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# Polynomial Examples

### Factoring Polynomial Examples

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)
8x2 + 12x = 4x ( 2x + 3 )
In the example above, 4x is the GCF of the term 8x2 + 12x

### Factoring Polynomial Example 1

Question
Factoring the polynomial x2 + 2x
Solution
x2 + 2x = x ( x + 2 )
In the question above, x is common factor of x2 + 2x on the left side of equation.

### Factoring Polynomial Example 2

Question
Factoring the polynomial 12x3 + 6x2
Solution
12x3 + 6x2 = 6x2 ( 2x + 1 )
In the question above, 6x2 is GCF of the term 12x3 and 6x2 on the left side of the equation.

### Factoring Polynomial Example 3

Question
Factoring the polynomial x2 - 1
Solution
x2 - 1
= x2 + x - x - 1
= x ( x + 1 ) - ( x + 1 )
= ( x + 1 ) ( x - 1 )
In the question above, (x + 1) is common factor and x2 - 1 can be factor as (x + 1)(x - 1)

### Factoring Polynomial Example 4

Question
Factoring the polynomial a2 - b2
Solution
a2 - b2
= a2 + ab - ab - b2
= a ( a + b ) - b ( a + b )
= ( a + b ) ( a - b )
In the question above, (a + b) is common factor and a2 - b2 can be factor as (a + b)(a - b)

### Factoring Polynomial Example 5

Question
Factoring the polynomils: x3 - 2x2 - 5x + 6
Solution
Since 6 = 2 × 3, so try to divide ( x - 3) first Thus, x3 - 2x2 - 5x + 6 = ( x - 3 )( x2 + x - 2 )
Now, factoring x2 + x - 2 Therefore, x3 - 2x2 - 5x + 6 = (x - 3)(x - 1)( x + 2)

### Rule of Multiply Two Polynomials

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

### Multiply Polynomials Example 1

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)
= x2 + (a + b)x + a b
note: bx and ax are similar (like) terms

### Multiply Polynomials Example 2

Example
Multiply two binomials ( x + 3 ) ( x + 4 ) and write the product directly
Solution ### Multiply Polynomials Example 3

Example
Multiply polynomial ( 2x + 3 ) ( 3x - 5 ) = ?
Solution
( 2x + 3 ) ( 3x - 5 )
= (2x)(3x) + (2x)(-5) + (3)(3x) + (3)(-5)
= 6x2 - 10x + 9x - 15
= 6x2 - x - 15