1. Short Answer. State the degree of the following polynomial: 6xy4 – 9xy – 9y
5 is the degree of polynomial Correct
2. Essay. List the terms, coefficients, and degree of the following polynomial: 7x5 – 3x3
+ x + Term=
Coefficient 7,-3,1, 2/5
Degree is 5
It seems that there is a term missing from the original polynomial. I suspect that is
where the coefficient of 2/5 came from.
Assuming that the polynomial is actually 7x5 – 3x3 + x + 2/5, then the terms are:
7x5, -3x3, x, and 2/5
The coefficients are:
7, -3, 1, and 2/5
The degree of the polynomial is 5.
3. Essay; show all work. Add the following polynomials: (1/4x^2+1/2x+3/4)+(1/2x^21/4x-1/2)=3/4x^2-3/4x-5/4
!1 2 1
3$ !1 2 1
1$
# x + x + &+# x ' x ' &
"4
2
4% "2
4
2%
!1
1 $ !1
1 $ !3 1$
= # x2 + x2 & + # x ' x& + # ' &
"4
2 % "2
4 % "4 2%
=
3 2 1
1
x + x+
4
4
4
4. Write all of the following statement(s) that apply to the following polynomial: x2 – 9x
+3
It is a binomial.(this one)
It can be evaluated at x = .1/3 (this one) These three were my choices
It has a coefficient of 9.(this one)
It is quadratic.
The first one is not correct. A binomial has only two terms.
5. Short Answer. Add the following polynomials:
(-3x2 – 7x + 1) + (-6x3 + 3x2 – 6)
Answer: -6x^3-7x-5
Correct
6. Short Answer. Find the difference:
(6x3 + 8x2 + 9) – (-x2 – 8x – 8)=(HELP)
(6x
3
+ 8x 2 + 9 ) ! (!x 2 ! 8x ! 8)
(
)
= 6x 3 + 8x 2 ! (!x 2 ) + ( 9 ! (!8))
Subtracting a negative value is equivalent to adding the corresponding positive value:
= 6x 3 + (8x 2 + x 2 ) + ( 9 + 8)
= 6x 3 + 9x 2 +17
7. Essay; show all work. Find the product:
(1/4x^2-2/7)(-1/2x-1/2)=(HELP)
" 1 2 2 %" 1 2 1 %
$ x ! '$ ! x ! '
#4
7 &# 2
2&
Use the same FOIL method that you would use with regular binomials:
" 1 2 2 %" 1 2 1 % " 1 2 %" 1 2 % " 1 2 %" 1 % " 2 %" 1 2 % " 2 %" 1 %
$ x ! '$ ! x ! ' = $ x '$ ! x ' + $ x '$ ! ' + $ ! '$ ! x ' + $ ! '$ ! '
#4
7 &# 2
2 & # 4 &# 2 & # 4 &# 2 & # 7 &# 2 & # 7 &# 2 &
1
1
2
2
= ! x4 ! x2 + x2 +
8
8
14
14
1
1
1
1
! x4 ! x2 + x2 +
8
8
7
7
1
7
8
1
! x4 ! x2 + x2 +
8
56
56
7
1
1
1
! x4 + x2 +
8
56
7
8. Short answer. Find the product: (HELP)
-x (-7x3 + 2x2 + 8x – 4)
Multiply each term in parentheses by x, which increased the value of the exponent
by one. Change signs as needed:
!x (!7x 3 + 2x 2 + 8x ! 4)
= (!x ) (!7x 3 ) + (!x ) ( 2x 2 ) + (!x ) (8x ) + (!x ) (!4)
= 7x 4 ! 2x 3 ! 8x + 4
9. Essay; show all work. Bob’s Barber Shop estimates their gross revenue for the second
quarter to be given by the polynomial 2x3 + 5x2 – x – 1. The shop estimates their costs
for that quarter to be given by 4x2 – 9x – 8. For the second quarter, find and simplify a
polynomial that will represent their profit.
Profit=Revenue-Cost
2x^3+5x^2-x-1-(4x^2-9x-8)
=2x^3+x^2+8x+7
Correct
10. Essay; show all work. Consider that the age, x, of a unicorn in human equivalent
years can be given by the formula f(x) = - 0.011718x4 + 0.187326x3 – 1.3367x2 +
12.46x + 2.914. When a unicorn is 2.5 years old, what is its age in human equivalent
years? What about when it is 12 years old?
f(x)=y
(x,y)=(2.5,28.2),(12,40.7)
Plug 2.5 in for x
Plug 12years for y What did I d wrong besides short cut.
The solutions, to four decimal places are 28.1789 and 40.6641.
These are the same as your answers, when rounded to one decimal place. Unless the
problem was asking for a particular number of decimal places, your answers are correct.
11. Multiply: (7x-2)(2x-7)
Ans: (2.x-7).7.x-(2.x-7).2 =(HELP)
7.x.2.x-7.x.7-(2.x-7).2
( 7x ! 2) (2x ! 7)
Use the FOIL method, multiplying:
First terms: (7x)(2x) = 14x2
Outer terms: (7x)(-7) = -49x
Inner terms: (-2)(2x) = -4x
Last terms: (-2)(-7) = 14
Adding the four results together gives:
( 7x ! 2) (2x ! 7)
= 14x2 – 49x – 4x + 14
Combining the two middle terms, the simplified solution is:
14x2 – 53x + 14
12. Multiply. Try to recognize the type of product to be multiplying: (x-4x^3)^2
=(HELP)
Rewrite this as (x – 4x3)(x – 4x3).
Now use the same FOIL method to multiply the two binomials:
(x – 4x3)(x – 4x3) = (x)(x) + (x)(-4x3) + (-4x3)(x) + (-4x3)(4x3)
= x2 – 4x4 – 4x4 – 16x6
= x2 – 8x4 – 16x6
If the answer is required to have the terms in descending degree, then the solution
is:
-16x6 – 8x4 + x2
13. 4x^4y-8x^6y^2+12x^8y^6
______________________
4x^4y
Answer:1-2x^(6y^2-4y)+3x^(8y^6-4y)
Factor the exponents
1-2x^2y(3y-2)+3x^4y(2y^5-1) =HELP(Lost)
Rewrite the big ugly fraction as three separate fractions so that you can deal with them
one at a time:
4x 4 y ! 8x 6 y 2 +12x 8 y 6 4x 4 y 8x 6 y 2 12x 8 y 6
= 4 !
+
4x 4 y
4x y 4x 4 y
4x 4 y
Now simplify each term by canceling common factors from the numerator and
denominator.
Rewrite the expression as:
4x 4 y 4 * 2 * x 4 * x 2 * y * y 4 * 3* x 4 * x 4 * y 5 * y
!
+
4x 4 y
4x 4 y
4x 4 y
This form makes it easier to see what can be canceled out. Terms that can be canceled
have been crossed out below:
4 x 4 y 4 * 2 * x 4 * x 2 * y * y 4 * 3* x 4 * x 4 * y 5 * y
!
+
4 x4y
4 x4y
4 x4y
After removing the crossed-out terms, the resulting expression is:
1!
2 * x 2 * y 3* x 4 * y 5
+
1
1
1! 2x 2 y + 3x 4 y 5