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.
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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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