Question

Have you done any factoring with variables? Which property (Commutative, Distributive, or Associative) do you think is most involved in factoring? Do you think a polynomial can be a factor of another polynomial? Answer in full sentences.

Answer 1

Idk how im supposed to answer this or whatevs bu
yes i have done factoring with variables.
distrubutive is the most involved in factoring method as i can tell.
i dont think ive studied this before or i mightve forgoten but im sure a polynomial can be factored into another one.
and yea. hope this helped in sum way

Answer 2

⇒x²y³=x*x*y*y*y=x*y*x*y*y=y*x*y*x*y--Writing factors in another way

⇒xy²z²=x*y*y*z*z=y*x*z*y*z=z*x*y*x*y*z---Writing factors in another way.

⇒xy+xy²=xy(1+y)

⇒y²z²-yzx=yz(yz-x)

Here ,we have used law of indices first, then used Commutativity , Associativity and Distributivity to factor Polynomial.

$1.\rightarrow x^{a+b}=x^a \times x^b\\\\2.\rightarrow x \times y=y \times x----\text{Commutative Property}\\\\3.\rightarrow x \times (y \times z)= (x \times y) \times z=(x \times z) \times y---\text{Associaitive Property}$

⇒Distributive Property of Multiplication with respect to addition and Subtraction

  →a×(b+c)=a×b+a×c

 → a×(b-c)=a×b-a×c

⇒Yes, A polynomial can be factor of another polynomial.

For Example:

⇒ x²-a², has two factors equal to , (x+a) and (x-a), where , x²-a², is a quadratic polynomial and two of it's factors are ,(x+a) and (x-a) which is also a polynomial of degree 1.