Divide 5x³-13x²+21x-14 by (3-2x+x²) and verify the division algorithm
Answers
Given f(x) = 5x^3 - 13x^2 + 21x - 14.
Given g(x) = 3 - 2x + x^2.
We need to divide f(x) by g(x).
5x - 3
---------------------------------
= > x^2 - 2x + 3) 5x^3 - 13x^2 + 21x - 14
5x^3 - 10x^2 + 15x
---------------------------------
-3x^2 + 6x - 14
- 3x^2 + 6x - 9
-----------------------------------
-5.
Here,
Dividend = 5x^3 - 13x^2 + 21x - 14
Divisor = 3 - 2x + x^2
Quotient = 5x - 3
Remainder = -5
Division Algorithm:
Dividend = Divisor * Quotient + Remainder
= (3 - 2x + x^2) * (5x - 3) + (-5)
= 15x - 9 - 10x^2 + 6x + 5x^3 - 3x^2 - 5
= 5x^3 - 13x^2 + 21x - 14.
LHS = RHS
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Answer:
Step-by-step explanation:
Given f(x) = 5x^3 - 13x^2 + 21x - 14.
Given g(x) = 3 - 2x + x^2.
We need to divide f(x) by g(x).
5x - 3
---------------------------------
= > x^2 - 2x + 3) 5x^3 - 13x^2 + 21x - 14
5x^3 - 10x^2 + 15x
---------------------------------
-3x^2 + 6x - 14
- 3x^2 + 6x - 9
-----------------------------------
-5.
Here,
Dividend = 5x^3 - 13x^2 + 21x - 14
Divisor = 3 - 2x + x^2
Quotient = 5x - 3
Remainder = -5
Division Algorithm:
Dividend = Divisor * Quotient + Remainder
= (3 - 2x + x^2) * (5x - 3) + (-5)
= 15x - 9 - 10x^2 + 6x + 5x^3 - 3x^2 - 5
= 5x^3 - 13x^2 + 21x - 14.
LHS = RHS
Hope this helps!