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:
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:
Visualize relationships between two-dimensional and three-dimensional objects.

Standard:
Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

Cluster:
Use probability to evaluate outcomes of decisions. [Include more complex situations.]

Standard:
(+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). *