Is Goblins free for teachers?

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.

How does Goblins work?

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.

Does Goblins prevent cheating?

Yes. Goblins uses a purpose-trained AI model that evaluates cheating signals in real time. It can detect when students are copying answers, using external tools inappropriately, or not genuinely working through problems. Copy-pasting answers is also blocked.

Can I use my own voice with Goblins?

Yes. Teachers can record their voice and take a selfie to create a custom 3D avatar in about 30 seconds. Students then hear help in their own teacher's voice and see a familiar face, making the experience more personal and effective.

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.

Is Goblins FERPA compliant?

Yes. Goblins is FERPA and state compliant. Student data privacy and security are a top priority.

Does Goblins support English Language Learners?

Yes. Goblins supports 30+ languages so teachers don't have to translate every worksheet. It is especially helpful for ELL students who need accessible math instruction in their native language.

NC.M3.A-APR.6

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).

Example Problems

Find:

\int \frac{12}{x(x - 4)} dx

Find:

\int \frac{2x + 7}{x(x + 3)} dx

Find:

\int \frac{1}{(x + 1)(3x + 1)} dx

Khan Academy Resources

Factoring monomials Factoring polynomials by taking a common factor Factoring quadratics in any form Factoring quadratics: Difference of squares Factoring quadratics: Perfect squares Factoring by grouping Factoring quadratics: leading coefficient = 1 Factoring quadratics: leading coefficient ≠ 1 Difference of squares Difference of squares intro Factor polynomials using structure Polynomial special products: perfect square Divide quadratics by linear expressions (no remainders)Divide quadratics by linear expressions (with remainders)Zeros of polynomials (with factoring)Factor monomials Solve equations using structure Polynomial special products: difference of squares Identify quadratic patterns Factor polynomials: common factor Factor higher degree polynomials Equivalent forms of exponential expressions Perfect squares intro Factorization with substitution Zeros of polynomials (factored form)Perfect squares GCF factoring introduction Factoring perfect squares Factoring using the difference of squares pattern Intro to grouping Intro to long division of polynomials Taking common factor from trinomial Factoring quadratics: common factor + grouping Factoring quadratics: negative common factor + grouping Factoring perfect squares: negative common factor Factoring using the perfect square pattern Factoring perfect squares: missing values Polynomial special products: difference of squares Perfect square factorization intro Dividing quadratics by linear expressions with remainders: missing x-term Factoring quadratics as (x+a)(x+b)Factoring higher-degree polynomials: Common factor Identifying perfect square form Solving quadratics using structure Worked example: finding missing monomial side in area model Taking common factor: area model Factoring difference of squares: shared factors Factoring perfect squares: shared factors Difference of squares intro Strategy in factoring quadratics (part 1 of 2)Factoring difference of squares: analyzing factorization Factoring difference of squares: leading coefficient ≠ 1 Strategy in factoring quadratics (part 2 of 2)Which monomial factorization is correct?Identifying quadratic patterns Factoring with the distributive property Worked example: finding the missing monomial factor Taking common factor from binomial Factoring higher degree polynomials Polynomial special products: perfect square Factorization with substitution Dividing quadratics by linear expressions (no remainders)Dividing quadratics by linear expressions with remainders Reasoning about unknown variables: divisibility Reasoning about unknown variables Worked example: Rewriting expressions by completing the square

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