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Class 10
Mathematics
Polynomials
check whether the first polynomial is a factor of...

Question:
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:
(i) t² – 3, 2t⁴ + 3t³ – 2t² – 9t – 12

(ii) x² + 3x + 1, 3x⁴ + 5x³ – 7x² + 2x + 2

(iii) x³ – 3x + 1, x⁵ – 4x³ + x² + 3x + 1

Answer:

Note: If on dividing the second polynomial by first we get zero remainder then we say that first Is factor of second polynomial.

(i) Given ,

First polynomial = t²-3

Second polynomial = 2t⁴+3t³-2t²-9t-12

As we can see the remainder is 0. Thereofre we can say that first polynomial is a factor of second polynomial.

(ii) Given,

First polynomial = x²+3x+1

Second polynomial = 3x⁴+ 5x^{3 –}7x²+ 2x + 2

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Question:
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:
(i) t² – 3, 2t⁴ + 3t³ – 2t² – 9t – 12

(ii) x² + 3x + 1, 3x⁴ + 5x³ – 7x² + 2x + 2

(iii) x³ – 3x + 1, x⁵ – 4x³ + x² + 3x + 1

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Question: Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial: (i) t2 – 3, 2t4 + 3t3 – 2t2 – 9t – 12 (ii) x2 + 3x + 1, 3x4 + 5x3 – 7x2 + 2x + 2 (iii) x3 – 3x + 1, x5 – 4x3 + x2 + 3x + 1

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Question:
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:
(i) t² – 3, 2t⁴ + 3t³ – 2t² – 9t – 12

(ii) x² + 3x + 1, 3x⁴ + 5x³ – 7x² + 2x + 2

(iii) x³ – 3x + 1, x⁵ – 4x³ + x² + 3x + 1