Question
Verify division algorithm for the polynomials $f(x)=8+20 x+x^2-6 x^3$ and $g(x)=2+5 x-3 x^2$
✓
Answer
We can write $f(x)$ as $-6 x^3+x^2+20 x+8$ and $g(x)$ as $-3 x^2+5 x+2$
Quotient = 2x + 3
Remainder = x + 2 By using division rule, we have Divided = Quotient × Divisor + Remainder
$\therefore$$ -6x^3 + x^2 + 20x + 8 = (-3x^2 + 5x + 2)(2x + 3) + x + 2$
$\Rightarrow -6x^3 + x^2 + 20x + 8 = -6x^3 + 10x^2 + 4x - 9x^2 + 15x + 6 + x + 2$
$ \Rightarrow -6x^3 + x^2 + 20x + 8 = -6x^3 + x^2 + 20x + 8$
Quotient = 2x + 3
Remainder = x + 2 By using division rule, we have Divided = Quotient × Divisor + Remainder
$\therefore$$ -6x^3 + x^2 + 20x + 8 = (-3x^2 + 5x + 2)(2x + 3) + x + 2$
$\Rightarrow -6x^3 + x^2 + 20x + 8 = -6x^3 + 10x^2 + 4x - 9x^2 + 15x + 6 + x + 2$
$ \Rightarrow -6x^3 + x^2 + 20x + 8 = -6x^3 + x^2 + 20x + 8$
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