factor this expression
x^2 + 11x + 28
I know the answer is (x+ 4) (X + 7)
BUT
can you walk me through each step
thank you from the bottom of my heart
the x^2 factors to x and x
the 28 has to factor into two numbers that sum to 11 ... like 4 and 7
when you FOIL the two binomials, (x + 4)(x + 7)
... you get ... x^2 + 11x + 28
Of course, I'd be happy to walk you through the steps of factoring the expression! To factor the quadratic expression x^2 + 11x + 28, follow these steps:
Step 1: Write down the expression: x^2 + 11x + 28.
Step 2: Look for two numbers whose product is equal to the product of the coefficient of x^2 (which is 1) and the constant term (which is 28 in this case). In other words, find two numbers whose product is 1 * 28 = 28 and whose sum is equal to the coefficient of x (which is 11).
In this case, the numbers that satisfy these conditions are 4 and 7 because 4 * 7 = 28 and 4 + 7 = 11.
Step 3: Rewrite the middle term of the quadratic expression (11x) using the two numbers found in Step 2. So, we can rewrite 11x as 4x + 7x.
Now, our expression becomes x^2 + 4x + 7x + 28.
Step 4: Group the terms in pairs and factor out the greatest common factor from each pair.
So, in this case, we have: x(x + 4) + 7(x + 4).
Step 5: Notice that we now have a common factor, (x + 4), in both terms. Factor out this common factor.
So, the expression can be written as: (x + 4)(x + 7).
And there you have it! The factored form of the expression x^2 + 11x + 28 is (x + 4)(x + 7).