Add the polynomials.
(7x^3y^2 + 14xy + 14) + (3xy - 2x^3y^2 - 7)
Question 1 options:
A) 5x^3y^2 + 17xy + 7
B) 22x^4y^3 + 7
C) 10x^3y^2 + 12xy + 7
D) 5x^6y^4 + 17x^2y^2 + 7
The correct answer is C) 10x^3y^2 + 12xy + 7
Categorize the expression as a monomial, a binomial, or a trinomial.
7z + 13z^2 - 15
The expression is a trinomial.
Subtract the polynomials.
(-4a^2b + 3ab^2 + ab) - (2a^2b - 3ab^2 - 5ab)
Question 3 options:
A) -6a^4b^2 - 4a^2b^2
B) 2a^2b + 6ab^2 - 4ab
C) -6a^2b - 4ab
D) -6a^2b + 6ab^2 + 6ab
The correct answer is C) -6a^2b - 4ab
What is the degree of the polynomial?
3x^5y^4 - 7x^6 + 3y^3
Question 4 options:
A) 9
B) 20
C) 6
D) 5
The degree of the polynomial is 6. The highest exponent in the polynomial is 6 (in the term -7x^6), which determines the degree. The answer is therefore C) 6.
Find a polynomial that represents the perimeter of the figure below.
(a) with superscript (2) + a 2(a) with superscript (2) + a - 5 2(a) with superscript (2) - 18
Question 5 options:
A)
7a^3 - 23
B)
(a^2 + a)(2a^2 - 18)(2a^2 + a - 5)
C)
5a^2 + 2a - 23
D)
5a^6 + 2a^2 - 23
The polynomial that represents the perimeter of the figure is B)
(a^2 + a)(2a^2 - 18)(2a^2 + a - 5)
Solve the equation.
3(y + 4) = 4(y - 4)
Question 6 options:
A)
-4
B)
4
C)
28
D)
-28
To solve the equation 3(y + 4) = 4(y - 4), we can start by simplifying both sides of the equation:
3(y + 4) = 4(y - 4)
3y + 12 = 4y - 16
Next, we can isolate the variable y by subtracting 3y from both sides of the equation:
12 = y - 16
To isolate the variable y, we can add 16 to both sides of the equation:
12 + 16 = y
Simplifying the equation gives us:
28 = y
Therefore, the solution to the equation is C) 28.
Find the slope of the line that passes through the points.
(8, 4) and (-8, -7)
To find the slope of the line that passes through the points (8, 4) and (-8, -7), we can use the formula for slope:
m = (y2 - y1) / (x2 - x1),
where (x1, y1) and (x2, y2) are the coordinates of the two points.
Plugging in the coordinates, we get:
m = (-7 - 4) / (-8 - 8)
m = -11 / -16
Simplifying the equation, we get:
m = 11/16
Therefore, the slope of the line is 11/16.
Perform the indicated operations.
(11t^4 - 10t^2 + 4t) + (10t^4 - 4t + 27) - (4t^4 + t^2 + 11)
Question 8 options:
A) 8t^4 + 16
B) 25t^4 - 11t^2 + 38
C) 17t^4 - 11t2 + 16
D) 5t^4 - 11t2 + 8t - 16
To perform the indicated operations, we can combine like terms:
(11t^4 - 10t^2 + 4t) + (10t^4 - 4t + 27) - (4t^4 + t^2 + 11)
= 11t^4 + 10t^4 - 4t^4 - 10t^2 - t^2 + 4t - 4t + 27 - 11
Combining like terms, we get:
= 17t^4 - 11t^2 + 8t + 16
Therefore, the correct answer is D) 17t^4 - 11t^2 + 8t + 16.
What is the leading coefficient of -3 + 2y - 5y^2 + 8y^4?
Question 9 options:
A) -3
B) 3
C) 8
D) 4
The leading coefficient is the coefficient of the highest degree term in the polynomial. In this case, the term with the highest degree is 8y^4. Therefore, the leading coefficient is 8.
The correct answer is C) 8.
Solve the inequality.
4x > 68
To solve the inequality 4x > 68, we can divide both sides of the inequality by 4:
4x/4 > 68/4
x > 17
Therefore, the solution to the inequality is x > 17.
Write the polynomial in descending order.
20x + 6x^3 + 12x^2 + 5x^5 + 1
Question 11 options:
A) 20x + 12x^2 + 6x^3 + 5x^5 + 1
B) 1 + 20x + 12x^2 + 6x^3 + 5x^5
C) It is already in descending order.
D) 5x^5 + 6x^3 + 12x^2 + 20x + 1
To write the polynomial in descending order, we arrange the terms in decreasing order of their exponents.
The polynomial 20x + 6x^3 + 12x^2 + 5x^5 + 1 can be rearranged as:
5x^5 + 6x^3 + 12x^2 + 20x + 1
Therefore, the correct answer is D) 5x^5 + 6x^3 + 12x^2 + 20x + 1.
What is the degree of the polynomial?
15x^4 - 18x^2 + 10x
Question 12 options:
A)
15
B)
4
C)
3
D)
10
The degree of a polynomial is determined by the highest exponent of the variable. In this case, the highest exponent is 4, so the degree of the polynomial 15x^4 - 18x^2 + 10x is 4.
Therefore, the correct answer is B) 4.