Download Algebra Trig

Algebra Trig
Quiz Review: 4.1 – 4.2
1.
(11  2i )  (3  6i )
3.
(1  i )(3  2i )
Name _____________________________
Date ________________________
2.
4.
5  10
( 2  2i )(3 2  2i )
5. What is the degree and the leading coefficient of the following polynomials?
a.
3x2 – 4x9 + 2x3
____________
____________
b.
6x11 + 15x2 – x7 – 3x4
____________
____________
6. Give the number of zeros and the y-intercept for the following?
a.
f(x) = 3x2 + 2x – 5
____________
____________
c.
f(x) = 81x5 + 2x2 – 12x10
____________
____________
7. Are the following numbers zeros of the polynomial x3 – 6x2 + 10x - 8 ?
i.
4
ii.
-2
iii.
8. Factor the following quadratics.
a.
x2 – 4x – 5
b.
2x2 – 3x + 1
3
9. Sketch the following polynomials: find the y-intercept and x-intercepts
a.
f(x) = – x2 – x + 2
b.
f(x) = 3x2 – 14x – 5
10. Sketch the following polynomials: Find the y-intercept, x-intercepts and use the end behavior.
a.
f(x) = – x3 – x2 + 12x.
b.
f(x) = x4 – 5x2 – 4
11a. Write the standard form polynomial that has 3, 2 and -4 as roots.
b. Write the standard form polynomial that has 5i, -5i and 1 as roots.
c. Write a standard form polynomial with the following zeros: x = -1, x = 2, x = -3i, x = 3i
12. Solve the following by completing the square.
a.
x2 – 4x –12 = 0
c.
2x2 – 8x – 5 = 0
b.
x2 – 5x – 114 = 0
13. Find the discriminant of each equation and describe the nature of the roots. Solve the equation by
using the quadratic formula, then graph it.
a.
4x2 – 7x – 4 = 0
b.
3m2 – 10m + 5 = 0
c.
x2 – x + 6 = 0
d.
a2 + 4a + 4 = 0