ST
1
SEMESTER ALGEBRA 2 REVIEW
Chapters 7 – 8
FIND THE QUOTIENT AND REMAINDER
When 3𝑥 5 − 2𝑥 4 − 15𝑥 3 + 2𝑥 2 + 5𝑥 + 8 is divided by 𝑥 + 2
Ans: 3𝑥 4 − 8𝑥 3 + 𝑥 2 + 5 with a remainder of -2
USE DESCARTE’S RULES OF SIGNS TO DETERMINE
THE POSSIBLE NUMBER OF POSITIVE ROOTS OF
𝑥 4 − 𝑥 3 + 𝑥 2 − 3𝑥 + 1 = 0
Ans: 4, 2, or 0
IF 2, -3, AND 1 − 𝑖 ARE ROOTS OF
𝑥 4 − 𝑥 3 − 6𝑥 2 + 14𝑥 − 12 = 0, what is the remaining
root?
Ans: 1 + 𝑖
IS X+3 A FACTOR OF
3
2
2𝑥 + 11𝑥 + 16𝑥 + 6?
Why or why not?
Ans: No, the remainder is not equal to zero.
IF -2 IS A ROOT OF
𝑥 3 + 3𝑥 2 − 4𝑥 − 12 = 0, what are the remaining roots?
Ans: 2 and -3
GIVEN: 𝑦 − 5 = 3(𝑥 + 1)
2
state (a) the vertex of the parabola, (b) the axis of symmetry, (c)
identify the direction the parabola opens, and (d) determine if the
vertex is a maximum or minimum point.
Ans: (-1,5), x = -1, opens up, minimum point
FIND THE VERTEX OF THE PARABOLA GIVEN
𝑦 = 2𝑥 2 − 12𝑥 + 24
Ans: (3,6) use 𝑥 =
the vertex
𝑏
−
2𝑎
to find the x-coordinate of
USE THE DISCRIMINANT TO DETERMINE THE
NATURE OF THE ROOTS OF
2𝑥 2 − 𝑥 + 3 = 0
(hint: 𝐷 = 𝑏 2 − 4𝑎𝑐)
Ans: D=-23; complex conjugate roots (or imaginary roots)
USE THE DISCRIMINANT TO DETERMINE THE
NATURE OF THE ROOTS OF
𝑥2 + 𝑥 = 6
Ans: D=25; Unequal, real rational roots
SOLVE BY WRITING AN EQUATION FIRST.
A rectangle is twice as long as it is wide. If the length and wide
are both increased by 5 cm, the resulting rectangle has an area of
50 sq cm. Find the dimensions of the original rectangle. Give your
answers to the nearest hundredth.
Hint: (2x+5)(x+5)=50
Ans: 1.40 cm by 2.81 cm