Factor: 9x^2 - 42x + 49
So far I have 3(3x^2 - 14x + ) I have no idea if this is right or if this equation is prime. Or if I'm solving it correctly.
tip
9x^2 - 42x + 49=0
divide through by 9
x^2 - 42x/9 + 49/9=0
then
x^2 - 14x/3 + 49/9=0
then
x^2 - 14x/3 + (7/9)^2=0
x^2 - (2)x7/3 + (7/3)^2=0
compare
(x-a)^2=x^2-2ax+a^2
does this help?
I'm even more confused then before.
2ax+4bx-3ay-6by
To factor the quadratic expression 9x^2 - 42x + 49 completely, we can follow the steps below:
Step 1: Check if the quadratic expression can be factored using the quadratic formula or by applying other factoring strategies. In this case, the given expression is in the form of a quadratic trinomial, so it can be solved by factoring.
Step 2: Write down the first term of the factored form, which is the square root of the first term of the quadratic expression. In this case, the first term is 9x^2, so the first term of the factored form is 3x.
Step 3: Write down the last term of the factored form, which is the square root of the last term of the quadratic expression. In this case, the last term is 49, so the last term of the factored form is 7.
Step 4: Find two numbers whose product is the product of the coefficient of the middle term (which is -42) and the constant term (which is 49) and whose sum is the coefficient of the middle term (-42). In this case, the numbers are -7 and -7, since (-7) * (-7) = 49 and (-7) + (-7) = -14.
Step 5: Rewrite the middle term (-42x) using the two numbers found in the previous step (-7 and -7), splitting the middle term. This gives us -7x - 35x = -42x.
Step 6: Now, we can write the factored form using the information collected so far. The factored form becomes:
(3x - 7)(3x - 7)
Step 7: Simplify the factored form. Since we ended up with the same binomial twice, we can rewrite it in a simpler form:
(3x - 7)^2
So, the factored form of the quadratic expression 9x^2 - 42x + 49 is (3x - 7)^2.