Algebra Polynomials Quiz

Questions and Answers

What is the GCF of the terms of the polynomial 64x²y³ - 32x³y² + 16x⁴y³?

8x²y²

16x²y² (correct)

16x²y³

8x²y³

Which of the following is NOT a perfect square trinomial?

9x² + 3xy + y³ (correct)

16x² + 24x + 9

49x² - 42xy + 9y²

4x²y² + 12xy + 9

What should be multiplied to (3x - 2) to get 9x² - 4?

3x - 2 (correct)

4x² + 12x + 9

3x + 2

4x² - 12x + 9

If one of the factors is 3x² + 4x - 15 and x + 3, what is the other factor?

3x - 5 Signup and view all the answers

If the area of the blackboard is (x² + 9x + 20) cm², what are the dimensions of the blackboard?

(x + 4) cm and (x + 5) cm Signup and view all the answers

What are the dimensions of Jana's dining table if the area is 40 square feet and the width is 3 feet less than the length?

8 ft x 5 ft Signup and view all the answers

Which expression is a rational algebraic expression?

2x / (x - 1) Signup and view all the answers

Is the expression 3x / (x + 5) a correct example of a rational algebraic expression?

Yes, because it is a ratio of polynomials Signup and view all the answers

What is the factored form of 4x² - 12x + 9?

(2x - 3)(2x - 3) Signup and view all the answers

Did Shiela's partner correctly add the rational expressions p² + 14p + 49 / p² + 8p + 7?

No, he did not copy the denominator correctly Signup and view all the answers

What is the equation of the line that passes through $(2,-1)$ with a slope of $rac{2}{3}$?

$2x - 3y = 7$ Signup and view all the answers

What is the equation of the line parallel to $y=4x-3$ with a y-intercept of 5?

$y = 4x + 5$ Signup and view all the answers

Based on the given data, what is the equation that describes the height $h$ of the candle as a function of time $t$?

$h = 10 - 2t$ Signup and view all the answers

Which mathematical model best represents the increase in out-of-school youth from 2019 to 2023?

$y = 8x + 52$ Signup and view all the answers

What can be concluded about the lines in the graph of an inconsistent system?

The system has no solution. Signup and view all the answers

What is the result of the division problem $rac{p^2 +14p+49}{p^2-49} imes rac{p-7}{p^2+8p+7}$?

$rac{p-1}{p-7}$ Signup and view all the answers

After 4 hours, what part of the job can Alex complete if he can complete it alone in x hours?

$rac{4}{x}$ Signup and view all the answers

If Bert can complete the project in 6 hours and Cris in 3 hours, how long will it take them to finish the project together?

2 hours Signup and view all the answers

How long will it take Alex, Bert, and Cris to finish the project if they work together, given their individual times of 6, 3, and 5 hours respectively?

2 hours Signup and view all the answers

In which quadrant is a point located if its abscissa is positive and its ordinate is negative?

Q IV Signup and view all the answers

Which coordinates represent the position of the Earth in December based on the given graph?

(4, 3) Signup and view all the answers

Which of the following represents a linear equation in two variables?

x + 2y = 4 Signup and view all the answers

What was the cost of 1/2 weight of fish Tilapia, based on the given price data?

$75 Signup and view all the answers

What does it indicate when two lines have the same slope and different y-intercepts?

The lines are parallel. Signup and view all the answers

If two lines have the same slope and y-intercepts, what can be concluded about their graph?

The lines are coinciding. Signup and view all the answers

Which solution corresponds to the system of equations: x + 2y = 5 and x - 2y = 9?

(7, -1) Signup and view all the answers

What total revenue does the canteen generate from selling chicken sandwiches at ₱2.00 each and egg sandwiches at ₱1.00 each, given they sold 420 sandwiches for ₱615.00?

₱615.00 Signup and view all the answers

How can the canteen achieve a revenue increase to Php 720 without raising the price per sandwich?

By selling 300 chicken sandwiches and 120 egg sandwiches. Signup and view all the answers

What is the slope of the line in the graph representing the woodcock's flight?

8 Signup and view all the answers

How far will the woodcock be able to travel in 8 hours at its recorded speed?

48 Signup and view all the answers

Which linear equation represents Alfred's relationship between hours worked and weekly salary?

y = 60_x_ + 500 Signup and view all the answers

How much would Alfred be paid for a 30-hour work week?

₱2,160.00 Signup and view all the answers

What is the first step in graphing the equation 2_x_ + 5_y_ = 10?

Solve for the x-and y-intercepts. Signup and view all the answers

What is the correct sequence of steps in graphing the line on the Cartesian plane?

IV, III, I, II Signup and view all the answers

How would you describe the graph of the linear equation x = 2?

The graph is a vertical line which passes through the x-axis at (2,0). Signup and view all the answers

Which of the following represents the graph of the linear equation y = 2_x_ + 3?

image 2 Signup and view all the answers

Study Notes

Mathematics Concepts

Greatest Common Factor (GCF): The GCF of 64x²y³ - 32x³y² + 16x⁴y³ is 16x²y².
Factors of Polynomials: Not all expressions are factors of a polynomial. For 9x⁴y³, (9x)(y³) is not a factor.
Multiplication for Quadratic Forms: To obtain 9x² - 4 from (3x - 2), multiply by (3x - 2).
Perfect Square Trinomials: 9x² + 3xy + y³ is not a perfect square trinomial.

Quadratic Expressions

Factorable Quadratics: The value of k for x² - 6x + k to be factorable is 9.
Finding Factors: If one factor of 3x² + 4x - 15 is (x + 3), the other factor is (3x - 5).
Area Calculation: The area given by (x² + 9x + 20) results in dimensions of (x + 4) cm and (x + 5) cm.

Pool Area Changes

Area Modification: Altering a square pool into a rectangle (length increased by 7 and width decreased by 7) results in a decrease in area by 49 square units.

Quadratic Factorization

Factored Forms: The factored form of 4x² - 12x + 9 is (2x - 3)².
Dividing Rational Expressions: Understanding rational algebraic expressions helps simplify ratios correctly.

Working and Time

Job Efficiency: If Alex can complete work in x hours, after 4 hours he can finish (4/x) of the job.
Cooperative Work: Bert (6 hours) and Cris (3 hours) together can finish the project in 2 hours working cooperatively.

Coordinate Geometry

Coordinate Quadrants: A point where the abscissa is positive and the ordinate is negative is located in Quadrant IV.
Linear Equations: The equation x = 2 represents a vertical line on the graph.

Salary Calculation

Pay Structure: Alfred's weekly salary based on hours worked is modeled by the equation y = 60x + 500.

Graphing Linear Equations

Finding Intercepts: To graph a line like 2x + 5y = 10, calculate the x- and y-intercepts and plot them.
Slope Intercepts: A line parallel to y = 4x - 3 with a y-intercept of 5 is y = 4x + 5.

Candle Burning Rate

Burning Equation: The candle height decreases as h = 10 - 2t, indicating a linear relationship with time.

Data Modeling

Youth Out of School: An increasing trend of out-of-school youths can be represented by the equation y = 8x + 52.

Inconsistent Systems

System Conclusion: For lines with the same slope and different y-intercepts, the graph indicates the lines are parallel.

Animal Count Problem

Graphing Relationships: For a count of 12 animals with 42 legs, a system of equations can help visualize the relationships.

Canteen Revenue

Revenue Calculation: Chicken and egg sandwich sales leading to revenue can be modeled for increased target revenues efficiently.

Summary

Multiple mathematical concepts including polynomials, rational expressions, factoring quadratics, and geometry are emphasized.
Real-world applications such as cooperative work rates and revenue generation are included for practical understanding.
Graphs and equations are essential for visualization and solving problems in various scenarios.

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Test your knowledge of polynomial expressions through a series of problems focused on finding the greatest common factor, identifying factors, and manipulating binomials. This quiz will challenge your understanding of algebraic principles and perfect squares.