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Brian McLogan
Find the zeros and multiplicity by factoring a polynomial
π Learn how to find all the zeros of a polynomial that cannot be easily factored. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros...
Brian McLogan
Applying synthetic division when your dividend is missing a term
π Learn about dividing by synthetic division when there is a missing power. Synthetic division is a method of dividing polynomials by linear expressions. To divide using synthetic division, we equate the divisor to 0 and then solve for...
Brian McLogan
Using Rational Zero Test and All Zeros of a Polynomial
π Learn how to find all the zeros of a polynomial that cannot be easily factored. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros...
Brian McLogan
Use the zero product property with polynomials to find the zeros
π Learn how to find all the zeros of a factored polynomial. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a polynomial are the...
Brian McLogan
Solving a Polynomial to Find all of the Zeros from the Factors
π Learn how to find all the zeros of a polynomial. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a polynomial are the values...
Brian McLogan
Learn how to find all the zeros and graph a polynomial using synthetic division
π Learn how to use the tools needed to graph a Polynomial function in standard form. The tools we will use to help us graph are end behavior, finding the zeros by factoring synthetic division as well as identify the multiplicity of each...
Brian McLogan
Solving a perfect square trinomial with multiple terms
πLearn how to solve quadratic equations by factoring. We will focus on factoring special techniques such as the zero product property, difference of two squares, box method and guess and check. Once we have factored the quadratic...
Brian McLogan
Given a table of points learn how to find the degree and number of turning points
π Learn how to classify polynomials based on the number of terms as well as the leading coefficient and the degree. When we are classifying polynomials by the number of terms we will focus on monomials, binomials, and trinomials, whereas...
Brian McLogan
Learn how to sketch the graph of a polynomial given factored form using multiplicity
π Learn how to use the tools needed to graph a polynomial function in factored form. A polynomial in factored form is when the polynomial is written as a product of its linear factors. Each linear factor represents an x-intercept and the...
Brian McLogan
Find all of the Zeros of a Polynomial by Factoring
π Learn how to find all the zeros of a polynomial. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros of a polynomial are the values...
Brian McLogan
Sketching the graph of a polynomial using the zeros and multiplicity
π Learn how to use the tools needed to graph a polynomial function in factored form. A polynomial in factored form is when the polynomial is written as a product of its linear factors. Each linear factor represents an x-intercept and the...
Brian McLogan
Using the remainder theorem and checking your answer with synthetic division
π Learn about and how to apply the remainder and factor theorem. The remainder theorem states that f(a) is the remainder when the polynomial f(x) is divided by x - a. Thus, given a polynomial, f(x), which is to be divided by a linear...
Brian McLogan
Write the linear factorization and solve quadratic
π Learn how to find all the zeros of a polynomial that cannot be easily factored. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros...
Brian McLogan
Graphing a quadratic function by finding the vertex and x - intercepts
π Learn how to graph quadratic equations by completing the square. A quadratic equation is an equation of the form y = ax^2 + bx + c, where a, b and c are constants. The graph of a quadratic equation is in the shape of a parabola which...
Brian McLogan
How to find the zeros, intercepts, and multiplicity
In this math tutorial I show you how to find the real zeros of a polynomial function by solving for x using algebraic techniques such as factoring, completing the square and the quadratic formula. I also show you how to determine the...
Brian McLogan
How to apply synthetic division when the zero is a fraction
π Learn about dividing by synthetic division when the divisor is a fraction. Synthetic division is a method of dividing polynomials by linear expressions. To divide using synthetic division, we equate the divisor to 0 and then solve for...
Brian McLogan
Find the roots of a quadratic equation by factoring
π Learn how to find all the zeros of a polynomial that cannot be easily factored. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. The zeros...
Brian McLogan
Find all the possible rational zeros given a polynomial
π Learn how to use the Rational Zero Test on Polynomial expression. Rational Zero Test or Rational Root test provide us with a list of all possible real Zeros in polynomial expression. Rational Zero Test can be helpful to find all the...
Brian McLogan
Sketch the graph of a factored polynomial using multiplicity
π Learn how to use the tools needed to graph a polynomial function in factored form. A polynomial in factored form is when the polynomial is written as a product of its linear factors. Each linear factor represents an x-intercept and the...
Brian McLogan
Multiplying a monomial by a binomial
In this video playlist I will show you the basics for polynomial functions. We will start with factoring polynomial equations to determine the zeros of a polynomial. We will then learn how to write the polynomial given a set of zeros....
Brian McLogan
Applying the rules of exponents to multiply to monomials
π Learn how to simplify expressions using the product rule of exponents. The product rule of exponents states that the product of powers with a common base is equivalent to a power with the common base and an exponent which is the sum of...
Brian McLogan
How to write a polynomial in standard form when divided by a number
π Learn how to classify polynomials based on the number of terms as well as the leading coefficient and the degree. When we are classifying polynomials by the number of terms we will focus on monomials, binomials, and trinomials, whereas...
Brian McLogan
How to use long division for dividing two polynomials
π Learn how to divide polynomials by quadratic divisors using the long division algorithm. Before dividing a polynomial, it is usually important to arrange the divisor in the descending order of powers of the variable(s). To divide a...
Brian McLogan
Learning how to apply long division between two polynomials
π Learn how to divide polynomials using the long division algorithm. To be able to solve a polynomial, we need to be able to get the factors and hence the zeros. To get the factors, we use the rational zeros theorem to get one of the...