Math, asked by nityamsingh27, 4 months ago

The expression 4x3 -- bx² + x - c leaves remainders
0 and 30 when divided by x + 1 and 2x - 3
respectively. Calculate the values of b and c.
Hence, factorise the expression completely.​

Answers

Answered by palash2810pbajjm
3

Answer:

4x^3 +8x^2 +x -3

Step-by-step explanation:

4x^3-bx^2 +x -c leaves remainder 0 when divided by ( x + 1)

it means ( x + 1) is factor of 4x^3 -bx^2+x-c

so , x = -1 is zero of given expression .

4(-1)^3-b(-1)^2+(-1)-c = 0

-4 -b-1 -c =0

b+ c = -5 --------------------(1)

now ,

when divided by (2x -3) leaves remainder is 30

hence,

4x^3-bx^2+x -c -30 completely divisible by (2x -3 )

=> 4(3/2)^3-b(3/2)^2 +(3/2) -c-30=0

=> 27/2 -9/4 b +3/2 -c-30 =0

=> -9/4 b -c -15 =0

=> 9b + 4 c +60 =0 ----------------(2)

solve equations (1) and (2)

b = -8 and c = 3

hence,

4x^3 +8x^2 +x -3

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