factor completely: 16x^2 + 16x-21
I got not factorable...
(4x-3)(4x+7)
i got it...
To factor the quadratic expression 16x^2 + 16x - 21 completely, you can use the factoring method or the quadratic formula.
Let's try factoring first:
Step 1: Multiply the coefficient of the squared term (16) by the constant term (-21).
16 * -21 = -336
Step 2: Find two numbers that multiply together to give you -336 and add up to the coefficient of the linear term (16).
The two numbers are 28 and -12 since 28 * -12 = -336 and 28 + (-12) = 16.
Step 3: Rewrite the middle term (16x) using the two numbers found in Step 2.
16x = 28x - 12x
Now we can rewrite the initial quadratic expression as:
16x^2 + 28x - 12x - 21
Step 4: Group the expression into two terms, taking common factors from each group.
(16x^2 + 28x) - (12x + 21)
4x(4x + 7) - 3(4x + 7)
Step 5: Notice that we now have a common binomial factor of (4x + 7). We can factor this out.
(4x + 7)(4x - 3)
So, the completely factored form of the quadratic expression 16x^2 + 16x - 21 is:
(4x + 7)(4x - 3)