When completing the square for X2+12X, what should be added?
±36
±9
9
36
Which of the following represents the factorization of the polynomial X2+X−20?
(X−4)(X−5)
(X+4)(X−5)
(X+4)(X+5)
(X−4)(X+5)
If X3+5X2−4X−20=(X+a)(X+b)(X+c), what is the value of a+b+c?
2
5
7
If X2+aX+15=(X+3)(X+b), what is the value of a×b?
8
13
40
Factorize X3−27 completely:
(X−3)(X2+6X+9)
(X−3)(X2+3X+9)
(X+3)(X2−3X+9)
(X−3)(X2−3X+9)
Factorize the trinomial 2X2+5X+32 using grouping:
(2X+3)(X+1)
(X+1)(2X+3)
(X+3)(2X+1)
(2X+1)(X+3)
Which of the following trinomials represents a perfect square?
X2−6X−9
5X2+20X+45
4X2+20X+25
X2+9X+81
If X+y=10 and a−b=7, what is the value of X(a−b)−y(b−a)?
3
17
51
70
Factorize X4+4y4 completely:
(X2+2y2−2Xy)(X2+2y2+2Xy)
(X2+2y2)2
(X2−2y2)2
(X2+2y2)(X2−2y2)
If the polynomial kX2−12X+9 is a perfect square trinomial, what is the value of k?
±2
4
±4
When completing the square for X2+9, what should be added?
±3X
±6X
±9X
±12X
Factorize the polynomial 6a−8b completely:
6(a−2b)
14(a−b)
4(2a−4b)
2(3a−4b)
Factorize aX+bX+b+a by grouping:
(a+b)(X+1)
(a+X)(1+b)
(X+1)(a-b)
(X+a)(X+b)
If aX2−b=(3X−2)(3X+2), what is the value of a+ b?
-13
-5
Factorize X2−9 completely:
(X−3)(X+3)
(X−3)(X−3)
(X−9)(X+9)
(X−9)2
If X⋅Y+5X+7Y+35=(X+a)(Y+b), what is the value of a−b?
-12
-2
12
If X2−b2=(X−3)(X+3), what is the value of b?
±1
±3
±6
If the polynomial 4X2+kX+1 is a perfect square trinomial, what is the value of k?
±8
If (X−5) is a factor of the trinomial 2X2−7X−15, what is the other factor?
X+3
X−3
2X−3
2X+3
Find the solution set in R for the equation X3+X2−4X=4:
{−1,1,4}
{−2,−1,2}
{−2,1,2}
{−2,2}
Which of the following represents the factorization of the polynomial 16X2−24X3 by taking out the GCF?
8(2X2−3X3)
4X2(4−6X)
8X2(2−3X)
8X(2X−3X2)
Find the solution set in R for the equation X2+8X+15=0:
{5,10}
{6,9}
{−3,− 5}
{5,3}
If X−y=−2 and X2−y2= −16, what is the arithmetic mean of X and y?
16
Factorize X2−y2−6X−6y completely:
(X−y−6)(X+y)
(X+y)(X−y−6)
(X−y)(X+y+6)
(X−y)(X+y−6)
If (X−3)(X+5)=0, which of the following is true?
X=−3 or X=5
X=−3 or X=−5
X=3 or X=−5
X=3X or X=5
If X2−11X+28=(X−a)(X−b), what is the value of a+ba+b?
-16
-11
11
If (X2+2X+2) is a factor of (X4+4), what is the other factor?
X2+X+2
X2−2X+2
X2−2X−2
X2−X+2
If a+b=3, what is the value of a3+3a2b+3ab2+b3?
18
27
81
Factorize the polynomial X2y−Xy2 completely:
Xy(X−y)
X2y(1−y)
Xy(y−X)
Xy2(X−1)
What is the Greatest Common Factor (GCF) of the terms of the polynomial 12X2−8X?
2X
4X