Question

Find the quotient when p(x)=8x^4+22x^3+21x^2+9x divided by g(x)=2x^2+3x

Answer 1

Quotient= 4x² + 5x + 3

P(x) = 8x⁴ + 22x³ + 21x² + 9x is divided by g(x) = 2x² + 3x , we have to find quotient.

2x² + 3x)8x⁴ +22x³ + 21x² + 9x(4x²+ 5x + 3

8x⁴ + 12x³

...........................................

0 + 10x³ + 21x²

10x³ + 15x²

..................................................

0 + 6x² + 9x

6x² + 9x

...............................................................

0

hence, remainder = 0 and quotient = 4x² + 5x + 3

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Answer 2

The quotient when $8x^{4}+22x^{3}+21x^{2}+9x$ divided by $2x^{2}+3x$ is $4x^{2}+5x+3$

STEPS:

• Divide first term of dividend i.e, $8x^{4}$ by first term of divisor i.e, $2x^{2}$, we get $4x^{2}$ which is the first term of quotient.
• Multiply $4x^{2}$ with $2x^{2}+3x$, we get $8x^{4}+12x^{3}$. After subtracting this from dividend, we are left with $10x^{3}$.
• Repeat the steps until the dividend is no more divisible.

Please see the attachment for division.