Question

if X3 - 2x2 + ax +b has factors (x+2)
and leaves a remainder 9 when divided by (x+1) , find the values of a and b​

Answer 1

Step-by-step explanation:

If x

2

+ax+b+6 has (x−2) as a factors and leaves a reminder 3 when divided by (x−3) Find a & b

Q2

If (x

3

+ax

2

+bx+6) has (x-2) as a factor and leaves a remainder 3 when divided by (x-3) find the values of a and b.

Q3

If (x

3

+ax

2

+bx+6) has (x−2) as a factor and leaves a remainder 3 when divided by (x−3), find the values of a and b.

Answer 2

solution,

P(x)=$x^3-2x^2+ax+b$

(i) factor{d(x')}= x+2

(ii) Remainder{R(a)}=9

(iii) factor{d(x)'}= x+1

a=?

b=?

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when factor of p(x) is (x+2),

comparing (x+2) with (x-a'), we get;

:. a'= -2

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then, using factor theorem;

P(a')=P(x)=$x^3-2x^2+ax+b$

or, 0= $(-2)^3-2(-2)^2-2a+b$

or, 0= -8-8-2a+b

:. b= 16+2a....(i)

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when factor of P(x) is d{x]', remainder is 9;

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comparing d{x}'= x+1 with x-a, we get;

a=-1

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Now, using remainder theorem,

P(x)=P(a)= R(a) =$x^3-2x^2+ax+b$        

or, 9=$(-1)^3-2*(-1)^2-a+b$

or, 9= -1-2-a+b

or, 9+3=b-a

or, 12= 16+2a-a

or, 12=16+a

or, a= 16-12

:. a= 4

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Again,

putting value of a to get b in equation(I),

:. b= 16+2*4

 = 16+8

= 24

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:. (a,b)=(4,24)

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Thus the new equation formed after implementing values;

:.P(x)= $x^3-2x^2+4x+24$