Search the California Content Standards

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:
Perform arithmetic operations with complex numbers.

Standard:
Know there is a complex number i such that i^2 = −1, and every complex number has the form a + bi with a and b real.

Cluster:
Perform arithmetic operations with complex numbers.

Standard:
Use the relation i^2 = −1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

Cluster:
Use complex numbers in polynomial identities and equations. [Polynomials with real coefficients]

Standard:
Solve quadratic equations with real coefficients that have complex solutions.

Cluster:
Use complex numbers in polynomial identities and equations. [Polynomials with real coefficients]

Standard:
(+) Extend polynomial identities to the complex numbers. For example, rewrite x^2 + 4 as (x + 2i)(x – 2i).

Cluster:
Use complex numbers in polynomial identities and equations. [Polynomials with real coefficients; apply N.CN.9 to higher degree polynomials.]

Standard:
(+) Extend polynomial identities to the complex numbers.

Cluster:
Use complex numbers in polynomial identities and equations. [Polynomials with real coefficients; apply N.CN.9 to higher degree polynomials.]

Standard:
(+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.