Which of the following is a factor of the polynomial 6x4+2x3+15x+5?
3x + 1
x + 1
2x + 1
x + 2
Correct answer is A
Using the remainder theorem, if (x - a) is a factor of f(x), then f(a) = 0.
Check the options and get the answer.
Given that P=(−2134) and Q=(5−32−1), find PQ - QP
(0000)
(271216−15)
(−20−612−8)
(111230−11)
Correct answer is D
P=(−2134);Q=(5−32−1)
= PQ=(−10+26−115+8−9−4)
= (−8523−13)
QP=(−10−95−12−4−32−4)
= (−19−7−7−2)
PQ−QP=(−8523−13)−(−19−7−7−2)
= (111230−11)
Given that 2x(x+6)(x+3)=Px+6+Qx+3, find P and Q.
P = 4 and Q = 2
P = 2 and Q = 4
P = 4 and Q = -2
P = -2 and Q = 4
Correct answer is C
2x(x+6)(x+3)=Px+6+Qx+3
2x(x+6)(x+3)=P(x+3)+Q(x+6)(x+6)(x+3)
Comparing equations, we have
2x=Px+3P+Qx+6Q
⟹3P+6Q=0...(1);P+Q=2....(2)
From equation (1), 3P=−6Q⟹P=−2Q
\therefore -2Q + Q = -Q = 2
Q = -2
P = -2Q = -2(-2) = 4
P = 4, Q = -2
Given that f : x \to x^{2} and g : x \to x + 3, where x \in R, find f o g(2).
25
9
7
5
Correct answer is A
f : x \to x^{2} ; g : x \to x + 3
g(2) = 2 + 3 = 5
f o g(2) = f(5) = 5^{2} = 25
Find the 3rd term of (\frac{x}{2} - 1)^{8} in descending order of x.
\frac{x^{7}}{8}
\frac{7x^{6}}{16}
\frac{7x^{5}}{4}
\frac{35x^{4}}{8}
Correct answer is B
(\frac{x}{2} - 1)^{8} = ^{8}C_{8}(\frac{x}{2})^{8}(-1)^{0} + ^{8}C_{7}(\frac{x}{2})^{7}(-1)^{1} + ^{8}C_{6}(\frac{x}{2})^{6}(-1)^{2} + ...
\text{The third term in the expansion =} ^{8}C_{6}(\frac{x}{2})^{6}(-1)^{2}
= \frac{8!}{6!2!}(\frac{x^{6}}{64})(1)
= 28 \times \frac{x^{6}}{64} = \frac{7x^{6}}{16}