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Factorization Paper 1

The document discusses factorization of polynomials using factor theorem and remainder theorem. Some key points: 1. It provides examples of finding the remainder when a polynomial is divided by a linear factor (x - a) and using that to determine unknown coefficients. 2. It shows how finding the same remainder for two polynomials divided by the same factor implies that factor is a common factor of both polynomials. 3. It gives examples of completely factorizing polynomials by finding linear and irreducible quadratic factors using the above concepts. 4. Determining unknown values that make a given expression a factor is also demonstrated. So in summary, the document covers factorization of polynomials using factor theorem and remainder theorem to find linear and irreducible

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126 views2 pages

Factorization Paper 1

The document discusses factorization of polynomials using factor theorem and remainder theorem. Some key points: 1. It provides examples of finding the remainder when a polynomial is divided by a linear factor (x - a) and using that to determine unknown coefficients. 2. It shows how finding the same remainder for two polynomials divided by the same factor implies that factor is a common factor of both polynomials. 3. It gives examples of completely factorizing polynomials by finding linear and irreducible quadratic factors using the above concepts. 4. Determining unknown values that make a given expression a factor is also demonstrated. So in summary, the document covers factorization of polynomials using factor theorem and remainder theorem to find linear and irreducible

Uploaded by

Anonymous FwL5h2mX
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Factorization

1. i) Find the reminder (without division) when 2x3 – 3x2 + 7x – 8 is divided by x – 1.


ii) Find the reminder (without division) on dividing 3x2 + 5x – 9 by (3x -2).
i) – 2 ii) – 11 (2000)
2. i) When divided by x – 3 the polynomials x –px + x + 6 and
3 2

2x2 = x2 – (p + 3) x – 6 leave the same reminder. Find the value of ‘p’. i) 1 (2010)
ii) Find ‘a’ if the two polynomials ax3 + 3x2 – 9 and 2x2 + 4x + a, leaves the same reminder
when divided by x + 3. ii) 3 (2015)
3. Show that (2x + 1) is a factor of 4x + 12x + 11x + 3. Hence factorise
3 2

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4x3 + 12x2 + 11x + 3. (2x + 1) (2x + 3) (x + 1)
4. Show that 2x + 7 is a factor of 2x + 5x – 11x – 14. Hence factorise the given expression
3 2

5.
completely, using the factor theorem.
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i) Use the Remainder Theorem to factorise the following expression :
(2x + 7) (x + 1) (x – 2) (2006)
z.
2x3 + x2 – 13x + 6. I) (x – 2) (x + 3) (2x – 1) (2010)
ii) Using the Reminder Theorem, factorise completely the following polynomial :
r
3x3 + 2x2 – 19x + 6 ii) (x – 2) (x + 3) (3x – 1) (2012)
pe

6. Using the Remainder and factor Theorem, factorise the following polynomial :
X3 + 10x2 – 37x + 26 (x – 1) (x – 2) (x + 13) (2014)
7. If (x - 2) is a factor of 2x – x – px – 2, then
3 2 i) 5
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i) Find the value of p. ii) (x – 2) (x + 1) (2x + 1)


ii) With this value of p, factorise the above expression completely. (2008)
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8. Find the value of ‘K’ for which x = 3 is a solution of the quadratic equation,
(K + 2)x2 – Kx + 6 = 0.
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Thus find the other root of the equation. – 4, - 1 (2015)


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. a = 3, b = - 4 (2001)
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. a = - 3, b = - 1. (2005)
11. If (x – 2) is a factor of the expression 2x + ax +bx – 14 and when the expression is divided
3 2

by (x – 3) , it leaves a remainder 52, find the values of a and b. a = 5, b = - 11. (2013)


12. Given f (x) = ax2 + bx +2 and g (x) = bx2 + ax + 1. If x – 2 is a factor of f (x) but leaves the
remainder – 15 when it divides g (x), find the values of a and b. With these values of a and
b, factorise the expression
f (x) + g (x) + 4x2 + 7x. a = 2, b = - 5; (x + 1)(x + 3)
13. If (x + 3) and (x – 4) are factors of x + ax – bx + 24, find the values of a and b.
3 2

With these values of a and b, factorise the given expression. a=-3,b=10; (x+3)(x-4)(x-2)
14. If 2x + ax – 11x + b leaves remainders 0 and 42 when divided by (x – 2) and (x – 3)
3 2

respectively, find the values of a and b. With these values of a and b, factorise the given
expression. a=3, b=-6; (x-2) (x+3)(2x+1)
15. If (2x + 1) is a factor of both the expressions 2x – 5x + p and 2x + 5x +q, find the values of p
2 2

and q. Hence find the other factors of both the polynomials. p=-3,q=2; x-3,x+2
16. When a polynomial f (x) is divided by (x – 1), the remainder is 5 and when it is divided by
(x – 2), the remainder is 7. Find the remainder when it is divided by (x – 1) (x – 2). 2x + 3

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