Search the California Content Standards

Cluster:
Understand the relationship between zeros and factors of polynomials.

Standard:
Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

Cluster:
Use polynomial identities to solve problems.

Standard:
Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x^2 + y^2)^2= (x^2 – y^2)^2 + (2xy)^2 can be used to generate Pythagorean triples.

Cluster:
Use polynomial identities to solve problems.

Standard:
(+) Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.

Footnote:
The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.

Cluster:
Rewrite rational expressions. [Linear and quadratic denominators]

Standard:
Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.

Cluster:
Rewrite rational expressions. [Linear and quadratic denominators]

Standard:
(+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

Cluster:
Create equations that describe numbers or relationships. [Equations using all available types of expressions, including simple root functions]

Standard:
Create equations and inequalities in one variable including ones with absolute value and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. CA *

Cluster:
Create equations that describe numbers or relationships. [Equations using all available types of expressions, including simple root functions]

Standard:
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. *

Cluster:
Create equations that describe numbers or relationships. [Equations using all available types of expressions, including simple root functions]

Standard:
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. *

Cluster:
Create equations that describe numbers or relationships. [Equations using all available types of expressions, including simple root functions]

Standard:
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. *

Cluster:
Apply trigonometry to general triangles.

Standard:
(+) Prove the Laws of Sines and Cosines and use them to solve problems.