Examples of slow division include restoring, non-performing restoring, non-restoring, and SRT d We have, p(x) = x4 – 3x2 + 4x + 5, g (x) = x2 + 1 – x We stop here since degree of (8) < degree of (x2 – x + 1). 0 ≤ r < b. Step 4: Continue this process till the degree of remainder is less than the degree of divisor. E.g. To find HCF ( Highest Common Factor) 2.) If d(x) is the gcd of a(x), b(x) there are polynomials p(x), q(x) such that d= a(x)p(x) + b(x)q(x). So, 3x4 + 6x3 – 2x2 – 10x – 5 = (3x2 – 5) (x2 + 2x + 1) + 0 Quotient = x2 + 2x + 1 = (x + 1)2 Zeroes of (x + 1)2 are –1, –1. Division Algorithm is useful for two scenarios : I.) The polynomial division calculator allows you to take a simple or complex expression and find the quotient and remainder instantly. Then there … Example 1:    Divide 3x3 + 16x2 + 21x + 20  by  x + 4. Find a and b. Sol. i.e Dividend = Divisor x Quotient + Remainder The same division algorithm of number is also applicable for division algorithm of polynomials. p(x) = x3 – 3x2 + x + 2    q(x) = x – 2    and     r (x) = –2x + 4 By Division Algorithm, we know that p(x) = q(x) × g(x) + r(x) Therefore, x3 – 3x2 + x + 2 = (x – 2) × g(x) + (–2x + 4) ⇒ x3 – 3x2 + x + 2 + 2x – 4 = (x – 2) × g(x) \(\Rightarrow g(\text{x})=\frac{{{\text{x}}^{3}}-3{{\text{x}}^{2}}+3\text{x}-2}{\text{x}-2}\) On dividing  x3 – 3x2 + x + 2  by x – 2, we get g(x) Hence, g(x) = x2 – x + 1. Sol. I'm using sage and was trying to implement univariate polynomial division with the pseudocode given by Wikipedia. Division Algorithm in Polynomial is very useful. Sol. Step 2: To obtain the first term of quotient divide the highest degree term of the dividend by the highest degree term of the divisor. It’s another division between two polynomials. Dividend = Quotient × Divisor + Remainder. We now state a very important algorithm called the division algorithm for polynomials over a field. Division Algorithm For Polynomials ,Polynomials - Get topics notes, Online test, Video lectures, Doubts and Solutions for CBSE Class 10 on TopperLearning. Example of polynomials satisfying Division Algorithm can be as below : This satisfies the division Algorithm in polynomial as. Recall that the division algorithm for integers (Theorem 2.9) says that if a a and b b are integers with b > 0, b > 0, then there exist unique integers q q and r r such that a =bq+r, a = b q + r, where 0 ≤r

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