back to *Algebra*
# Polynomial Examples

### Factoring Polynomial Examples

### Factoring Polynomial Example 1

### Factoring Polynomial Example 2

### Factoring Polynomial Example 3

### Factoring Polynomial Example 4

### Factoring Polynomial Example 5

### Rule of Multiply Two Polynomials

### Multiply Polynomials Example 1

### Multiply Polynomials Example 2

### Multiply Polynomials Example 3

**Common Factors**- xy + xz = x ( y + z )
- In the example above, x is a common factor of xy and xz on the left side of the equation.

**Greatest Common Factor (GCF)**- 8x
^{2}+ 12x = 4x ( 2x + 3 ) - In the example above, 4x is the GCF of the term 8x
^{2}+ 12x

- Question
- Factoring the polynomial x
^{2}+ 2x

- Solution
- x
^{2}+ 2x = x ( x + 2 ) - In the question above, x is common factor of x
^{2}+ 2x on the left side of equation.

- Question
- Factoring the polynomial 12x
^{3}+ 6x^{2}

- Solution
- 12x
^{3}+ 6x^{2}= 6x^{2}( 2x + 1 ) - In the question above, 6x
^{2}is GCF of the term 12x^{3}and 6x^{2}on the left side of the equation.

- Question
- Factoring the polynomial x
^{2}- 1

- Solution
- x
^{2}- 1 - = x
^{2}+ x - x - 1 - = x ( x + 1 ) - ( x + 1 )
- = ( x + 1 ) ( x - 1 )
- In the question above, (x + 1) is common factor and x
^{2}- 1 can be factor as (x + 1)(x - 1)

- Question
- Factoring the polynomial a
^{2}- b^{2}

- Solution
- a
^{2}- b^{2} - = a
^{2}+ ab - ab - b^{2} - = a ( a + b ) - b ( a + b )
- = ( a + b ) ( a - b )
- In the question above, (a + b) is common factor and a
^{2}- b^{2}can be factor as (a + b)(a - b)

- Question
- Factoring the polynomils: x
^{3}- 2x^{2}- 5x + 6

- Solution
- Since 6 = 2 × 3, so try to divide ( x - 3) first
- Thus, x
^{3}- 2x^{2}- 5x + 6 = ( x - 3 )( x^{2}+ x - 2 ) - Now, factoring x
^{2}+ x - 2 - Therefore, x
^{3}- 2x^{2}- 5x + 6 = (x - 3)(x - 1)( x + 2)

- Multiply two polynomials,
- multiply each term of one polynomial by each term of the other and then simplify the result by combining like terms.

- Question
- Multiply two binomials ( x + a ) ( x + b ) = ?

- Solution:
- ( x + a ) ( x + b )
- = (x)(x) + (x)(b) + (a)(x) + (a)(b)
- = (x)(x) + (b)(x) + (a)(x) + (a)(b)
- = x
^{2}+ (a + b)x + a b - note: bx and ax are similar (like) terms

- Example
- Multiply two binomials ( x + 3 ) ( x + 4 ) and write the product directly

- Solution

- Example
- Multiply polynomial ( 2x + 3 ) ( 3x - 5 ) = ?

- Solution
- ( 2x + 3 ) ( 3x - 5 )
- = (2x)(3x) + (2x)(-5) + (3)(3x) + (3)(-5)
- = 6x
^{2}- 10x + 9x - 15 - = 6x
^{2}- x - 15

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