Question

solve for x using the factor theorem and long division. a. 2x^3-3x^2-5x+6=0   b. 8x^3+4x^2-18x-9=0   c. 2x^3+10x^2+13x+5=0  ...

solve for x using the factor theorem and long division. a. 2x^3-3x^2-5x+6=0   b. 8x^3+4x^2-18x-9=0   c. 2x^3+10x^2+13x+5=0   d. -2x^3-12x^2+x+60=0

Homework Answers

Answer #1

From Rational Zeroes Theorem, the rational zeroes of the polynomial are of the form where p is factor of constant term and q is factor of the leadin coefficient. For the given equation, factors of constant 6 are 1,2,3,6 and factors of leading coefficinet 2 are 1, 2

Therefore, rational zeroes are of the form

Find Remainder Theorem, if f(a)=0 implies a=root of f(x)

Therefore, x=1 is root of f(x) implies (x-1) is a factor of f(x)

Divide f(x) by (x-1) by Long Division

Therefore, f(x) can be written as

Factorize the quadratic term

That is

Therefore,

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
solve the equations a). 4x-(-3x-3) =2x +1-1/2x+1 b) 8x-x^2=2 solvee by completing square c) x-2x^2=5 solve...
solve the equations a). 4x-(-3x-3) =2x +1-1/2x+1 b) 8x-x^2=2 solvee by completing square c) x-2x^2=5 solve by quadraticformula
1. Let f(x)=−x^2+13x+4 a.Find the derivative f '(x) b. Find f '(−3) 2. Let f(x)=2x^2−4x+7/5x^2+5x−9, evaluate...
1. Let f(x)=−x^2+13x+4 a.Find the derivative f '(x) b. Find f '(−3) 2. Let f(x)=2x^2−4x+7/5x^2+5x−9, evaluate f '(x) at x=3 rounded to 2 decimal places. f '(3)= 3. Let f(x)=(x^3+4x+2)(160−5x) find f ′(x). f '(x)= 4. Find the derivative of the function f(x)=√x−5/x^4 f '(x)= 5. Find the derivative of the function f(x)=2x−5/3x−3 f '(x)= 6. Find the derivative of the function g(x)=(x^4−5x^2+5x+4)(x^3−4x^2−1). You do not have to simplify your answer. g '(x)= 7. Let f(x)=(−x^2+x+3)^5 a. Find the derivative....
Verify the quotient rule for each of the following: 1. f(x)=4x^5-4x^4+13x^3-2x^2+7x+6/x^2-x+2 2.  f(x)=20x^8-28x^6+29x^4-35x^2+5/5x^4-7x^2+1
Verify the quotient rule for each of the following: 1. f(x)=4x^5-4x^4+13x^3-2x^2+7x+6/x^2-x+2 2.  f(x)=20x^8-28x^6+29x^4-35x^2+5/5x^4-7x^2+1
Solve using Gaussian Elimination with back subsitution: 3x(1) - 2x(2) + x(3) =3 2x(1) + 4x(2)...
Solve using Gaussian Elimination with back subsitution: 3x(1) - 2x(2) + x(3) =3 2x(1) + 4x(2) - 2x(3) = 2 4x(1) - 2x(2) - 3x(2) = -12
i) Simplify the following equations 3(2x – 5) – 2(5x - 7) + 9 = (4...
i) Simplify the following equations 3(2x – 5) – 2(5x - 7) + 9 = ii) Solve 3x – 2 divided by 2= 4x - 5 divided by 4 (5marks) c) Solve the following pairs of simultaneous equations 2x + y = 7 and x - 2y = -1
1. solve the following (a) Solve −x 2 +2x = 1, by factorization. (b) Solve 5x...
1. solve the following (a) Solve −x 2 +2x = 1, by factorization. (b) Solve 5x 2 −4x −2 = 0, by completing the square. (c) Solve 5x 2 + x −1 = 0, by quadratic formula
Solve the following a) 2 cos^2(4x) + 5 cos(4x) + 2 = 0. b) arctan(3x +...
Solve the following a) 2 cos^2(4x) + 5 cos(4x) + 2 = 0. b) arctan(3x + 3) = π/4 c) 2^1+sin^2(x) = 4^sin(x) d) ln(x + 3) = ln(x) + ln(3)
Part I If P(x) = 2x 4 - x 2 + 3x - 1, use synthetic...
Part I If P(x) = 2x 4 - x 2 + 3x - 1, use synthetic division to find P (2). A. 17 B. 21 C. 33 Solve x 4 - 11x 2 + 18 = 0. A. {±2, ±9} B. {±√2, ±3} C. {±2,± √3} Part II If P(x) = x 5 + 1 is divided by x + 1, find the remainder. A. -1 B. 0 C. 2 A soccer ball is kicked from the ground in an...
Are the following polynomials irreducible over Q? Prove why or why not. (a) 2x^13−25x^3+ 10x−30 (b)...
Are the following polynomials irreducible over Q? Prove why or why not. (a) 2x^13−25x^3+ 10x−30 (b) 5x^3+ 6x^2−9x+ 21 (c) x^4+ 7x^3+ 14 (d) x^5+ 18x + 6
Solve the following: a) 2cos2(4x)+5cos(4x)+2=0 b) arctan(3x+3)= π/4 c) 21+sin2 (x) = 4sin(x) d) ln(x +...
Solve the following: a) 2cos2(4x)+5cos(4x)+2=0 b) arctan(3x+3)= π/4 c) 21+sin2 (x) = 4sin(x) d) ln(x + 3) = ln(x) + ln(3).