Podcast
Questions and Answers
What is the degree of the polynomial $x^2+x+3$?
What is the degree of the polynomial $x^2+x+3$?
2
What is the degree of the polynomial $3x^2+x+33$?
What is the degree of the polynomial $3x^2+x+33$?
2
Add these polynomials: $(2x^2+6x+5) + (3x^2−2x−1)$.
Add these polynomials: $(2x^2+6x+5) + (3x^2−2x−1)$.
5x^2+4x+4
Subtract the polynomials: $(x^3 + 3x^2 + 5x - 4) - (3x^3 - 8x^2 - 5x + 6)$.
Subtract the polynomials: $(x^3 + 3x^2 + 5x - 4) - (3x^3 - 8x^2 - 5x + 6)$.
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Multiply the binomials: $(x-5)(x+5)$.
Multiply the binomials: $(x-5)(x+5)$.
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Multiply the binomials: $(7x^2 + 3)(7x^2 + 3)$.
Multiply the binomials: $(7x^2 + 3)(7x^2 + 3)$.
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Multiply the polynomial: $3x^2(4x^2 - 5x + 7)$.
Multiply the polynomial: $3x^2(4x^2 - 5x + 7)$.
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Multiply the polynomials: $(4x - 5)(2x^2 + 3x - 6)$.
Multiply the polynomials: $(4x - 5)(2x^2 + 3x - 6)$.
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Find the GCF of $6x + 4$.
Find the GCF of $6x + 4$.
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Factor the polynomials: $5x(2x-4) - 3(2x-4)$.
Factor the polynomials: $5x(2x-4) - 3(2x-4)$.
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Factor by polynomials: $2x^3 + 18x^2 + 10x$.
Factor by polynomials: $2x^3 + 18x^2 + 10x$.
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Find x in the equation $3x^2 + 8x + 4 = 0$.
Find x in the equation $3x^2 + 8x + 4 = 0$.
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Multiply the polynomials: $(x+2)(x^2+3x+4)$.
Multiply the polynomials: $(x+2)(x^2+3x+4)$.
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Factor the polynomial by grouping: $3x^2 + 6x + 4x + 8$.
Factor the polynomial by grouping: $3x^2 + 6x + 4x + 8$.
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Simplify $(t + 6)^2$.
Simplify $(t + 6)^2$.
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Factor the perfect square trinomial: $4x^2 - 16x + 16$.
Factor the perfect square trinomial: $4x^2 - 16x + 16$.
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What is the difference between the perfect squares $4x^2 - 81y^2$?
What is the difference between the perfect squares $4x^2 - 81y^2$?
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Find the zeros of the equation $x^2 + 3x + 2 = 0$.
Find the zeros of the equation $x^2 + 3x + 2 = 0$.
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Find the vertex of the function $y=(x-3)^2 + 2$.
Find the vertex of the function $y=(x-3)^2 + 2$.
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Find the inverse of $f(x)=2x-1$.
Find the inverse of $f(x)=2x-1$.
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Find the inverse of $f(x)=4x-5$.
Find the inverse of $f(x)=4x-5$.
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Study Notes
Polynomial Degree
- The degree of the polynomial x² + x + 3 is 2.
- For the polynomial 3x² + x + 33, the degree is also 2.
Polynomial Operations
- The sum of (2x² + 6x + 5) and (3x² − 2x − 1) results in 5x² + 4x + 4.
- Subtracting (3x³ − 8x² − 5x + 6) from (x³ + 3x² + 5x - 4) gives -2x³ + 11x² + 10x - 1.
Binomial Multiplication
- The product of the binomials (x - 5)(x + 5) simplifies to x² - 25.
- Multiplying (7x² + 3)(7x² + 3) results in 49x⁴ + 42x² + 9.
Polynomial Multiplication
- The polynomial 3x²(4x² - 5x + 7) expands to 12x⁴ - 15x³ + 21x².
- The product of (4x - 5)(2x² + 3x - 6) simplifies to 8x³ + 2x² - 39x + 30.
Factoring
- The greatest common factor (GCF) of 6x + 4 is 2(3x + 2).
- The polynomial 5x(2x - 4) - 3(2x - 4) factors to (2x - 4)(5x - 3).
- Factoring by grouping leads to 2x(x² + 9x + 5) for the expression 2x³ + 18x² + 10x.
Solving Quadratic Equations
- The solutions for the equation 3x² + 8x + 4 = 0 are x = -2 and x = -2/3.
Additional Polynomial Multiplication
- Multiplying (x + 2)(x² + 3x + 4) yields x³ + 5x² + 10x + 8.
- Factoring the expression 3x² + 6x + 4x + 8 gives (x + 2)(3x + 4).
Simplification
- The expression (t + 6)² simplifies to t² + 12t + 36.
- The perfect square trinomial 4x² - 16x + 16 factors to (2x - 4)².
Difference of Perfect Squares
- The expression 4x² - 81y² factors into (2x - 9y)(2x + 9y).
Finding Zeros and Vertex
- The zeros of the equation x² + 3x + 2 = 0 are found from factors x + 2 = 0 and x + 1 = 0.
- The vertex of the parabola represented by y = (x - 3)² + 2 is at the point (3, 2).
Inverse Functions
- The inverse of the function f(x) = 2x - 1 is f⁻¹(x) = ½x + ½.
- For the function f(x) = 4x - 5, its inverse is f⁻¹(x) = x/4 + 5/4.
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Prepare for your Algebra 1 final with these flashcards that cover key concepts such as polynomial degrees, addition, subtraction, and multiplication of polynomials. Test your understanding and reinforce your knowledge through these concise questions and answers.
