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 d. -2x^3-12x^2+x+60=0

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,**

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 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

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 =
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 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 + 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 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) 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 + 3) = ln(x) + ln(3).

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