Question

Part A: Factor 3x2c2 + 5xc2 − 2c2. Show your work. (4 points) Part B: Factor x2 + 6x + 9. Show your work. (3 points) Part C: Factor x2 − 9. Show your work. (3 points) (10 points)

Answer 1

`\boxed{\mathrm{view \: explanation}}`

Explanation:

A) 3x²c² + 5xc² - 2c²

Factor c² from all terms in the expression.

c²(3x² + 5x - 2)

Factor 3x² + 5x - 2

c²(3x-1)(x+2)

B) x² + 6x + 9

x² + 3x + 3x + 9

Factor common terms.

x(x+3)+3(x+3)

Take x+3 common.

(x+3)(x+3)

C) x² - 9

x² -3²

Apply formula : a² - b² = (a+b)(a-b)

(x+3)(x-3)

Answer 2

A)
`c^2(3x-1)(x+2)`

B)
`(x+3)(x+3)`

C)
`(x+3)(x-3)`

Explanation:

Part A:

`3x^2c^2+5xc^2-2c^2`

Taking
`c^2` common

`c^2(3x^2+5x-2)`

Using mid term break formula

`c^2 (3x^2+6x-x-2)`

`c^2[3x(x+2)-1(x+2)]`

`c^2(3x-1)(x+2)`

Part B:

`x^2 + 6x + 9.`

`(x)^2+2(x)(3)+(3)^2`

`(x+3)^2`

`(x+3)(x+3)`

Part C:

`x^2-9`

`(x)^2-(3)^2`

`(x+3)(x-3)`