CSS - PMS - CCE - PCS - Mathematics
Algebra
If a polynomial of degree 4 is multiplied by a nonzero polynomial of degree 3, what is the degree of the product?
A. 4
B. 3
C. 12
D. 7
Correct Answer: D
For nonzero polynomials, degrees add under multiplication: 4+3=7.
CSS - PMS - CCE - PCS - Mathematics
Algebra
Solve x^3 - 6x^2 + 11x - 6 = 0.
A. x=0,1,6
B. x=1,2,3
C. x=1,2,6
D. x=-1,-2,-3
Correct Answer: B
The cubic factors as (x-1)(x-2)(x-3), so its roots are 1, 2, and 3.
CSS - PMS - CCE - PCS - Mathematics
Algebra
What is the remainder when P(x)=x^2+3x+5 is divided by x+1?
A. 3
B. 1
C. 5
D. -3
Correct Answer: A
By the Remainder Theorem, the remainder is P(-1)=1-3+5=3.
CSS - PMS - CCE - PCS - Mathematics
Algebra
If x+2 is a factor of P(x), which statement must be true?
A. P(-2)=1
B. P(0)=2
C. P(-2)=0
D. P(2)=0
Correct Answer: C
By the Factor Theorem, x-a is a factor exactly when P(a)=0; x+2=x-(-2).
CSS - PMS - CCE - PCS - Mathematics
Algebra
Factor x^3 - 6x^2 + 11x - 6 completely.
A. (x+1)(x+2)(x+3)
B. (x-1)(x+2)(x-3)
C. (x-1)(x-2)(x-3)
D. (x-6)(x^2+1)
Correct Answer: C
The roots are 1, 2, and 3, so the complete factorization is (x-1)(x-2)(x-3).
CSS - PMS - CCE - PCS - Mathematics
Algebra
If the determinant of a 2×2 matrix is nonzero, the matrix is:
A. A zero matrix
B. Not square
C. Invertible
D. Singular
Correct Answer: C
Nonzero determinant means invertible.
CSS - PMS - CCE - PCS - Mathematics
Algebra
Which equation represents a direct variation?
A. y=x+5
B. y=5x
C. y=x^2+5
D. y=5/x
Correct Answer: B
Direct variation is y=kx.
CSS - PMS - CCE - PCS - Mathematics
Algebra
For nonzero x, simplify x^3·x^-5.
A. 1/x^8
B. 1/x^2
C. x^8
D. x^2
Correct Answer: B
Add exponents: -2.
CSS - PMS - CCE - PCS - Mathematics
Algebra
Solve x^2=49.
A. x=49
B. x=7
C. x=-7
D. x=7 or x=-7
Correct Answer: D
Both 7 and -7 square to 49.
CSS - PMS - CCE - PCS - Mathematics
Algebra
If f(x)=x^2 and g(x)=x+1, what is (g∘f)(3)?
A. 9
B. 7
C. 16
D. 10
Correct Answer: D
f(3)=9 then g(9)=10.
CSS - PMS - CCE - PCS - Mathematics
Algebra
If P(6)=0, which must be a factor of P(x)?
A. x - 6
B. x - 7
C. x + 6
D. x + 1
Correct Answer: A
Factor Theorem.
CSS - PMS - CCE - PCS - Mathematics
Algebra
If P(5)=0, which must be a factor of P(x)?
A. x + 1
B. x + 5
C. x - 5
D. x - 6
Correct Answer: C
Factor Theorem.
CSS - PMS - CCE - PCS - Mathematics
Algebra
If P(4)=0, which must be a factor of P(x)?
A. x + 4
B. x - 5
C. x + 1
D. x - 4
Correct Answer: D
Factor Theorem.
CSS - PMS - CCE - PCS - Mathematics
Algebra
If P(3)=0, which must be a factor of P(x)?
A. x + 1
B. x + 3
C. x - 4
D. x - 3
Correct Answer: D
Factor Theorem.
CSS - PMS - CCE - PCS - Mathematics
Algebra
If P(2)=0, which must be a factor of P(x)?
A. x - 3
B. x + 1
C. x + 2
D. x - 2
Correct Answer: D
Factor Theorem.
CSS - PMS - CCE - PCS - Mathematics
Algebra
What is the remainder when x^3-216 is divided by x-6?
A. 216
B. 0
C. 6
D. 1
Correct Answer: B
Remainder=P(6)=0.
CSS - PMS - CCE - PCS - Mathematics
Algebra
What is the remainder when x^3-125 is divided by x-5?
A. 0
B. 125
C. 5
D. 1
Correct Answer: A
Remainder=P(5)=0.
CSS - PMS - CCE - PCS - Mathematics
Algebra
What is the remainder when x^3-64 is divided by x-4?
A. 1
B. 4
C. 0
D. 64
Correct Answer: C
Remainder=P(4)=0.
CSS - PMS - CCE - PCS - Mathematics
Algebra
What is the remainder when x^3-27 is divided by x-3?
A. 0
B. 3
C. 27
D. 1
Correct Answer: A
Remainder=P(3)=0.
CSS - PMS - CCE - PCS - Mathematics
Algebra
What is the remainder when x^3-8 is divided by x-2?
A. 0
B. 1
C. 2
D. 8
Correct Answer: A
Remainder=P(2)=0.