y^3-13y^2+36y

Can someone please show me step by step that way I can understand. Thank you

first notice that you can factor out the y, leaving

y(y^2-13y+36)
Now you want two numbers that add to -13 and multiply to 36. Obviously they must both be negative. Easy factors of 36 are

1,36 2,18 3,12 4,9

It's clear that we want 4 and 9, so our polynomial is

y(y-4)(y-9)

This factoring by inspection is mainly a skill acquired by doing a lot of problems, so you get to recognize likely factors.

Thank you soo much.. I have a lot of trouble with factoring

Certainly! Let's break it down step by step.

To factor the expression y^3 - 13y^2 + 36y, we can find the common factor of the terms, if any, and then use other methods such as factoring by grouping or applying specific factoring formulas.

Step 1: Look for common factors
In this case, we can see that all the terms have a common factor of "y". Factoring out "y" gives us:

y(y^2 - 13y + 36)

Step 2: Factor the remaining quadratic expression
Now, we need to factor the quadratic expression y^2 - 13y + 36. We are looking for two binomial factors such that when multiplied together, they give us the original quadratic expression.

To factor the quadratic expression, we need to find two numbers whose sum is -13 (the coefficient of the middle term) and whose product is 36 (the constant term). In this case, the numbers are -4 and -9, because (-4) + (-9) gives us -13 and (-4) * (-9) gives us 36.

Therefore, we can factor the quadratic expression as:

y(y - 4)(y - 9)

So, the fully factored form of the expression y^3 - 13y^2 + 36y is:

y(y - 4)(y - 9)

That's it! We have successfully factored the given expression.