High school algebra

MAPLE V can do high school algebra. It can manipulate polynomials and rational functions of one or more variables quite easily.

https://www.w3.org/1998/Math/MathML"> >   p ⁢     : = x ∧ 2 + 5 * x + 6 ; https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429332968/4e6f0b6f-bf75-44ee-bdcb-9f24177aac7c/content/inline-math1.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>

p:= x ² + 5x + 6

> factor(p);

(x + 3)(x + 2)

https://www.w3.org/1998/Math/MathML"> >   b ⁢     : = 1 − q ∧ 7 − q ∧ 8 − q ∧ 9 + q ∧ 15 + q ∧ 16 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429332968/4e6f0b6f-bf75-44ee-bdcb-9f24177aac7c/content/inline-math2.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> := 1 - q^A7 - q^A8 - q^A9 + q^A15 + q^A16

12 https://www.w3.org/1998/Math/MathML"> +       q ∧ 17 − q ∧ 24 ; https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429332968/4e6f0b6f-bf75-44ee-bdcb-9f24177aac7c/content/inline-math3.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> ^A17 https://www.w3.org/1998/Math/MathML"> b ⁢     : = 1 − q 7 − q 8 − q 9 + q 15 + q 16 + q 17 − q 24 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429332968/4e6f0b6f-bf75-44ee-bdcb-9f24177aac7c/content/inline-math4.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>

> factor(b);

https://www.w3.org/1998/Math/MathML"> − ( q + 1 ) ( q 2 + 1 ) ( q 2 + q + 1 ) ( q 6 + q 3 + 1 ) ( q 4 + 1 ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429332968/4e6f0b6f-bf75-44ee-bdcb-9f24177aac7c/content/inline-math5.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> https://www.w3.org/1998/Math/MathML"> ( q 6 + q 5 + q 4 + q 3 + q 2 + q + 1 ) ( q − 1 ) 3 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429332968/4e6f0b6f-bf75-44ee-bdcb-9f24177aac7c/content/inline-math6.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/>

To factor a polynomial or rational function we use factor. We let p = x ² + 5x + 6 and found the factorization using factor(p). This could have easily been done by hand. Factoring b = 1 — q ⁷ — https://www.w3.org/1998/Math/MathML"> q 8 − q 9 + q 15 + q 16 + q 17 − q 24 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429332968/4e6f0b6f-bf75-44ee-bdcb-9f24177aac7c/content/inline-math7.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> is not so easy, but child's play for MAPLE V.