Practice Algebraic Invariance in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Algebraic properties or quantities that remain unchanged when specific algebraic transformations are applied to an expression or system.
The degree of a polynomial doesn't change when you multiply it by a non-zero constant.
Example 1
mediumThe polynomial 2x^3 + 5x^2 - x + 3 can be rewritten as 2(x+1)^3 + (x+1)^2 - 4(x+1) + 5. What is invariant?
Example 2
hardShow that the discriminant b^2 - 4ac is invariant under the substitution x = t + k in ax^2 + bx + c = 0.
Example 3
easyWhen you factor x^2 + 5x + 6 = (x+2)(x+3), what is invariant?
Example 4
mediumWhat changes and what stays the same when multiplying both sides of 2x = 6 by 3?