Simplifying
The final simplified answer for \( \left(\frac{a^{2}}{b^{4}}\right)^{5} \) is
Multiplication
Expand and simplify the expression \((3x^2 - 2x + 1)(2x^2 + x - 3)\)
Polynomial Addition
Simplify the following polynomial expression: \(3x^2 + 2x - 1 + 5x^2 - 3x + 4\)
Polynomial Subtraction
$\left(3 x^{2}+2 x\right)-\left(8 x^{2}+7\right)$
Polynomial Multiplication
Multiply the polynomials \((3x^{2} - 2x + 1)\) and \((4x^{2} + 3x - 2)\)
Evaluate the Expression Using the Given Values
Given the polynomial expression \(2x^{2} - 3x + 5\), evaluate the expression when \(x = 3\).
Determining if the Expression is a Polynomial
$x^{2}-13 x+12$
Multiplying Polynomials Using FOIL
\( (2 x-1)(2 x-1) \)
Operations on Polynomials
$(3 x+4)(x-5)+(2 x+1)^{2}$
Simplifying Expressions
[Maximum mark: 6]
(a) Write down and simplify the expansion of $(2+x)^{4}$ in ascending powers of $x$.
Negative Exponents
问题
Simplify $\left(7 b^{3}\right)^{2} \cdot\left(4 b^{2}\right)^{-3}$, given that bis non-zero. 标准答案
Rewriting Using Negative Exponents
Simplify the polynomial expression \(\frac{x^5}{x^2}\) and rewrite it using negative exponents.
Polynomial Division
Divide the polynomial \(5x^4 - 3x^2 + 2x - 7\) by the polynomial \(x^2 - 1\).
Synthetic Division
Use synthetic division to divide the polynomial \(2x^3 - 5x^2 + 4x - 3\) by the binomial \(x - 2\).
Identifying Degree
7. Identify the degree of each polynomial and what the polynomial could be used to represent (length/perimeter, area, or volume)
\[
(x-4)(x+8)
\]
Maximum Number of Real Roots/Zeros
Given the polynomial function \(f(x) = 2x^5 - 3x^4 + 5x^3 - 2x^2 + 3x - 5\), how many real roots/zeros can this function have at maximum?
Finding All Roots with Rational Root Test (RRT)
Find all roots of the polynomial \(2x^3 - 3x^2 - 5x + 6\)
Finding the Remainder
Find the remainder when the polynomial \(3x^3 - 5x^2 + 2x - 7\) is divided by the binomial \(x - 2\).
Finding the Remainder Using Long Polynomial Division
Use the method of polynomial division to find the remainder when \(3x^4 - 2x^3 + 7x^2 - 5x + 1\) is divided by \(x^2 - 3x + 1\).
Reordering the Polynomial in Ascending Order
Write each polynomial in ascending powers of $\mathbf{x}$.
$1.26-3 x+5 x^{3}+1+x^{2}$
Reordering the Polynomial in Descending Order
Reorder the polynomial \(5x^3 - 2x^2 + 7x - 3\) in descending order
Finding the Leading Term
Simplify the following polynomial and find the leading term: \(3x^4 - 5x^3 + 2x^2 - 3x + 1 - (2x^4 + x^3 - x^2 + 2x -1)\)
Finding the Leading Coefficient
Simplify the polynomial \(7x^4 - 5x^2 + 3x - 2x^4 + 4x^2 - 2x\) and find its leading coefficient.
Finding the Degree, Leading Term, and Leading Coefficient
Answer the questions about the following polynomial.
\[
x+10-x^{3}
\]
The expression represents a polynomial with terms. The constant term is the leading term is and the leading coefficient is