5
For the given polynomial function, use the remainder theorem to find f(3). Write the coordinates of the respective point on the graph of the function f(x).
f(x) = x3 - 5x2 - 6x + 7
Perform synthetic division:
(5x3 + 8x2 - 11x + 370)/(x + 5)
For the given polynomial function, use synthetic division to find f(4).
f(x) = 4x3 - 9x2 + 5x - 20
For the given polynomial function, use synthetic division to find f(1).
f(x) = 7x4 - 16x2 + 9x - 10
For the given polynomial function, use synthetic division to find f(5).
f(x) = x5 - 8x2 - 11x - 15
For the following value of k, divide ƒ(x) by x - k using synthetic division. Write the answer in the form f(x) = (x - k)q(x) + r.
f(x) = 3x3 - 6x2 + 5x - 11; k = 3
f(x) = -7x3 + 2x - 8; k = -2
For the given polynomial function, perform synthetic division to test if k = 3/4 is a zero. In case it's not, just evaluate f(k).
ƒ(x) = 4x4 + 4x3 - 5x + 1; k = 3/4
For the given polynomial function, perform synthetic division to test if k = 3 - i is a zero. In case it's not, just evaluate f(k).
f(x) = x2 - 6x + 10; k = 3 - i
(x3 + 15x2 + 57x + 7) / (x + 7)
(4x4 + 12x3 + 6x2 + 17x - 3) / (x + 3)
x4 + 6x3 + 6x2 + 40x + 24 / (x + 6)
(x5 + 6x4 + 8x3 + 5x2 + 17x - 10) / (x + 4)
(-7x3 + 37x2 + 17x + 54) / (x - 6)
(x4 - 2x3 - 17x2 + 36x) / (x - 4)
(x3 - 1728) / (x - 12)
(x4 - 1296) / (x - 6)
By synthetic division, divide f(x) by x-k. Then, write f(x) in the form f(x) = (x - k)q(x) + r, where q(x) and r are the quotient, and remainder, respectively:
f(x) = 3x3 + 19x2 + 14x - 22; k = -5
f(x) = 7x4 + 23x3 + x2 - 12x + 10; k = -3
Evaluate f(k) using the remainder theorem:
f(x) = x2 + 25x + 136; k = -8
f(x) = 5x2 - 8x + 7; k = 6
f(x) = -2x3 + 11x2 + 16; k = 2
f(x) = -x3 + 5x2 - 8x + 12; k = -3
f(x) = x2 - 3x + 5; k = 4 + i
f(x) = x2 + 64; k = 8i
f(x) = 6x5 - 15x3 + 8x2 - 36; k = 2