Question

x2 + 3x + 1, 3x4 + 5x3 - 7x2 + 2x + 2
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Answer 1

Answer:

Divisor = x^2+3x+1x2+3x+1

Dividend = 3x^4+5x^3-7x^2+2x+23x4+5x3−7x2+2x+2

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

3x^4+5x^3-7x^2+2x+2= (x^2+3x+1 \times 3x^2)+(-4x^3-10x^2+2x+2)3x4+5x3−7x2+2x+2=(x2+3x+1×3x2)+(−4x3−10x2+2x+2)

3x^4+5x^3-7x^2+2x+2= (x^2+3x+1 \times 3x^2-4x)+(2x^2+6x+2)3x4+5x3−7x2+2x+2=(x2+3x+1×3x2−4x)+(2x2+6x+2)

3x^4+5x^3-7x^2+2x+2= (x^2+3x+1 \times 3x^2-4x+2)+(0)3x4+5x3−7x2+2x+2=(x2+3x+1×3x2−4x+2)+(0)

Thus remainder is 0

So, x^2+3x+1x2+3x+1 is a factor of 3x^4+5x^3-7x^2+2x+23x4+5x3−7x2+2x+2

Hence x^2+3x+1x2+3x+1 is a factor of 3x^4+5x^3-7x^2+2x+23x4+5x3−7x2+2x+2

Step-by-step explanation:

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