Question

Divide 3x³ + x² + 2x + 5 by 1 + 2x + x² and find the quotient and the remainder. Is 1 + 2x + x² a factor of 3x³ + x² + 2x + 5?

Answer 1

Dividend = 3x³ + x² + 2x + 5

Divisor = x² + 2x + 1

Now, dividend and divisor both are in the standard form.

Now, on dividing p(x) by g(x) we get the following division process

Quotient = 3x – 5

Remainder = 9x + 10

No, x² + 2x + 1 is not a factor of 3x³ + x² + 2x + 5 because remainder ≠ 0