Divide the following polynomials using long division.
Problem 1 :
(x² + x - 17) ÷ (x - 4)
Solution :
Step 1 :
In the first step, we are going to divide the first term of the dividend by the first term of the divisor.
After changing the signs, +x^{2} and -x^{2} will get canceled. By simplifying, we get 5x - 17.
Step 2 :
In the second step again we are going to divide the first term that is 5x by the first term of divisor that is x.
Quotient = x + 5
Remainder = 3
Problem 2 :
(3x² - 14x – 5) ÷ (x - 5)
Solution :
Quotient = 3x + 1
Remainder = 0
So, the given polynomial is divisible by (x - 5).
Problem 3 :
(x³ + x² + x + 2) ÷ (x² - 1)
Solution :
Quotient = x + 1
Remainder = 2x + 3
Problem 4 :
(7x³ + x² + x) ÷ (x² + 1)
Solution :
Quotient = 7x + 1
Remainder = - 6x - 1
Problem 5 :
(5x^{4} – 2x³ - 7x² - 39) ÷ (x² + 2x - 4)
Solution :
Quotient = 5x² - 12x + 37
Remainder = - 122x + 109
Problem 6 :
(4x^{4} + 5x - 4) ÷ (x² - 3x - 2)
Solution :
Quotient = 4x² + 12x + 44
Remainder = 161x + 84
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