Question

$p(x) = 3 {x}^{4} + 5 {x}^{3} + 9 {x}^{2} + 12x - 15 \\ g(x) = 1 - {x}^{3} - 3x \\ divide \: p(x) \: with \: g(x)$

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Answer 1

LONG METHOD DIVISION : -

⋆ Arrange the indices of the polynomial in descending order. Replace the missing term(s) with 0.

⋆ Divide the first term of the dividend (the polynomial to be divided) by the first term of the divisor. This gives the first term of the quotient.

⋆ Multiply the divisor by the first term of the quotient.

⋆ Subtract the product from the dividend then bring down the next term. The difference and the next term will be the new dividend. Note: Remember the rule in subtraction "change the sign of the subtrahend then proceed to addition".

⋆ Repeat step 2 – 4 to find the second term of the quotient.

⋆ Continue the process until a remainder is obtained. This can be zero or is of lower index than the divisor.

⋆ If the divisor is a factor of the dividend, you will obtain a remainder equal to zero. If the divisor is not a factor of the dividend, you will obtain a remainder whose index is lower than the index of the divisor.

Solution :-

-x³ -3x+1 )3x⁴ + 5x³ + 9x² + 12x - 15( -3x -5

3x⁴ + 9x² - 3x

5x³ + 15x - 15

5x³ +15x - 5

(-10).

Therefore, if we divide p(x) with g(x) we get :-

→ Remainder = (-10) .

→ Quotient = (-3x - 5)

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