Question

X2+5x+6 by (x+3) divide and verify the division algorithm of following polynomials

Answer 1

x+3)x2+5x+6 you will get x+2

VERIFICATION:

x2+5x+6=(x+3)(x+2)+0

x2+5x+6=x2+2x+3x+6

x2+5x+6=x2+5x+6

its equal so it is thus proves that x+2 is the quotient

Answer 2

The quotient of division is (x+2) and remainder is 0.

Verification by division algorithm has been done.

Given:

• ${x}^{2} + 5x + 6$
• $x + 3$

To find:

• Divide and verify the division algorithm of following polynomials.

Solution:

Concept to be used:

Division Algorithm:

Divisor polynomial= Dividend polynomial×quotient polynomial+ Remainder

or

$\bf f(x)=g(x)q(x)+r(x)$

Step 1:

Perform division.

$x + 3 \: ) \: {x}^{2} + 5x + 6 \: (x + 2 \\ {x}^{2} + 3x \: \: \: \: \: \: \: \\ ( - ) \: \: \: \: ( - ) \: \: \: \: \: \: \: \: \\ - - - - - - - \\ 2x + 6 \\ 2x + 6 \\ ( - )( - ) \\ - - - - - \\ 0 \\ - - - - - -$

Quotient of division is x+2 and remainder is 0.

Step 2:

Verify division by division algorithm.

Let

$f(x) = {x}^{2} + 5x + 6$

$g(x) = x + 3$

$q(x) = x + 2$

and

$r(x) = 0$

Put these values in division algorithm.

${x}^{2} + 5x + 6 = (x + 3 )(x + 2) + 0$

or

${x}^{2} + 5x + 6 = {x}^{2} + 2x + 3x + 6$

or

$\bf {x}^{2} + 5x + 6 = {x}^{2} + 5x + 6$

Thus,

This way, division is verified by division algorithm too.

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Learn more:

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