Download Algebra Trig

Algebra Trig
4.1-4.3 Review
5  10
1.
(11  2i )  (3  6i )
2.
3.
(1  i )(3  2i )
4.
5.
What is the degree and the leading coefficient of the following polynomials?
6.
( 2  3i )( 2  3i )
a.
3x2 – 4x9 + 2x3
____________
____________
b.
6x11 + 15x2 – x7 – 3x4
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c.
9x2 + 222x5 – x5
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How many zeros do the polynomials have?
a.
f(x) = 3x2 + 2x – 5
____________
b.
f(x) = 5x – 10x4 + 7
____________
c.
f(x) = 81x5 + 2x2 – 12x10
____________
7.
a.
Are the following numbers zeros of the polynomial x3 – 6x2 + 9x – 4?
i) 4
ii) -2
iii) 3
b.
State the number of zeros the polynomial will have and find them. Sketch the polynomial.
8. Write the standard form polynomial that has 3, 2 and -4 as roots.
9. Write the standard form polynomial that has 5i, -5i and ½ as roots.
10. Write the standard form polynomial that has 1 + i, 1 – i and 0 as roots.
11. Solve the following by completing the square.
a.
x2 – 4x –12 = 0
c.
x2 + 6x + 40 = 0
b.
x2 – 5x – 114 = 0
12. Find the discriminant of each equation and determine the type of zeros. Solve the equation by using
the quadratic formula. Sketch a graph.
a.
4x2 – 6x – 4 = 0
b.
m2 – 4m + 5 = 0
c.
6 + x – x2 = 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 using the given information:
a.
3x3 – 11x2 – 6x + 8; 2 3 is a zero
b.
x3 + x2 – 10x + 8;
(x – 2) is a factor.
15. What is the value of k in the polynomial, if (x -1) is a factor? f(x) = 2x3 + 3x2 + kx + 3