Question

Check whether x2 + 3x + 1 is a factor of 3x4 + 5x3 - 7x2 + 2x + 2

Answer 1

It is a factor. Use the division method to find it. I have included the answer below. Enjoy.

Answer 2

Answer:

$x^2+3x+1$ is a factor of $3x^4+5x^3-7x^2+2x+2$

Step-by-step explanation:

Divisor = $x^2+3x+1$

Dividend = $3x^4+5x^3-7x^2+2x+2$

Now , $Dividend = (Divisor \times Quotient)+Remainder$

$3x^4+5x^3-7x^2+2x+2= (x^2+3x+1 \times 3x^2)+(-4x^3-10x^2+2x+2)$

$3x^4+5x^3-7x^2+2x+2= (x^2+3x+1 \times 3x^2-4x)+(2x^2+6x+2)$

$3x^4+5x^3-7x^2+2x+2= (x^2+3x+1 \times 3x^2-4x+2)+(0)$

Thus remainder is 0

So, $x^2+3x+1$ is a factor of $3x^4+5x^3-7x^2+2x+2$

Hence $x^2+3x+1$ is a factor of $3x^4+5x^3-7x^2+2x+2$