Alg1 - Ch.7 Factoring

Here's a comprehensive guide to factoring:

Factoring Numbers:

• Find factors by division:

• Start dividing the number by 2, 3, 4, and so on, up to the square root of the number.

• Any divisor that leaves no remainder is a factor.

• Example: To factor 24, divide by 2, 3, 4, etc. You'll find factors 2, 3, 4, and 6.

Factoring Polynomials:

• Identify the type of polynomial: Trinomials (3 terms), binomials (2 terms), or other forms have different factoring methods.

• Common Factoring Methods:

1. Greatest Common Factor (GCF):

• Find the largest factor common to all terms and factor it out.

• Example: 6x² + 9x = 3x(2x + 3)

1. Factoring Trinomials:

• Perfect Square Trinomials:

• Form: a²x² + 2abx + b²

• Factor: (ax + b)²

• Difference of Squares:

• Form: a²x² - b²

• Factor: (ax + b)(ax - b)

• Other Trinomials:

• Find two numbers that add up to the middle coefficient (bx term) and multiply to the constant term (c).

• Use these numbers to rewrite the middle term and factor by grouping.

1. Factoring Binomials:

• Difference of Squares: (ax + b)(ax - b)

• Sum or Difference of Cubes:

• Sum: (a + b)(a² - ab + b²)

• Difference: (a - b)(a² + ab + b²)

• Additional Methods:

• Factoring by Grouping

• Quadratic Formula (for trinomials that don't factor easily)

Key Points:

• Factoring is reversible: Multiplying the factors should give back the original expression.

• Practice is essential to master factoring techniques.

• Factoring has applications in solving equations, simplifying expressions, and other areas of mathematics.

Remember:

• Factoring involves breaking down an expression into smaller, simpler expressions that multiply to give the original expression.

• The specific method used depends on the type of expression you're factoring.

Ch. 7 Factoring! And solving factoring equations .pdf

Download PDF • 49KB

Ch. 7 Factoring! And solving factoring equations .pdf

Download PDF • 49KB