Question
Verify the division algorithm i.e., Dividend = Divisor × Quotient + Remainder, in the following. Also write the quotient and remainder.
Dividend: $15 z^3-20 z^2+13 z-12$
Divisor: $3 z-6$
Dividend: $15 z^3-20 z^2+13 z-12$
Divisor: $3 z-6$
✓
Answer
Quotient $=5\text{z}^2+\frac{10}{3}\text{z}+11$
Remainder $=54$
Divisor × Quotient + Remainder $=(3\text{z}-6)\Big(5\text{z}^2+\frac{10}{3}\text{z}+11\Big)+54$
$=15\text{z}^3+10\text{z}^2+33\text{z}-30\text{z}^2-20\text{z}-66+54$
$15\text{z}^3-20\text{z}^2+13\text{z}-12$
$=\text{Dividend}$
Thus,
Divisor × Quotient + Remainder = Dividend
Hence verified.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Hema bought two pairs of jeans for Rs. 1450 each. She sold one of them at a gain of 8% and the other at a loss of 4%. Find her gain or loss percent in the whole transaction.
Find the difference between the simple interest and the compound interest on Rs. 5000 for 2 years at 9% per annum.
Plot the points (5, 0), (5, 1), (5, 8). Do they lie on a line? What is your observation?
Locate the points A (1, 2), B (4, 2) and C (1, 4) on a graph sheet taking suitable axes. Write the coordinates of the fourth point D in order to complete the rectangle ABCD.
Solve the following equation and verify your answer:
$\frac{2\text{x}}{3\text{x}+1}=-3$
→$\frac{2\text{x}}{3\text{x}+1}=-3$
Simplify : $\frac{4 x^2-11 x+6}{16 x^2-9}$
→Divakaran deposited a sum of Rs. 6250 in the Allahabad Bank for 1 year, compounded half-yearly at 8% per annum. Find the compound interest he gets.
Find the area of a quadrilateral one of whose diagonals is 40 cm and the lengths of the perpendiculars drawn from the opposite vertices on the diagonal are 16 cm and 12 cm .
A can do a piece of work in 14 days while B can do it in 21 days.They began together and worked at it for 6 days. Then, A fell ill and B had to complete the remaining work alone. In how many days was the work completed?
Find the following product and verify the result for $x=-1, y=-2$ :
$(3 x-5 y)(x+y)$
→$(3 x-5 y)(x+y)$