Beginning & Intermediate Algebra
What is the numerical value of 404^0?
Simplify the product x5⋅x−2⋅x3x^5\(\cdot\) x^{-2}\(\cdot\) x^3.
Simplify the expression (a−1b2ab−3)−1\(\left\)(\(\frac{a^{-1}\)b^2}{ab^{-3}}\(\right\))^{-1} by simplifying from the inside out, and write the final answer using only positive exponents.
Which statement correctly expresses the defining property of a polynomial?
Find the degree of the term 4x2y3z4x^2 y^3 z.
Simplify the expression E(x)=x3−2xE(x) = \(\frac{x^3-2}{x}\) and determine if it is a polynomial.
Compute and simplify: 3x2⋅5x33x^2\(\cdot\)5x^3
Multiply and simplify using FOIL: (x+5)(x−2)(x + 5)(x - 2)
Multiply and simplify (x2+x−2)(x+3)\(\left\)(x^2+x-2\(\right\))\(\left\)(x+3\(\right\)). Use distribution by splitting the shorter polynomial.
What is the value of (ab)0\(\left\)(\(\frac{a}{b}\)^{}\(\right\))^0 for nonzero aa and bb?
Simplify (6x23x)2\(\left\)(\(\frac{6x^2}{3x}\]\right\))^2. Show two distinct methods (simplifying inside the parentheses first vs. distributing the exponent first) and confirm they produce the same result.
A student claims (x+1)2=x2+1(x+1)^2 = x^2 + 1 by distributing the exponent across the sum. Evaluate the claim, demonstrate the correct expansion, and explain why the student's step is invalid.
