Question

X power 4 + 4 x cube minus 2 x square - 20 X - 15÷x square - 5

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.

Sᴏʟᴜᴛɪᴏɴ :-

x² - 5 )x⁴ + 4x³ - 2x² - 20x - 15( x² + 4x + 3

x⁴ - 5x²

4x³ +3x² - 20x

4x³ -20x

3x² - 15

3x² - 15

0

Hence,

→ Quotient :- x² + 4x + 3

→ Remainder :- 0.

_________________________

Answer 2

$\huge\tt quotient = x^2+4x+3 \\\tt\huge Remainder= 0$

Solution refer to the attachment