Polynomials ~ Factor and Solve.

Front

What is a polynomial?

Back

A polynomial is a mathematical expression consisting of variables (also called indeterminates) raised to non-negative integer powers and coefficients, combined using addition, subtraction, and multiplication.

Front

What are the degrees of polynomials?

Back

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

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What is the Factor Theorem?

Back

The Factor Theorem states that a polynomial f(x) has a factor (x - c) if and only if f(c) = 0, meaning c is a root of the polynomial.

Tags

CCSS.HSA.APR.B.2

Front

How do you find the roots of a polynomial?

Back

To find the roots of a polynomial, set the polynomial equal to zero and solve for the variable. This can involve factoring, using the quadratic formula, or synthetic division.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division that is used to divide a polynomial by a linear factor of the form (x - c).

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CCSS.HSA.APR.D.6

Front

What is the difference between real and complex roots?

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Real roots are solutions to a polynomial equation that are real numbers, while complex roots include imaginary numbers and are of the form a + bi, where a and b are real numbers.

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CCSS.HSN.CN.C.9

Front

What is the quadratic formula?

Back

The quadratic formula is used to find the roots of a quadratic equation ax^2 + bx + c = 0 and is given by x = (-b ± √(b² - 4ac)) / (2a).

Tags

CCSS.HSA-REI.B.4B

Front

What is the process of factoring a polynomial?

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Factoring a polynomial involves rewriting it as a product of its factors, which can include linear factors and irreducible polynomials.

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What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b² - 4ac) determines the nature of the roots of a quadratic equation: if it is positive, there are two distinct real roots; if zero, one real root; if negative, two complex roots.

Tags

CCSS.HSA-REI.B.4B

Front

What is the Rational Root Theorem?

Back

The Rational Root Theorem states that any rational solution (or root) of a polynomial equation with integer coefficients is of the form ±p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

Tags

CCSS.HSA.APR.B.2