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Yes. Goblins offers a generous free tier that includes 1 live feedback assignment per week, insights on student mastery and replays, and the ability to upload your own content. The Max plan adds unlimited assignments, superadaptive mode, grade exports, standards growth reports, and SSO/LMS integration, with per-student pricing for schools and districts.

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Three simple steps: (1) Share an assignment from thousands of standards-aligned topics using a share code. (2) Students speak and draw their thinking naturally, and Goblins responds with Socratic questioning that sounds just like their teacher. (3) Teachers get real-time formative insights showing what students struggle with and suggestions to inform instruction.

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Can I use my own voice with Goblins?

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What math levels does Goblins cover?

Goblins covers math from Grade 5 through AP Calculus, including thousands of standards-aligned topics. Teachers can also upload their own content for custom assignments at any level.

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What grade level is A-APR taught?

This standard is part of the A-APR curriculum in Alaska Mathematics Standards.

A-APR: Arithmetic with Polynomials and Rational Expressions

Arithmetic with Polynomials and Rational Expressions

Print

Arithmetic with Polynomials and Rational Expressions covers operations on polynomial and rational expressions, treating them as closed algebraic systems. Adding, subtracting, multiplying, and dividing polynomials and rational expressions mirror integer arithmetic with an eye toward structure. Factoring techniques unlock simplification and connect to equation-solving across algebra and precalculus.

A-APR.1Add, subtract, and multiply polynomials. Understand that polynomials form a system similar to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication.A-APR.2Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).A-APR.3Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.A-APR.4Prove 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.A-APR.5(+) 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.A-APR.6Rewrite 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.A-APR.7(+) Add, subtract, multiply, and divide rational expressions. Understand that rational expressions form a system similar to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression.

Example Problems

Multiply:

(-x)(5x^9)

Does the polynomial

L(x) = 4x^4 - 16

have

(x - 2)

as a factor?

Factor completely:

x^2 + x - 6

Factor completely using the difference of squares method:

25 - y^2

Expand and combine like terms:

(9y^5 + 2)^2

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