Q7 of 90 Page 2

Applying the Division Algorithm, check whether the first polynomial is a factor of the second polynomial:

t – 1, t3 + t2 – 2t + 1

Let us divide t3 + t2 – 2t + 1 by t – 1


The division process is



Here, the remainder is 1, therefore t – 1 is not a factor of t3 + t2 – 2t + 1


More from this chapter

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7

Applying the Division Algorithm, check whether the first polynomial is a factor of the second polynomial:

x2 – 3x + 4,2x4 – 11x3 + 29x2 – 30x + 29

 7

Applying the Division Algorithm, check whether the first polynomial is a factor of the second polynomial:

x2 – 4x + 3,x3 – x3 – 3x4 – x + 3

 7

Applying the Division Algorithm, check whether the first polynomial is a factor of the second polynomial:

t2 – 5t + 6,t2 + 11t – 6

 8

Give examples of polynomials p(x), g(x), q(x) and r(x) satisfying the Division Algorithm

p(x) = g(x).q(x) + r(x),deg r(x)<deg g(x)


And also satisfying


(i) deg p(x) = deg q(x) + 1


(ii)deg q(x) = 1


(iii) deg q(x) = deg r(x) + 1