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Applications of Factoring x² + bx + c

Determine prime factors, greatest common factor, least common multiple, square root, and cube root of whole numbers

Understanding the number systems

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Prime factorization

Greatest common factors (GCF)

Least common multiple (LCM)

Square and square roots

Cubic and cube roots

Represent, identify, simplify, and order irrational numbers

Evaluating and simplifying radicals

Rational vs. Irrational numbers

Converting repeating decimals to fractions

Converting radicals to mixed radicals

Converting radicals to entire radicals

Demonstrate understanding of powers with integral and rational exponents

Product rule of exponents

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Negative exponent rule

Combining the exponent rules

Scientific notation

Convert between radicals and rational exponents

Solving for exponents

Multiply polynomial expressions concretely, pictorially, and symbolically

What is a polynomial?

Polynomial components

Multiplying monomial by monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

Applications of polynomials

Demonstrate understanding of common factors and trinomial factoring concretely, pictorially, and symbolically

Solving polynomials with the unknown "b" from ax^2 + bx + c

Factoring polynomials: ax^2 + bx + c

Factoring perfect square trinomials: (a + b)^2 = a^2 + 2ab + b^2 or (a - b)^2 = a^2 - 2ab + b^2

Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)

Factor by taking out the greatest common factor

Factor by grouping

Factoring difference of squares: \(x^2 - y^2\)

Factoring trinomials

Common factors of polynomials

Factoring polynomials by grouping

Solving polynomials with unknown coefficients

Solving polynomials with unknown constant terms

Factoring polynomials: x^2 + bx + c

Applications of polynomials: x^2 + bx + c

Solve problems involving linear measurement using SI and imperial units, estimation, and measurement strategies

Upper and lower bound

Conversions between metric and imperial systems

Metric systems

Imperial systems

Conversions involving squares and cubic

Solve problems using SI and imperial units for surface area and volume of 3-D objects including cones, cylinders, prisms, pyramids, and spheres

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

Develop and apply primary trigonometric ratios to solve problems involving right triangles

Use sine ratio to calculate angles and sides (Sin = o / h)

Use cosine ratio to calculate angles and sides (Cos = a / h)

Combination of SohCahToa questions

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Use tangent ratio to calculate angles and sides (Tan = o / a)

Interpret and explain relationships among data, graphs and contexts

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

Demonstrate understanding of relations and functions

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Midpoint formula: \(M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)\)

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope intercept form:  y = mx + b

General form:  Ax  + By  + C = 0

Point-slope form: y - y_1 = m(x - x_1)

Demonstrate understanding of slope with respect to rise and run, line segments, rate of change, parallel and perpendicular lines

Rate of change

Parallel and perpendicular lines in linear functions

Applications of linear relations

Describe and represent linear relations using words, ordered pairs, tables of values, graphs, and equations

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

Determine characteristics of linear relation graphs including intercepts, slope, domain, and range

Introduction to linear equations

Introduction to nonlinear equations

Special case of linear equations: Horizontal lines

Special case of linear equations: Vertical lines

Relate linear relations in slope-intercept, general, and slope-point forms to their graphs

Parallel line equation

Perpendicular line equation

Combination of both parallel and perpendicular line equations

Determine equation of a linear relation given various inputs such as graph, point and slope, two points

Applications of linear equations

Solve problems involving systems of linear equations in two variables graphically and algebraically

Money related questions in linear equations

Unknown number related questions in linear equations

Distance and time related questions in linear equations

Rectangular shape related questions in linear equations

Determining number of solutions to linear equations

Solving systems of linear equations by graphing

Solving systems of linear equations by elimination

Solving systems of linear equations by substitution

Assignments

Challenge Zone

Foundation Review

Grade 10 Math

Develop algebraic reasoning and number sense

Develop spatial sense and proportional reasoning

Develop algebraic and graphical reasoning through the study of relations

math

Ex. 1:

Finding dimensions of a rectangular prism by factoring a polynomial

Setting up the volume expression for an open-top box

When area or another real quantity is written as x squared plus bx plus c, factoring it into (x+p)(x+q) reveals the two dimensions multiplied to create it. Learn to factor a trinomial application, solve for an unknown using the actual value, and recover the real-world dimensions.

Applications of polynomials: x^2 + bx + c

Applications of polynomials: x^2 + bx + c

Applications of Factoring Polynomials | StudyPug

Factoring polynomials: x^2 + bx + c

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Overview

Applications of Factoring x² + bx + c

What You'll Learn

A trinomial x squared+bx+c representing area factors into two dimensions, (x+p)(x+q).

Find p and q as two numbers that multiply to c and add to b.

If the actual area is known, substitute it and solve the resulting equation for x.

Substitute the solved x back into each factor to get real length and width.

This uses the same technique as finding the unknown b or c.

What You'll Practice

Factoring volume expressions to find three dimensions of prisms

Solving cardboard box problems by identifying dimensions after cutting

Extracting common factors from multi-variable polynomial expressions

Verifying factored dimensions match given volume formulas

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

2 Video lessons

Practice exercises

Learning resources

Skills

Polynomial Factoring

Volume

Rectangular Prisms

Word Problems

Geometry Applications

Common Factors

Trinomials