Question

divide by long division method and check your answer 9x^4 +15x^3 -2x^2 +7x -8 by 3x-2​

Answer 1

Answer:

here is your answer

hope this will help you.

Answer 2

The result of long division is:

Quotient : $\bf 3{x}^{ 3} + 7{x}^{2} + 4x + 5$

Remainder : 2

Given:

• $(9x^4 +15x^3 -2x^2 +7x -8) \div (3x-2)$

To find:

• Perform long division and check your result.

Solution:

Step 1:

Perform division.

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:3x - 2 \: ) \: 9x^4 +15x^3 -2x^2 +7x -8 (3{x}^{ 3} + 7{x}^{2} + 4x + 5 \\ \: \: \: \: \: \: 9 {x}^{4} \: \: \: - 6 {x}^{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\\ ( - ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ( + ) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ - - - - - - - - - \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ 21 {x}^{3} - 2{x}^{2} + 7x \\ 21 {x}^{3} \: \: \: - 14 {x}^{2} \: \: \: \: \: \: \\ ( - ) \: \: \: \: \: \: \: \: \: \: ( + ) \: \: \: \: \: \: \: \: \\ \: - - - - - - - - \\ 12 {x}^{2} + 7x - 8 \\ 12 {x}^{2} - 8x \: \: \: \: \: \\ ( - ) \: \: ( + ) \: \: \: \: \: \: \: \\ - - - - - - - \\ 15x - 8 \\ 15x - 10 \\ ( - ) \: \: ( + ) \\ - - - - - \\ 2 \\ - - - - -$

Thus,

Quotient of division is $3{x}^{ 3} + 7{x}^{2} + 4x + 5$

Remainder is 2.

Step 2:

Verification can be done using division algorithm.

Divisor = Dividend×Quotient + remainder

$(9x^4 +15x^3 -2x^2 +7x -8) = (3x - 2)(3 {x}^{3} + 7 {x}^{2} + 4x + 5) + 2$

If LHS = RHS, then division is correct.

Take RHS

$(3x - 2)(3 {x}^{3} + 7 {x}^{2} + 4x + 5) + 2$

or

$= 9 {x}^{4} + 21 {x}^{3} + 12x^2 + 15x - 6 {x}^{3} - 14 {x}^{2} - 8x - 10 + 2$

or

$= 9 {x}^{4} + 15 {x}^{3} - 2 {x}^{2} + 7x - 8$

LHS= RHS

Thus,

Division is correct.

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