How do you divide ( -3x^3+ 16x^2-24x+9 )/(x + 1 )−3x3+16x2−24x+9x+1?
2 Answers
Explanation:
If we descompose
Explanation:
"one way is to use the divisor as a factor in the numerator"one way is to use the divisor as a factor in the numerator
"consider the numerator"consider the numerator
color(red)(-3x^2)(x+1)color(magenta)(+3x^2)+16x^2-24x+9−3x2(x+1)+3x2+16x2−24x+9
=color(red)(-3x^2)(x+1)color(red)(+19x)(x+1)color(magenta)(-19x)-24x+9=−3x2(x+1)+19x(x+1)−19x−24x+9
=color(red)(-3x^2)(x+1)color(red)(+19x)(x+1)color(red)(-43)(x+1)color(magenta)(+43)+9=−3x2(x+1)+19x(x+1)−43(x+1)+43+9
=color(red)(-3x^2)(x+1)color(red)(+19x)(x+1)color(red)(-43)(x+1)+52=−3x2(x+1)+19x(x+1)−43(x+1)+52
"quotient "=color(red)(-3x^2+19x-43)," remainder "=52quotient =−3x2+19x−43, remainder =52
rArr(-3x^3+16x^2-24x+9)/(x+1)⇒−3x3+16x2−24x+9x+1
=-3x^2+19x-43+52/(x+1)=−3x2+19x−43+52x+1
