r

PCSE 2018:SPECIMEN; k =28)

(7) What must be subtracted from 16x3 - axz +4x +7 so that the resulting expression has 2x+1 as

a factor pcse 20 11; k=11

(S) Fild the value of a and b if x - 1 and :x - 2 are factors of :x3 _ ax + b (Ans: a=J;b=6; SPECIMEN 2017)
9
( ) Using remainder theorem, find the value of kif on dividing 2x3 + 3x2- kx + s by x - 2, leaves a
remainder 7.
[Ans: k = 13; ICSE 2016]

(10) Find 'a' if the two polynomials ax3 + 3i- 9 and 2r + 4x + a, leaves the same remaitder when divided by
x+3
(Ans: a= 3; ICSE 2015]
(11) Using the Remainder Theorem factorise completely the foOowing polynomial:

:x3 +10x2 - 37:x +26 [Ans:(x - l)(x - 2)(:x +13); ICSE 2014]

(12) 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'? [Ans: a= 5; b = -11; ICSE 2013]

(13) Using the RemainderTheorem factorise completely the following polynomial:

3:x3 + 2x2 - 19:x +6 (Ans: (x - 2)(:x +3)(3x - l);ICSE 2012]

(14) Find the value of 'k' if (x-2) is a factor of :x3 +2x2 -kx +10. Hence determine whether (x + 5) is also

a factor. [Ans: k=13, yes, (x+S) is also factor; ICSE 2011]

(15) Use the remainder theorem to factorise the following expression: 2.x3 +x2 -13:x +6

[Ans:(x-2X2x-1 Xx +3); ICSE 2010]

(16) When divided by x _ 3 the polynomials :x3 - px2 +x +6 and 2.x3 - x2 - (p +3)x - 6 have the same

Remainder. Find t"le value of 'p' . [A.'1s: p =i; ICSE 201CJ

(17 ) Given that x + 2 and x + 3 are factors of 2.x3 + ax2 + 7x - b. Determine !he values cl 'a' and 'b'.

[Ans: a =9; b =6 ; ICSE 2009)

, • fa"'
{18)1f(x-211Sa vtOr of 2r-r-p
._1 • .2 x - 2 (i)· fnd the value of p (iQ. with this 'ialue of 'p' factorise the

above expression completely? [Ans: p=S; (x-2)(x+1 X2x+1 ); iCSE 2008]

16
 ------..,
(19) Show that (x 1).1 J
· - s a factor of x - 7x? + 14x - 8. Hence, completely factorise the above expression.
[Ans: (x - 1)(x - 4)(x - 2); ICSE 2007]
(20) Show that 2x+7.15 fa 3 •.2
a ctor of 2x + 5l{- -11 x - 14. Hence factorize the given expression completely.
[Ans: (x-2)(x+1)(2x+7); ICSE 2006]
21
< ) Given (x- 2) is a factor of the expression x3 +ax2 +bx+ 6 .when this expression is divided by (x- 3)

it leaves the remainder is 3 • Find the values of ·a· and 'b'. [Ans: a = -3; b= -1; ICSE 2005]

(22) Use the factor theorem to completely x3 + x2 - 4x - 4[Ans: (x+1 )(x+2)(x-2);1CSE 2004]
(23) Find the value of a, if (x-a) is a factor of x3. a2x + x + 2 [Ans: a = -2; ICSE 2003)
24
< ) Using factor theorem, show that (x-3) is a fact~r of x3-7x2+15x-9. Hence factorize given expression
Completely. [Ans: (x-1)(x-3)(x-3); ICSE 2002)
(25) Find the value of constants a and b if (x-2) and (x+3) are both factors of the expression
3
x + ax2 + bx-12 (Ans: a= 3, b = -4; ICSE 2001)
3
(26) Given (x+2) and (x-3) are factors of x +ax+b. Calculate the values of a and b, and find the remaining
factors. [Ans: a= -7,b= -6 ;x+1 ISC 1990)
(27) Use Remainder theorem to find the value of k for which (x+2) is a factor of (x+1 >7+(2x+k)3•
[Ans: k = 5; ISC 1958)
(28) Find the value of b if x-2 is a factor of 2x3-11 x2+bx-6 and in this case find the other factors:
[Ans: 17, (x-3)(2x-1); SAMPLE PAPER)
3
(29).Find the value of a and b ff the expression 2x - 15x2 +ax+ bis divisible by both (x-4) and (2x-1)
[Ans: (x-2) (x+3) (3x-1); SAMPLE PAPER)
3 2
(30) If 2x + x + ax + b has factors (x-2) and (x+1 ). Calculate the values of a and b.
[Ans: a= -7, b = -6; SAMPLE PAPER)
3
(31) If (x- 2) is a factor of 2x - x2- px- 2 find the value of 'P' and factorize the above expression
completely. [Ans: p=S: (x-2)(x+1)(2x+1); SAMPLE PAPER)

(32) Given that x+2 and x-3 are factors of x3+ax+b: calculate the values of 'a' and 'b' .
[Ans: a= -7 : b= -6 ; SAMPLE PAPER]

(.)~3) ,o oIynom.ial ,._ l{- + bx - 6 leaves remainder - 8 when divided by x -1 and x - 2 is a factor of it . Find
..,3 _ a·.2

the values of 'a' and 'b'. [Ans: a= 2; b = -5; SAMPLE PAPER)

LESSON NO • 08 MATRICES MATH

r~ 11