Question
Verify the division algorithm i.e., Dividend = Divisor × Quotient + Remainder, in the following. Also write the quotient and remainder.
Dividend: $14 x^2+13 x-15$
Divisor: $7 x -4$
Dividend: $14 x^2+13 x-15$
Divisor: $7 x -4$
✓
Answer
Quotient $=2 x+3$
Remainder $=-3$
Divisor $=7 x -4$
Divisor $\times$ Quotient + Remainder $=(7 x-4)(2 x+3)-3$
$14 x^2+21 x-8 x-12-3$
$=14 x^2+13 x-15$
$=$ Dividend
Thus,
Divisor $\times$ 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
Find the number of sides of a regular polygon when each of its angles has a measures of:-
162°
162°
Solve:
$a^2+4 a b+3 b^2$
→$a^2+4 a b+3 b^2$
Subtract:
$\frac{\text{ab}}{7}-\frac{35}{3}\text{bc}+\frac{6}{5}\text{ac}$ from $\frac{3}{5}\text{bc}-\frac{4}{5}\text{ac}$
→$\frac{\text{ab}}{7}-\frac{35}{3}\text{bc}+\frac{6}{5}\text{ac}$ from $\frac{3}{5}\text{bc}-\frac{4}{5}\text{ac}$
A dishonest shopkeeper professes to sell pulses at his cost peice but uses a false weight of 950 for each kilogram. Find his gain percent.
A certain sum amounts to Rs. 5832 in 2 years at 8% compounded interest. Find the sum.
By what number should $(-15)^{-1}$ be ddivded so that the quotient may be equal to $(-15)^{-1}?$
→Solve the following equation and also check your result in case:
$\frac{\text{a}-8}{3}=\frac{\text{a}-3}{2}$
→$\frac{\text{a}-8}{3}=\frac{\text{a}-3}{2}$
Find the cube root of each of the following natural numbers:
134217728
134217728
From a rope 11m long, two pieces of lengths $2\frac{3}{5}\text{m}$ and $3\frac{3}{10}$ are cut off. What is the length of the remaining rope?
→7 teps of the same size fill a tank in 1 hour 36 minutes. How long will 8 taps of the same size take to fill the tank?