find the remainder when x^3 + 3x^2 + 3x + 1 is divided by 5 + 2x
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Answered by
1
5+2x=o
2x=-5
x=-5/2
(-5/2)^3+3(-5/2)^2+3(-5/2)+1
(-125/8)+3(25/4)+(-15/2)
2x=-5
x=-5/2
(-5/2)^3+3(-5/2)^2+3(-5/2)+1
(-125/8)+3(25/4)+(-15/2)
Answered by
12
Givenx^3+3x^2+3x+1 is divided by 5+2x
Then remainder=?
Let f (x)=x^3+3x^2+3x+1
By remainder theorem
f (-5/2)=(-5/2)^3+3 (-5/2)^2+3 (-5/2)+1
=(-125/8)+3 (25/4)-15/2+1
=[-125+(75×2)-(15×4)+8]÷8
=[-125+150-60+8]÷8
=[25-52]÷8
=(-27)/8
=-27/8 is the remainder when f (x) is divided by 5+2x
Then remainder=?
Let f (x)=x^3+3x^2+3x+1
By remainder theorem
f (-5/2)=(-5/2)^3+3 (-5/2)^2+3 (-5/2)+1
=(-125/8)+3 (25/4)-15/2+1
=[-125+(75×2)-(15×4)+8]÷8
=[-125+150-60+8]÷8
=[25-52]÷8
=(-27)/8
=-27/8 is the remainder when f (x) is divided by 5+2x
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