Question

What should be added to p(x) =x^(5)-4x³+x²+3x+1 so that g(x)=x³-3x+1 becomes its factor. Also, find new p(x).​

Answer 1

111

Question Bank Solutions 20334

Concept Notes & Videos 224

Time Tables 12

Syllabus

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Sum

Check whether g(x) is a factor of p(x) by dividing polynomial p(x) by polynomial g(x),

where p(x) = x5 − 4x3 + x2 + 3x +1, g(x) = x3 − 3x + 1

SOLUTION

We have been given two polynomials

P(x) = x5 - 4x3 + x2 + 3x + 1 and g(x) = x3 - 3x + 1

We will say g(x) is factor of p(x) if remainder is zero when we divide p(x) by g(x).

x3 -3x + 1)

x

x

x

x

x

x2-1x5-4x3+x2+3x+1

x

x

x

x5-x3+x2

- + -

-x3 + 3x +1

-x3 + 3x - 1

+ - +

2

Here, the remainder is 2 ≠ 0

g(x) is not a factor of p(x)

NOTES

x3 -3x + 1)

x

x

x

x

x

x2-1x5-4x3+x2+3x+1

x

x

x

x5-x3+x2

- + -

-x3 + 3x +1

-x3 + 3x - 1

+ - +