For each expression, find: - The factors of the first term - The factors of the second term - The greatest common factor of the two terms Expressions: 1. 3x + 6y 2. 4a³ + 2a 3. 5x - 2x² 4. ax² - bx 5. 12a²b + 18ab² Example: Expression: 3x + 6y Factors of the first term: 3; x Factors of the second term: 2; 3; y Greatest common factor: 3 Factor form: 3(x + 2y)
Answer (1)
Let's analyze each expression to find the factors of the two terms and then determine the greatest common factor (GCF).
Expression: 3 x + 6 y
Factors of the first term ( 3 x ): 3 , x
Factors of the second term ( 6 y ): 2 , 3 , y
Greatest common factor: 3
Factor form: 3 ( x + 2 y )
Expression: 4 a 3 + 2 a
Factors of the first term ( 4 a 3 ): 2 , 2 , a , a , a
Factors of the second term ( 2 a ): 2 , a
Greatest common factor: 2 a
Factor form: 2 a ( 2 a 2 + 1 )
Expression: 5 x − 2 x 2
Factors of the first term ( 5 x ): 5 , x
Factors of the second term ( − 2 x 2 ): − 1 , 2 , x , x
Greatest common factor: x
Factor form: x ( 5 − 2 x )
Expression: a x 2 − b x
Factors of the first term ( a x 2 ): a , x , x
Factors of the second term ( b x ): b , x
Greatest common factor: x
Factor form: x ( a x − b )
Expression: 12 a 2 b + 18 a b 2
Factors of the first term ( 12 a 2 b ): 2 , 2 , 3 , a , a , b
Factors of the second term ( 18 a b 2 ): 2 , 3 , 3 , a , b , b
Greatest common factor: 6 ab
Factor form: 6 ab ( 2 a + 3 b )
In each expression, we first identify the factors of the individual terms. Then, we find the greatest common factor by identifying the shared factors between the two terms. Finally, we factor the expression by dividing each term by the GCF and rewriting it in factor form.
