Question

5√5x^2+20x+3√5
need an answer by polynomial long division a soon as possible!!

Answer 1

Answer: x3−12x2+38x−17x−7=x2−5x+3+4x−7

Step-by-step explanation:

Step 1: Divide the leading term of the dividend by the leading term of the divisor: x3x=x2.

Write down the calculated result in the upper part of the table.

Multiply it by the divisor: x2(x−7)=x3−7x2.

Subtract the dividend from the obtained result: (x3−12x2+38x−17)−(x3−7x2)=−5x2+38x−17.

x−7x2x3−12x2+38x−17−x3−7x2−5x2+38x−17x3x=x2x2(x−7)=x3−7x2

Step 2: Divide the leading term of the obtained remainder by the leading term of the divisor: −5x2x=−5x.

Write down the calculated result in the upper part of the table.

Multiply it by the divisor: −5x(x−7)=−5x2+35x.

Subtract the remainder from the obtained result: (−5x2+38x−17)−(−5x2+35x)=3x−17.

x−7x2−5xx3−12x2+38x−17−x3−7x2−5x2−−5x2+38x+35x3x−17−17−5x2x=−5x−5x(x−7)=−5x2+35x

Step 3: Divide the leading term of the obtained remainder by the leading term of the divisor: 3xx=3.

Write down the calculated result in the upper part of the table.

Multiply it by the divisor: 3(x−7)=3x−21.

Subtract the remainder from the obtained result: (3x−17)−(3x−21)=4.

x−7x2−5x+3x3−12x2+38x−17−x3−7x2−5x2−−5x2+38x+35x3x−3x−17−17−2143xx=33(x−7)=3x−21

Since the degree of the remainder is less than the degree of the divisor, then we are done.

The resulting table is shown once more:

x−7x2−5x+3x3−12x2+38x−17−x3−7x2−5x2−−5x2+38x+35x3x−3x−17−17−214Hintsx3x=x2x2(x−7)=x3−7x2−5x2x=−5x−5x(x−7)=−5x2+35x3xx=33(x−7)=3x−21

Therefore, x3−12x2+38x−17x−7=x2−5x+3+4x−7

Answer: x3−12x2+38x−17x−7=x2−5x+3+4x−7