The degree of the product = 4 = the degree of the multiplicand (= 2) + the degree of the multiplier (= 2) We can observe that in multiplication of Polynomials, the degree of the product equals the sum of the degrees of themultiplicand and multiplier.
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step 1: Arrange the Polynomials in descending powers of the variable x. step 2: Divide the first term of the dividend by the first term of the divisor i.e. 10x2 ÷ 2x = 5x. Write the result as the term of the quotient. step 3: Multiply the term of the quotient i.e. 5x with each term of the divisor i.e. 2x - 3 giving 5x(2x - 3) = 10x2 - 15x and put the result under dividendfor subtracting. The subtraction gives 14x. step 4: Bring down one of the remaining terms of the dividend. This gives the remainder as 14x + 21. step 5: Now, use the remainder 14x + 21 as new dividend and repeat the steps 2 to 4. step 6: Stop when the remainder is zero or the degree of the remainder is less than the degree of the divisor. ∴ quotient = 5x + 7; remainder = 42. step 7: verification Check whether dividend = divisor x quotient + remainder is satisfied or not. Here divisor x quotient + remainder = (2x - 3)(5x + 7) + 42 = 10x2 + 14x - 15x - 21 + 42 = 10x2 - x +21 = dividend (verified.)
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