Question

Which method would be appropriate to factor the polynomial below. 55x^3-40x^2 -Difference of Squares -Basic Trinomial Factoring -AC Method -Sums of Cubes -Greatest Common Factor -Factors by grouping

Answer 1

Greatest Common Factor

Explanation:

Let
`55\cdot x^(3)-40\cdot x^(2)`, we proceed to demonstrate the appropriate form to factor the polynomial:

1)
`55\cdot x^(3)-40\cdot x^(2)` Given.

2)
`(5\cdot 11)\cdot (x^2\cdot x) +[5\cdot (-8)]\cdot x^(2)` Definition of multiplication and subtraction/
`a^(b+c) = a^(b)\cdot a^(c )`/
`-a\cdot b = (-a)\cdot b`/Associative property

3)
`(5\cdot x^(2))\cdot (11\cdot x)+ (5\cdot x^(2))\cdot (-8)` Commutative and associative properties

4)
`5\cdot x^(2)\cdot (11\cdot x-8)` Distributive property/Definition of subtraction/Result

Hence, we conclude that this polynomial can be factored by Greatest Common Factor.