Polynomial Factoring and Solving

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What is a polynomial?

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A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients. For example, 4x^3 + 5x^2 - 16x is a polynomial.

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What does it mean to factor a polynomial?

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Factoring a polynomial means expressing it as a product of its factors, which are polynomials of lower degrees. For example, the polynomial x^2 - 9 can be factored as (x - 3)(x + 3).

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What is the zero-product property?

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The zero-product property states that if the product of two or more factors is zero, at least one of the factors must be zero. This is used to solve polynomial equations.

Tags

CCSS.HSA-REI.B.4B

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How do you solve a polynomial equation?

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To solve a polynomial equation, you can set the equation to zero and factor it, then use the zero-product property to find the values of the variable that satisfy the equation.

Tags

CCSS.HSA-REI.B.4B

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What is the degree of a polynomial?

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The degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 4x^3 + 5x^2 - 16x, the degree is 3.

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What is a quadratic equation?

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A quadratic equation is a polynomial equation of degree 2, typically in the form ax^2 + bx + c = 0, where a, b, and c are constants.

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What is the difference of squares?

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The difference of squares is a special factoring pattern that states a^2 - b^2 = (a - b)(a + b).

Tags

CCSS.HSA.APR.C.4

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What is the sum of cubes?

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The sum of cubes is a factoring pattern that states a^3 + b^3 = (a + b)(a^2 - ab + b^2).

Tags

CCSS.HSA.APR.C.4

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What is the product of cubes?

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The product of cubes is a factoring pattern that states a^3 - b^3 = (a - b)(a^2 + ab + b^2).

Tags

CCSS.HSA.APR.C.4

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How do you factor a polynomial with a common factor?

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To factor a polynomial with a common factor, identify the greatest common factor (GCF) of all terms and factor it out. For example, in 4x^3 + 8x^2, the GCF is 4x^2, so it can be factored as 4x^2(x + 2).