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# 1-How is the distributive property used to multiply two polynomials?

2. Two students used the distributive property to expand (a+b)^2 . Which student is incorrect? Identify their error. student 1- (a+b)^2 =a^2+b^2

student 2- (a+b)^2 =(a+b)(a+b) =a^2+ab+ab+a^2 =a^2+ab+b^2

4. Explain how you factor:

by common factoring;

• trinomials of the form ;
• trinomials of the form ;
• binomials of the form  (differences of squares);
• trinomials of the form  (perfect square trinomials).

5. Your friend factors a binomial 2x^3-10x  to give 2x(x^2-5) . Why isn't the factor x^2-5 factored further?

6. How do we determine when a polynomial cannot be factored any further?

7. Your friend attempted to factor a polynomial and produced the following result. 3x^3+x^2+3x+1

=3x^2(x+1)+3(x+1) =3(x^2+1)(x+1)

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