Download Algebra Trig

Algebra Trig
Quiz Review: 4.1 – 4.2
Name _____________________________
Date ________________________
1. (1  2i )  (7  5i )
2.
3. ( 1  4i )(3  2i )
4.
12  3
d4  2iid3  2ii
5. Give the degree, the leading coefficient and the y-intercept of the following polynomial.
a.
– 2 + 3x2 – 4x9 + 2x3
____________
____________
___________
6. Which of the following numbers are zeros (x-intercepts) of the polynomial x3 – 6x2 + 10x – 4 ?
i.
1
ii.
2
iii.
3
7a. Determine the zeros (x-intercepts) of the polynomial shown.
b. Write the factors of the polynomial shown.
8. Factor the following quadratics.
a.
x2 – 7x + 6
b.
2x2 – 9x – 5
9. Solve the following by completing the square:
a.
x2 + 6x – 5 = 0
b.
10. Solve the following by using the quadratic formula:
a.
x2 – 8x + 4 = 0
b.
-2x2 + 4x + 11=0
2x2 – 3x+2 = 0
11. Find the determinant for the following quadratic functions and describe the nature of the zeros.
a.
f(x) = x2 – 8x + 9
b.
f(x) = x2 + 10x + 36
c. Graph the quadratic with imaginary zeros.
12. Sketch the following polynomials. use the y-intercept, x-intercepts and end behavior.
a.
f(x) = (x + 1)2(x – 2)(x + 3)
b.
f(x) = x3 – x2 + 12x
13. Write a polynomial with the following zeros: x = -1, x = 2, x = ½
14. Write the standard form polynomial with the following zeros: x = 0, x = -3, x = 2i
9.
Write the standard form polynomial that has 3, 2 and -4 as roots.
10.
Write the standard form polynomial that has 5i, -5i and 1 as roots.
11. Solve the following by completing the square.
a.
x2 – 4x –12 = 0
b.
x2 – 5x – 114 = 0
c.
2x2 – 7x – 4 = 0
12. 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
13. Divide using synthetic division. Write your answer as an algebraic expression.
a.
x2 – 4x + 3 ÷ (x – 1)
b.
2x3 – 5x – 3 ÷ (x – 3)
c.
x3 – 3x2 + 5x + 2 ÷ (x + 2)
d.
x4 – 6x2 + 9 ÷ (x – 2)
14.
Find all the factors for the following.
a.
3x3 – 11x2 – 6x + 8
b.
x3 + x2 – 10x + 8
15. What is the value of k in the polynomial, if (x -1) is a factor? f(x) = 2x3 + 3x2 + kx + 3