options: Perform arithmetic operations on polynomials.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Represent and solve equations and inequalities graphically.

Add and subtract within 20.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Understand solving equations as a process of reasoning and explain the reasoning.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Solve systems of equations.

Generate and analyze patterns.

Use properties of operations to generate equivalent expressions.

Write expressions in equivalent forms to solve problems.

Multiply and divide within 100.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Represent and solve problems involving addition and subtraction.

Understand the connections between proportional relationships, lines, and linear equations.

Gain familiarity with factors and multiples.

Work with addition and subtraction equations.

Work with equal groups of objects to gain foundations for multiplication.

Use the four operations with whole numbers to solve problems.

Create equations that describe numbers or relationships

Understand properties of multiplication and the relationship between multiplication and division.

Understand and apply properties of operations and the relationship between addition and subtraction.

Represent and solve problems involving multiplication and division.

Work with radicals and integer exponents.

Reason about and solve one-variable equations and inequalities.

Interpret the structure of expressions.

Understand the relationship between zeros and factors of polynomials.

Analyze patterns and relationships.

Write and interpret numerical expressions.

Solve equations and inequalities in one variable.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Use polynomial identities to solve problems.

Rewrite rational expressions.

Represent and analyze quantitative relationships between dependent and independent variables.
problem_activity: Task
Suppose $f$ is a quadratic function given by the equation $f(x) = ax^2 + bx + c$
where $a,b,c$ are real numbers and $a$ is non-zero.
Explain why $f$ can have at most two roots; that is explain why there can be at most two distinct real numbers $r_1,r_2$ so that $f(r_1) = f(r_2) = 0$.
Give examples to show that it is possible for $f$ to have zero, one, or two
real roots.


correct_option_index: 26