Simplifying Polynomials

Simplifying

The final simplified answer for

{(\frac{a^{2}}{b^{4}})}^{5}

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Multiplication

Expand and simplify the expression

(3 x^{2} - 2 x + 1) (2 x^{2} + x - 3)

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Polynomial Addition

Simplify the following polynomial expression:

3 x^{2} + 2 x - 1 + 5 x^{2} - 3 x + 4

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Polynomial Subtraction

(3 x^{2} + 2 x) - (8 x^{2} + 7)

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Polynomial Multiplication

Multiply the polynomials

(3 x^{2} - 2 x + 1)

and

(4 x^{2} + 3 x - 2)

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Evaluate the Expression Using the Given Values

Given the polynomial expression

2 x^{2} - 3 x + 5

, evaluate the expression when

x = 3

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Determining if the Expression is a Polynomial

x^{2} - 13 x + 12

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Multiplying Polynomials Using FOIL

(2 x - 1) (2 x - 1)

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Operations on Polynomials

(3 x + 4) (x - 5) + (2 x + 1)^{2}

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Simplifying Expressions

[Maximum mark: 6] (a) Write down and simplify the expansion of

(2 + x)^{4}

in ascending powers of

x

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Negative Exponents

问题 Simplify

{(7 b^{3})}^{2} \cdot {(4 b^{2})}^{- 3}

, given that bis non-zero. 标准答案

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Rewriting Using Negative Exponents

Simplify the polynomial expression

\frac{x^{5}}{x^{2}}

and rewrite it using negative exponents.

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Polynomial Division

Divide the polynomial

5 x^{4} - 3 x^{2} + 2 x - 7

by the polynomial

x^{2} - 1

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Synthetic Division

Use synthetic division to divide the polynomial

2 x^{3} - 5 x^{2} + 4 x - 3

by the binomial

x - 2

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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)

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Maximum Number of Real Roots/Zeros

Given the polynomial function

f (x) = 2 x^{5} - 3 x^{4} + 5 x^{3} - 2 x^{2} + 3 x - 5

, how many real roots/zeros can this function have at maximum?

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Finding All Roots with Rational Root Test (RRT)

Find all roots of the polynomial

2 x^{3} - 3 x^{2} - 5 x + 6

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Finding the Remainder

Find the remainder when the polynomial

3 x^{3} - 5 x^{2} + 2 x - 7

is divided by the binomial

x - 2

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Finding the Remainder Using Long Polynomial Division

Use the method of polynomial division to find the remainder when

3 x^{4} - 2 x^{3} + 7 x^{2} - 5 x + 1

is divided by

x^{2} - 3 x + 1

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Reordering the Polynomial in Ascending Order

Write each polynomial in ascending powers of

x

1.26 - 3 x + 5 x^{3} + 1 + x^{2}

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Reordering the Polynomial in Descending Order

Reorder the polynomial

5 x^{3} - 2 x^{2} + 7 x - 3

in descending order

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Finding the Leading Term

Simplify the following polynomial and find the leading term:

3 x^{4} - 5 x^{3} + 2 x^{2} - 3 x + 1 - (2 x^{4} + x^{3} - x^{2} + 2 x - 1)

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Finding the Leading Coefficient

Simplify the polynomial

7 x^{4} - 5 x^{2} + 3 x - 2 x^{4} + 4 x^{2} - 2 x

and find its leading coefficient.

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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

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Simplifying

Multiplication

Polynomial Addition

Polynomial Subtraction

Polynomial Multiplication

Evaluate the Expression Using the Given Values

Determining if the Expression is a Polynomial

Multiplying Polynomials Using FOIL

Operations on Polynomials

Simplifying Expressions

Negative Exponents

Rewriting Using Negative Exponents

Polynomial Division

Synthetic Division

Identifying Degree

Maximum Number of Real Roots/Zeros

Finding All Roots with Rational Root Test (RRT)

Finding the Remainder

Finding the Remainder Using Long Polynomial Division

Reordering the Polynomial in Ascending Order

Reordering the Polynomial in Descending Order

Finding the Leading Term

Finding the Leading Coefficient

Finding the Degree, Leading Term, and Leading Coefficient

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