How do you simplify \frac { x ^ { 3} + 5x ^ { 2} - 5x + 8} { x - 3}x3+5x2−5x+8x−3?
2 Answers
Use long division to factorise the numerator
Explanation:
Using long division, we divide the numerator by the denominator to give ourselves a quadratic and a remainder.
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)(x^2)(x-3)color(magenta)(+3x^2)+5x^2-5x+8x2(x−3)+3x2+5x2−5x+8
=color(red)(x^2)(x-3)color(red)(+8x)(x-3)color(magenta)(+24x)-5x+8=x2(x−3)+8x(x−3)+24x−5x+8
=color(red)(x^2)(x-3)color(red)(+8x)(x-3)color(red)(+19)(x-3)color(magenta)(+57)+8=x2(x−3)+8x(x−3)+19(x−3)+57+8
=color(red)(x^2)(x-3)color(red)(+8x)(x-3)color(red)(+19)(x-3)+65=x2(x−3)+8x(x−3)+19(x−3)+65
"quotient "=color(red)(x^2+8x+19)," remainder "=65quotient =x2+8x+19, remainder =65
=x^2+8x+19+65/(x-3)=x2+8x+19+65x−3
