Podcast
Questions and Answers
What is the standard form of the polynomial $w + 3 - 2w + 8w^3$?
What is the standard form of the polynomial $w + 3 - 2w + 8w^3$?
- $-w + 3 + 8w^3$
- $3 - w + 8w^3$
- $8w^3 + w + 3$
- $8w^3 - w + 3$ (correct)
Which of the following correctly classifies the polynomial $14d - d + 3d$?
Which of the following correctly classifies the polynomial $14d - d + 3d$?
- Degree: 1st term, Term: binomial
- Degree: 2nd term, Term: binomial
- Degree: 1st term, Term: monomial (correct)
- Degree: 1st term, Term: trinomial
Given the polynomial $4x + x^2 - 1$, which of the following identifies the degree and term?
Given the polynomial $4x + x^2 - 1$, which of the following identifies the degree and term?
- Degree: cubic, Term: trinomial
- Degree: quadratic, Term: binomial
- Degree: quadratic, Term: trinomial (correct)
- Degree: linear, Term: trinomial
Simplify the expression $(5x^2 + 3x^2 - 7x + 10) - (3x^2 - x^2 + 4x - 1)$. What is the coefficient of the $x$ term in the simplified form?
Simplify the expression $(5x^2 + 3x^2 - 7x + 10) - (3x^2 - x^2 + 4x - 1)$. What is the coefficient of the $x$ term in the simplified form?
What is the simplified form of $(4m^3 + 7m - 4) + (2m^3 - 6m + 8)$?
What is the simplified form of $(4m^3 + 7m - 4) + (2m^3 - 6m + 8)$?
Simplify $(8t^2 + t + 10) - (9t^2 - 9t - 1)$.
Simplify $(8t^2 + t + 10) - (9t^2 - 9t - 1)$.
A rectangle has sides of length $4t - 1$ and $5t + 9$. What expression represents the perimeter of the rectangle?
A rectangle has sides of length $4t - 1$ and $5t + 9$. What expression represents the perimeter of the rectangle?
A triangle has side lengths $4t - 3$ and $10 - 2t$. The perimeter of the triangle is $t^2 + 11t - 18$. What is the length of the third side?
A triangle has side lengths $4t - 3$ and $10 - 2t$. The perimeter of the triangle is $t^2 + 11t - 18$. What is the length of the third side?
What is the product of $2y(y + 1)$ in standard form?
What is the product of $2y(y + 1)$ in standard form?
What is the standard form of the polynomial obtained by multiplying $-3x(x^2 + 3x - 1)$?
What is the standard form of the polynomial obtained by multiplying $-3x(x^2 + 3x - 1)$?
Flashcards
Standard Form
Standard Form
Arranging a polynomial so the term with the highest degree is first and degrees descend.
Degree of a Polynomial
Degree of a Polynomial
Highest exponent value of a single term in standard form.
Trinomial
Trinomial
An expression with 3 terms.
Binomial
Binomial
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Monomial
Monomial
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Quadratic Polynomial
Quadratic Polynomial
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Cubic Polynomial
Cubic Polynomial
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Perimeter
Perimeter
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Study Notes
- The sheet contains a review of polynomials, covering standard form, degree, term identification, simplification and expressions for shapes.
Polynomial Standard Form, Degree, and Term Identification
- 4x + x² - 1 written in standard form is x² + 4x - 1.
- x² + 4x - 1 is a quadratic trinomial
- 2n² + 3n³ written in standard form is 3n³ + 2n².
- 3n³ + 2n² is a cubic binomial
- -4y is already in standard form and its degree is linear.
- -4y is a monomial
- w + 3 - 2w + 8w³ written in standard form is 8w³ - w + 3.
- 8w³ - w + 3 is a cubic trinomial.
- 5 is already in standard form and is a constant monomial.
- 14d - d³ + 3d written in standard form is -d³ + 17d.
- -d³ + 17d is a 4th term binomial.
Simplifying Polynomials
- (5x² + 3x - 7x + 10) - (3x² - x² + 4x - 1) simplifies to 2x² + 4x - 11.
- (4m³ + 7m - 4) + (2m³ - 6m + 8) simplifies to 6m³ + m + 4.
- (8t² + t + 10) - (9t² - 9t - 1) simplifies to -t² + 10t + 11.
Perimeter Expressions
- The sides of a rectangle are 4t - 1 and 5t + 9, so the perimeter is 18t + 16.
- A triangle has sides 4t - 3 and 10 - 2t, given a perimeter of t² + 11t - 18, the third side length is x² + 5x - 11.
Polynomial Product Simplification
- 2y(y + 1) simplifies to 2y² + 2y.
- -3x(x² + 3x - 1) simplifies to -3x³ - 9x² + 3x.
- 9c(c² - 3c + 5) simplifies to 9c³ - 27c² + 45c.
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