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Factor Theorem

The document contains a series of mathematical problems related to polynomials, including finding values of constants, determining factors, and applying the remainder theorem. Each problem requires specific calculations or factorizations to achieve the desired results. The problems involve various polynomial expressions and their properties.

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Sangeeta Kulkarni
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29 views1 page

Factor Theorem

The document contains a series of mathematical problems related to polynomials, including finding values of constants, determining factors, and applying the remainder theorem. Each problem requires specific calculations or factorizations to achieve the desired results. The problems involve various polynomial expressions and their properties.

Uploaded by

Sangeeta Kulkarni
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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1) Using remainder theorem, find the value of k if on dividing 2𝑥 3 + 3𝑥 2 − 𝑘𝑥 + 5

by ( x – 2), leaves a remainder 7.

2) What number must be subtracted from 2x2 – 5x so that the resulting


polynomial leaves the remainder 2, when divided by 2x + 1?

3) When divided by x – 3 the polynomials x2 – px2 + x + 6 and


2x3 – x2 – (p + 3) x – 6 leave the same remainder. Find the value of ‘p’

4) Factorise the expression x3 – 5x2 – x + 5 completely.

5) Show that (x – 3) is a factor of x3 – 7x2 + 15x – 9. Hence factorise it


completely

6) If (x – 2) is a factor of the expression 2x3 + ax2 + bx – 14 and when the


expression is divided by (x – 3), it leaves a remainder 52, find the values of a
and b
7) Given that x + 2 and x + 3 are factors of 2x3 + ax2 + 7x – b. Determine the
values of a and b.

8) Find the value of ‘K’ for which x = 3 is a solution of the quadratic equation,
(K + 2)x2 – Kx + 6 = 0. Also, find the other root of the equation.

9) Find the value of the constants a and b, if (x – 2) and (x + 3) are both factors
of the expression x3 + ax2 + bx – 12.

10) (x – 2) is a factor of the expression x3 + ax2 + bx + 6. When this expression is


divided by (x – 3), it leaves the remainder 3. Find the values of a and b.

11) What must be added from 𝑥 3 − 3𝑥 2 − 12𝑥 + 19so that the result will be exactly
divisible by 𝑥 2 + 𝑥 − 6

12) If x-2 is a factor of 𝑥 5 − 3𝑥 4 − 𝑎𝑥 3 + 3𝑎𝑥 2 + 2𝑎𝑥 + 4

13) Find the values of p and q , so that 𝑥 4 + 𝑝𝑥 3 − 2𝑥 2 − 3𝑥 + 𝑞 is divisible by


(𝑥 2 − 1)

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