MAT.105X A7

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MAT.105X A7

Special Products

Factor the Sum and Difference of Two Cubes

a^3 + b^3 = (a+b)(a^2 - ab + b^2)

a^3 - b^3 = (a-b)(a^2 + ab + b^2)

Factor the Difference of Squares

a^2 - b^2 = (a+b)(a-b)

Factor a Perfect Square Trinomial

a^2 + 2ab + b^2 = (a+b)^2

a^2 - 2ab + b^2 = (a-b)^2

Solve a Quadratic Equation by Factoring

Zero Product Rule

If ab = 0, then a = 0 or b = 0.

Quadratic Equation

A quadratic equation can be written in the form ax^2 + bx + c = 0, where a, b, and c are real numbers and a is not zero.

Use the Pythagorean Theorem to Solve an Applied Problem

Pythagorean Theorem

Given a right triangle with legs of length a and b and hypotenuse of length c,

a^2 + b^2 = c^2

or

(leg)^2 + (other leg)^2 = (hypotenuse)^2

Right Triangle

A right triangle is a triangle that contains a 90 degree angle.

The two sides of the triangle that meet to form the 90 degree angle are called legs.

The remaining side, opposite the 90 degree angle, is called the hypotenuse.

Factor Trinomials of the Form ax^2 + bx + c (a not 1)

If the trinomial is not prime, trinomials of the form ax^2 + bx + c can be written using four terms and then applying factoring by grouping.

Consider the nonprime trinomial ax^2 + bx + c. We begin by finding the product ac. Then we find a factorization of ac, let's say mn, where ac=mn and m+n=b. Now we can write the trinomial as ax^2 + mx + nx + c. Apply factor by grouping to this polynomial with four terms.

Remember to look for a GCF first.

Another method called the trial-and-error method can also be used to factor trinomials of this type.

Factor Trinomials of the Form x^2 + bx + c

If the trinomial is not prime, trinomials of the form x^2 + bx + c can be written as (x + m)(x + n) where mn=c and m+n=b.

Remember to look for a GCF first.

Factor by Grouping

This can be a good method when factoring a polynomial with four terms.

Factor Out the Greatest Common Factor

Factor a Polynomial

To factor a polynomial is to write it as a product of two or more polynomials.

Factoring polynomials is the opposite of multiplying polynomials.

Factoring out the GCF of a polynomial (if one exists) should always be the first step when factoring a polynomial completely.

Factoring a polynomial can take many more steps than just one.

Factor an Integer

To factor an integer is to write it as the product of two or more integers.

GCF

The greatest common factor (GCF) of a group of monomials is the largest common factor of the terms in the group.