Search the California Content Standards

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:
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:
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:
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:
Extend the domain of trigonometric functions using the unit circle.

Standard:
Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

Cluster:
Extend the domain of trigonometric functions using the unit circle.

Standard:
Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

Cluster:
Extend the domain of trigonometric functions using the unit circle.

Standard:
Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.