Question

factor.

1. $18x^{2}+24x+8$
2. $25x^{3}-10x^{2}+x$
3. $9x^{3}+6x^{2}+x$
4. $50x^{3}+20x^{2}+2x$

Explanation:

1. Factor $18x^2 + 24x + 8$

Step1: Factor out GCF

$18x^2 + 24x + 8 = 2(9x^2 + 12x + 4)$

Step2: Factor quadratic trinomial

$9x^2 + 12x + 4 = (3x+2)^2$

Step3: Combine results

$2(3x+2)^2$

2. Factor $25x^3 - 10x^2 + x$

Step1: Factor out GCF

$25x^3 - 10x^2 + x = x(25x^2 - 10x + 1)$

Step2: Factor quadratic trinomial

$25x^2 - 10x + 1 = (5x-1)^2$

Step3: Combine results

$x(5x-1)^2$

3. Factor $9x^3 + 6x^2 + x$

Step1: Factor out GCF

$9x^3 + 6x^2 + x = x(9x^2 + 6x + 1)$

Step2: Factor quadratic trinomial

$9x^2 + 6x + 1 = (3x+1)^2$

Step3: Combine results

$x(3x+1)^2$

4. Factor $50x^3 + 20x^2 + 2x$

Step1: Factor out GCF

$50x^3 + 20x^2 + 2x = 2x(25x^2 + 10x + 1)$

Step2: Factor quadratic trinomial

$25x^2 + 10x + 1 = (5x+1)^2$

Step3: Combine results

$2x(5x+1)^2$

Answer:

1. $2(3x+2)^2$
2. $x(5x-1)^2$
3. $x(3x+1)^2$
4. $2x(5x+1)^2$