Ahhh! A Homework dump. Well, here are some hints.
#1. Note that 8x^3 divides each term
#2,3: you must have these identities in your text. If not, google sum of cubes
#4. 2(x^2+2x-8) ... now, which two factors of 8 differ by 2?
#5,6 Use the Remainder Theorem
#7 It's a polynomial of even degree, so f(x) → +∞ for both ±x
#8,9 y^2 = 2px has focus at (p,0) and directrix at x = -p
#10 f(x-h) shifts right by h f(x)+k shifts up by k
#11 the zeroes are the values of x that make each factor 0
The multiplicities are the powers of each root.
1. Find the GCF of the polynomial. 8x^6+32x^3
2. Polynomial identities tell us that the square of the sum of a and b, (a+b)^2, can be rewritten as ______.
3. The sum of cubes identity is very powerful, although a little hard to remember. It tells us that a^3+b^3=______.
4. Factor the expression completely. 2x^2+4x-16
5. Is (x-4) a factor of (x^3+x^2-16x-16)?
6. What is the remainder when 2x^3+3x^2-x+1 is divided by x+3?
7. Describe the end behavior of the function. f(x)=2x^4-4x^2
8. What are the co-ordinates of the focus of the parabola y^2=12x?
9. What is the equation of the directrix of the parabola x^2=20y?
10. List the transformations to the parent function in y=-(x+4)^2-3
11. Find and select each real zero and its multiplicity. f(x)=x^2(x-2)^3(x-7)
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