Question

check in which case the first
polynomial is a factor of the second
Polynomial by dividing the second
Polynomial by the first polynomial:
P(x) = 3x⁴+5x³-7x²+2x+2
g(x)=x²+3x+1​

Answer 1

Answer:

quotient= 3x²-4x+2

remainder= 0

so g(x) is a factor of f(x)

Step-by-step explanation:

P(x) = 3x⁴+5x³-7x²+2x+2

g(x)=x²+3x+1

x²+3x+1)3x⁴+5x³-7x²+2x+2( 3x²-4x+2

3x⁴+9x³+3x²

- - -

___________

-4x³-10x²+2x

- 4x³-12x²-4x

+ + +

____________

2x²+6x+2

2x²+6x+2

__________

0

___________

quotient= 3x²-4x+2

quotient= 3x²-4x+2remainder= 0

quotient= 3x²-4x+2remainder= 0so g(x) is a factor of f(x)

Answer 2

Answer:

3x²-4x+2 is a factor of the given polynomial as it leaves the remainder 0.