Look for a GCF first, then trinomial or difference of 2 squares
1. 2x3 - 32x
2. 4x2 + 24x + 20

2x (x-4) (x+4)

4(x+3)(x+2)

Step-by-step explanation:

1. 2x^3 - 32x

Factor out 2x

2x(x^2 - 16)

2x( x^2 - 4^2)  

This is the difference of squares ( a^2 - b^2) = (a-b) (a+b)

2x (x-4) (x+4)

2. 4x^2 + 24x + 20

Factor out 4

4 (x^2 +6x +5)

What 2 numbers multiply to 5 and add to 6

3*2 =6

3+2 =5

4(x+3)(x+2)

1. 2x(x - 4)(x + 4)

2. 4(x + 1)(x + 5)

Step-by-step explanation:

1. 2x³ - 32x

2x(x² - 16)

2x(x² - 4²)

2x(x - 4)(x + 4)

2. 4x² + 24x + 20

4(x² + 6x + 5)

4(x² + 5x + x + 5)

4[x(x + 5) + 1(x + 5)]

4(x + 1)(x + 5)

Smallest number = 3500

Step-by-step explanation:

Rounding of numbers involve replacing numbers with simpler numbers. In order to round a number to the nearest thousand, the last 3 digits of the number should be considered. If the last 3 digits are less than 500, the number is rounded down(the thousand figure is unaffected), but if the last 3 digits are greater or equal to 500, the number is rounded up.

In this case, Yuri is thinking of a 4-digit whole number and he rounds his number to the nearest thousand. Since his answer is 4000, the smallest number yuri could be thinking of would be 3500 and the highest number he could be thinking of is 4499.

Thus, the smallest number Yuri could be thinking of is 3500