Polynomials and roots
Synthetic Division
Remainder/Factor Theorem and more roots
Value of K and factors
100

What is the degree of this polynomial: q2 + 6 - q3 +3q4

What is 4

100

x4+x3+23x2+25x-50

What is x=-2    x= 1    x=+5i   x=-5i

100
When can we use the factor theorem to find the zero's?
What is when the quotient does not have a remainder.
100

If (x-3) is a factor of 2x3-5x2+kx-7. What is the value of k?

k=-2/3

200

What is the degree of this polynomial: 15y - 84y3 + 200 - 3y2

What is 3
200

Synthetic Division: (8x^3 -4x +9) * (2x+1)-1

What is 8x2-4x-2 with a remainder of 10/2x+1

200

What is remainder of x3+3x2+4x+12 if divided by (x-2)

What is the remainder of 40

200

Given (x-3)2(x+4)3(x-2) what are the roots and multiplicities?

What is x=3 multiplicity 2   x=-4 multiplicity 3     x=2 multiplicity 1

300

Put the Polynomial in Standard Form:

a- 12a + 5a+ 1

5a+ a- 12a + 1

300

Use synthetic division: 3x^2 -21x + 21 / x-6

What is 3x-3 with a remainder of 3/x-6

300

p(x): -2(x+1)2(x-3)3(x-2)

What are the factors and multiplicities?  What are the roots?


What are the roots x=-1 multiplicity of 2, x=3 multiplicity of 3 and x=2 multiplicity of 1.

300

If x3+2x2+kx+3 and (x-3) is a factor what is the value of k?

What is the value of k=-9

400

Find all the roots of x3+x2-5x+3 and state each roots multiplicity.

x=-3 multiplicity of 1    and    x=1 multiplicity of 2

400

Find all roots of the polynomial x+x2-17x+15


What is x=-5, x=1, x=3

400

Find remainder when x3-4x2-10x+13 is divided by (x-1)

What is remainder=0

400

What is the leading coefficient of this polynomial:  2a3 + 4a2 + a4

What is: 1

500

Polynomial 5x3-8x2+2x+4. What is the end behavior?

Left: As x goes to - infinity, y goes to - infinity

Right: As x goes to + infinity, y goes to + infinity

500

p(x)= 14-8x2-5x3+20x

What is the leading coefficient? Degree?

End behavior?

What is leading coefficient of -5, Degree of 3

 End behavior: Left: As x goes to - infinity, y goes to + infinity.

Right: As x goes to + infinity, y goes to - infinity

500

Find all roots of x3-3x2+16x-48

what is x=3   x=+4i    x=-4i

500

Write an equation of a polynomial that has roots of 2 (multiplicity of 3) and -4 (multiplicity of 2) and passes through the point (3,7).

What is y=1/7 (x-2)3 (x+4)2

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