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[4 marks sum]

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34 questions · timed · auto-graded

Question 14 Marks
What must be subtracted from $8 x^4+14 x^3-2 x^2+7 x-8$ so that the resulting polynomial is exactly divisible by $\left(4 x^2+3 x-2\right)$ ?
Answer
$14 x-10$
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Question 24 Marks
Find the quotient and remainder : $\left(3 t^5+7 t^4-11 t^3+8 t^2-32 t+5\right)$ is divided by $\left(2+3 t+t^2\right)$
Answer
$Q =3 t^3-2 t^2-11 t+45, R =-145 t-85$
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Question 34 Marks
Find the quotient and remainder : $\left(2 x^4-x^3+10 x^2+8 x-5\right)$ is divided by $\left(x^2-x+6\right)$
Answer
$Q =2 x^2+x-1, R =x+1$
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Question 94 Marks
Divide : $\left(6 x^5-28 x^3+3 x^2+30 x-9\right)$ by $\left(2 x^2-6\right)$
Answer
$3 x^3-5 x+\frac{3}{2}$
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Question 224 Marks
Divide : $\frac{1}{2} p^2 q^3-\frac{5}{8} p^3 q^2+\frac{1}{4} p^3 q^3$ by $-\frac{1}{4} p^2 q^2$
Answer
$-2 q+\frac{5}{2} p-p q$
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Question 334 Marks
If a sum of $₹\left(16 x^3-46 x^2+39 x-9\right)$ is to be divided equally among $(8 x-3)$ persons, find the amount received by each person.
Answer
$₹\left(2 x^2-5 x+3\right)$
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Question 344 Marks
The length and breadth of a rectangle are $(a+5 b)$ units and $(7 a-b)$ units respectively. The perimeter of this rectangle is equal to the perimeter of a square. Find how much is the area of the rectangle less than that of the square?
Answer
$9 a^2-18 a b+9 b^2$
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[4 marks sum] - MATHS STD 8 Questions - Vidyadip