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1. Which of the following represents the difference of (3x^3-9x^2+6x)-(8x^3+4x^2-3x)?
2. The graph of a linear equation contains the points (12, 18), (14, 22), and (16, 26). Graph the line below that contains all of the ordered pairs.
3. A polynomial has factors of x-3, x+6, and x+2. Which of the following represents the graph of the polynomial?
4. Which of the following expressions is equivalent to the expression, (x-3)/(x^3-6x^2-9x+54)?
5. Rewrite using fractional exponents: 5v(3&2^2 ) +v(7& 3^2 ).
1. A: After distributing the minus sign across the second trinomial, the expression can be rewritten as 3x^3-9x^2+6x-8x^3-4x^2+3x. Combining like terms gives -5x^3-13x^2+9x.
2. The first thing to do is to find the function that contains all of the points. Linear lines are given in the form y=mx+b. The function y=2x-6 will hit all of the points. Next find some points that would fall on the graph given. If, x=2 then y=-2, if x=4 then y=2, and if x=6 then y=6. Plot those points and then graph the line. The line should look like:
3. A: Given the factors of x-3, x+6, and x+2, it can be determined that the polynomial has zeros at x=3, x=-6, and x=-2. Choice A correctly shows these x-intercepts.
4. B: The denominator may be factored as (x^2-9)(x-6). The first binomial may be factored as (x-3)(x+3). Thus, the given expression may be rewritten as (x-3)/((x-3)(x+3)(x-6)), which simplifies to 1/((x+3)(x-6)).
5. B: Fractional exponential notation can be obtained with the following identity: v(y&b^x )=b^(x/y). 5?(2^2 ) +v(7& 3^2 )=5·2^?+3^(2/7). This cannot be simplified further by other rules governing exponentials because the bases are not the same.