i am doing factoring with quadratic trinomials, And I don't understand any of it!
The problem im working on is
5p2-22p+8
I factored it out to be
(5p2-20p)(40p2-2p)
I am so stuck, can anyone help
Of course, I can help you with factoring quadratic trinomials. Let's start by understanding the process step by step.
To factor a quadratic trinomial, we are essentially trying to find two binomials that, when multiplied together, give us the original trinomial.
In the case of the trinomial you provided, 5p^2 - 22p + 8, we need to find two binomials in the form (ap + b)(cp + d) that can be multiplied to give us this trinomial.
Here's how we can proceed:
Step 1: Multiply the coefficient of the leading term (5p^2) by the constant term (8). In this case, it is 5 x 8 = 40.
Step 2: We need to find two numbers that multiply to give 40 and add up to the coefficient of the middle term (-22p). In this case, the numbers are -20 and -2 because (-20) x (-2) = 40 and (-20) + (-2) = -22.
Step 3: Rewrite the middle term (-22p) using the two numbers (-20 and -2) found in step 2. This gives us 5p^2 - 20p - 2p + 8.
Step 4: Group the terms into two pairs. The first pair is 5p^2 - 20p and the second pair is -2p + 8.
Step 5: Factor out the greatest common factor (GCF) from each pair. In the first pair, the GCF is 5p, and in the second pair, the GCF is -2.
Step 6: After factoring out the GCF, we obtain: 5p(p - 4) - 2(p - 4).
Step 7: Notice that we now have a common binomial factor of (p - 4). Factor out this binomial: (p - 4)(5p - 2).
Therefore, the completely factored form of the quadratic trinomial 5p^2 - 22p + 8 is (p - 4)(5p - 2).
So, your original factorization of (5p^2 - 20p)(40p^2 - 2p) was not correct. But by following the steps I just explained, we can correctly factor the given trinomial.