x^2+13x+42
what is the expression in factored form? show all steps
To factor the expression x^2 + 13x + 42, we need to find two numbers that multiply to 42 and add up to 13.
The numbers that fit these criteria are 6 and 7.
Now we can rewrite the expression:
x^2 + 13x + 42 = (x + 6)(x + 7)
Therefore, the factored form of the expression x^2 + 13x + 42 is (x + 6)(x + 7).
now factor: 9x^2-4
To factor the expression 9x^2 - 4, we recognize it as a difference of squares because it can be written as (3x)^2 - 2^2.
The formula for factoring a difference of squares is: a^2 - b^2 = (a + b)(a - b)
Using this formula, we can rewrite the expression:
9x^2 - 4 = (3x + 2)(3x - 2)
Therefore, the factored form of the expression 9x^2 - 4 is (3x + 2)(3x - 2).