What is the quotient of (3x^4-4x^2+8x-1)div(x-2)(3x4−4x2+8x−1)÷(x−2)?
1 Answer
Explanation:
One way of dividing is to use the divisor as a factor in the numerator.
"consider the numerator"consider the numerator
color(red)(3x^3)(x-2)color(magenta)(+6x^3)-4x^2+8x-13x3(x−2)+6x3−4x2+8x−1
=color(red)(3x^3)(x-2)color(red)(+6x^2)(x-2)color(magenta)(+12x^2)-4x^2+8x-1=3x3(x−2)+6x2(x−2)+12x2−4x2+8x−1
=color(red)(3x^3)(x-2)color(red)(+6x^2)(x-2)color(red)(+8x)(x-2)color(magenta)(+16x)+8x-1=3x3(x−2)+6x2(x−2)+8x(x−2)+16x+8x−1
=color(red)(3x^3)(x-2)color(red)(+6x^2)(x-2)color(red)(+8x)(x-2)color(red)(+24)(x-2)color(magenta)(+48)-1=3x3(x−2)+6x2(x−2)+8x(x−2)+24(x−2)+48−1
=color(red)(3x^3)(x-2)color(red)(+6x^2)(x-2)color(red)(+8x)(x-2)color(red)(+24)(x-2)+47=3x3(x−2)+6x2(x−2)+8x(x−2)+24(x−2)+47
rArr"quotient "=color(red)(3x^3+6x^2+8x+24)⇒quotient =3x3+6x2+8x+24
"remainder "=47remainder =47
