R. 4 # 20Factor Each Polynomial by Grouping

Assignment # 2

R. 4 # 20Factor each polynomial by grouping

I will first reorder the terms, separate into two groups, factor the groups, then factor out the common term from the groups.

R. 4 # 26Factor each trinomial

The first term of the binomials must be y and 9y, or 3y and 3y. The second term of each must be negative since the middle term above is negative but the last term is positive. This gives the choices -1 and -8, -2 and -4, -4 and -2, and -8 and -1. Testing each of these possibilities gives the answer

R. 4 # 38

For this one, first note that all terms share a 5, so this leaves Now, note that the term in parentheses has the form of So the answer is

R. 4 #74

For this one, it will be easier to see if we call . The equation then becomes To factor this, the first term is 6x and x, or 2x and 3x. For the second term, one is positive and the other is negative since the last term in the trinomial is negative. Trying the possibilities gives

Now, plug 4z-3 back in for x giving

Finally, note that the last expression has a 2 in common in both 12 and 10, so it can be simplified to

R. 5 #4Find the domain of each rational expression

The denominator cannot be 0. It will be 0 if either of the two terms is 0, so we have to exclude those values of x.

means cannot be included. Likewise, cannot be included. Therefore, the domain is all real numbers except -3/2 and 5.

R. 5 #60Simplify each expression

Multiply the top and bottom by y, then factor and divide out a common factor of 2.

R. 6 # 46(b)

Match each expression from column I with its equivalent expressions from Column II.

The negative power means to invert the fraction. The 3 in the denominator means to take the cube root, and the 2 in the numerator means to take the square.

Eight Choices from column II :

R.6 #54Perform the indicated operation. Write each answer using only positive exponents. Assume all variables represent positive real numbers.

Same as before, except the 2 in the denominator means take the square root and the 3 in the numerator means take the cube.

R. 7 #76

=

The above are not equal if the numerator really has a cube root of a cube root. Since you have a cube root of a cube root, you will end up with 9th roots. I will use the fact that the cube root of m2 is the same as m2/3. When you multiply two terms with the same base, add the powers. Also, to take a power to a power, multiply the powers. Using these rules, follow the steps below:

If instead this shouldn’t be a cube root of a cube root, then you have the following: