How do you factor 4x(squared)+12x+40?

Thanks!

4x2+12x+40=
4(x2+3x+10)

Is there any way to get it like ( ) *( )?

I don't think the term within the parentheses can be factored. The only factors of 10 are 10*1 and 5*2 and neither of those will add to 3.

To factor the expression 4x^2+12x+40, we first look for common factors. In this case, all three terms have a common factor of 4, so we can factor that out:

4x^2+12x+40 = 4(x^2+3x+10)

Now we focus on factoring the expression within the parentheses: x^2+3x+10.

To factor this expression, we look for two binomials in the form (ax+b)(cx+d) that multiply to give us x^2+3x+10. We then find the values of a, b, c, and d.

The first terms of the binomials must be x, so we have (x+a)(x+c).

The last terms of the binomials multiply to give 10, so we need to find factors of 10: 1*10 and 2*5.

Now we look for the combination of factors where the sum of the middle terms, 3x, is obtained. From the factors of 10, we see that 1+10 and 2+5 are the options.

The combination that gives us the middle term is 2+5, so we have (x+2)(x+5).

Now we can put the whole expression together:

4x^2+12x+40 = 4(x+2)(x+5)

This is the factored form of the expression.