Question

Identify the least common multiple of x^2 − 10x + 21 and x^2 − 5x − 14.

Answer 1

Answer:

$(x-7)(x-3)(x+2)$

Step-by-step explanation:

To answer this question we factor the expressions.

For

$x^2-10x +21$

We are looking for 2 numbers that add up and give as a result -10 and when they multiply they give as a result 21.

These numbers are -7 and -3.

Then

$x^2-10x +21 = (x-7)(x-3)$

For

$x^2 -5x -14$

We are looking for 2 numbers that add up and give as a result -5 and when they multiply they give as a result -14.

These numbers are -7 and 2.

Then

$x^2-5x -14 =(x-7)(x+2)$

Finally the minimum common multiple is the common and not common factors with its greatest exponent

$(x-7)(x+2)(x-3)$