Find the quotient and remainder. 15 x 3 - 4 x + 3

Given, 15 x 3 - 4 x + 3 . Write this in division format and do the long division process, until we get the remainder 0 or we get a remainder which cannot be further divided. 15 x 2 - 45 x + 135 x + 3 15 x 3 - 4 - 15 x 3 + 45 x 2 - 45 x 2 - 4 - - 45 x 2 - 135 x 135 x - 4 - 135 x + 405 - 409 So, quotient = 15 x 2 - 45 x + 135 and remainder = - 409 .

Find the quotient and remainder. 2 x 3 - 7 x + 6 x 2 - 4 x - 3

Given, 2 x 3 - 7 x + 6 x 2 - 4 x - 3 . Rearranging the numerator in decreasing order of degree, it becomes 2 x 3 + 6 x 2 - 7 x - 4 x - 3 . Write this in division format and do the long division process, until we get the remainder 0 or we get a remainder which cannot be further divided. 2 x 2 + 12 x + 29 x - 3 2 x 3 + 6 x 2 - 7 x - 4 - 2 x 3 - 6 x 2 12 x 2 - 7 x - 4 - 12 x 2 - 36 x 29 x - 4 - 29 x - 87 83 So, quotient = 2 x 2 + 12 x + 29 and remainder = 83 .

E M B I B E

Discovering Mathematics Book 8>Chapter 7 - Multiplication and Division>REVISION EXERCISE>Q 17

MEDIUM

8th CBSE

IMPORTANT

Earn 100

If $\frac{2 x^{3} + 6 x^{2} - 7 x - 87}{x - 3} = a x^{2} + b x + c$ , then find the value of $a + b + c$ .

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Important Questions on Multiplication and Division

MEDIUM

8th CBSE

IMPORTANT

Discovering Mathematics Book 8>Chapter 7 - Multiplication and Division>REVISION EXERCISE>Q 18

If

x - 5

notebooks cost

₹ (x^{2} - 13 x + 40)

, then cost of one book is

₹ (x - k)

. Find the value of

k

.

MEDIUM

8th CBSE

IMPORTANT

Discovering Mathematics Book 8>Chapter 7 - Multiplication and Division>REVISION EXERCISE>Q 19

Find the quotient and remainder.

$\frac{15 x^{3} - 4}{x + 3}$

MEDIUM

8th CBSE

IMPORTANT

Discovering Mathematics Book 8>Chapter 7 - Multiplication and Division>REVISION EXERCISE>Q 19

Find the quotient and remainder.

$\frac{2 x^{3} - 7 x + 6 x^{2} - 4}{x - 3}$

MEDIUM

8th CBSE

IMPORTANT

Discovering Mathematics Book 8>Chapter 7 - Multiplication and Division>REVISION EXERCISE>Q 20

If the expansion of $(2 x + 3 y)^{3} = a x^{3} + b y^{3} + c x^{2} y + d x y^{2}$ , then find the value of $a + b + c + d$ .

MEDIUM

8th CBSE

IMPORTANT

Discovering Mathematics Book 8>Chapter 7 - Multiplication and Division>REVISION EXERCISE>Q 20

If the expansion of ${(3 x - 1)}^{3} = a x^{3} + b x^{2} + 9 x + 1$ , then find the value of $a + b$ .

MEDIUM

8th CBSE

IMPORTANT

Discovering Mathematics Book 8>Chapter 7 - Multiplication and Division>REVISION EXERCISE>Q 20

If the expansion of ${(\frac{1}{2} x + y)}^{3} = \frac{x^{3}}{8} + a y^{3} + b x^{2} y + \frac{3}{2} x y^{2}$ , then find the value of $\frac{a}{4} + b$ .