Use what you have learned about these special cases and the process of factoring completely to answer the ques

Question

Use three or more sentences to describe how you identify whether or not a polynomial is a difference of two squares. Then, factor the polynomial 4x2-36.

Use three or more sentences to describe how you identify whether or not a polynomial is a perfect square trinomial. Then, factor the polynomial x2-40x+400.

Consider the factoring process that has been illustrated below. Use three or more sentences to describe the process used to factor this polynomial.

3y3+4y2-12y-16
=y2(3y+4)-4(3y+4)
=(3y+4)(y2-4)
=(3y+4)(y+2)(y-2)

Use three or more sentences to describe the process you would follow to completely factor the polynomial 3x6+24.

Honors Only: Look at the equation y10n - 2y5n+1 and determine if it fits the conditions of one of the special cases listed above. Explain why the trinomial is or is not a special case and describe your process for factoring it completely. Be sure to use three or more sentences in your explanation. If the polynomial can be factored, then factor

Answer 1

y^10n - 2y^5n + 1
=
(y^5n - 1)^2
Special Case: Perfect Square Tirnomial
Why:
By law of exponents square root of y^10n = y^(10n/2), or y^5n.
Square root of 1 = 1.
Double the product of the square roots of first and second terms equals the middle term.

Answer 2

4x² is the square of 2x.
36 is the square of 6
The 2 terms are connected by a minus sign, which makes the expression a difference.
4x² - 36 = (2x+6)(2x-6)

x² is the square of x.
400 is the square of -20.
-40x is twice the product of x and -20, so
x² - 40x + 400 = (x-20)²

factor y², the common monomial factor, out of the 1st 2 terms, and -4 out of the last 2 terms.
factor the common binomial 3y+4 out of the 2 terms.
factor the difference of squares y² - 4 into (y+2)(y-2).

since y^(10n) = [y^(5n)]², and since the middle term is [y^(5n)] times -1 times 2, this is a trinomial square:
y^(10n) - 2y^(5n) + 1 = [y^(5n) - 1]²

you'll have to break that up into 3 sentences for your OCD teacher. I learned to think a little more fluidly and complexly than that.

Answer 3

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