I need help factoring a problem and cant seem to get it right. The one I'm stumped on is 2x^2+7x+2. I have to compute as indicated and write final in the lowest terms.
The whole problem is
x^2-7x-18/x^2-6x-27*2x^2+7x+2/2x^2+5x+2
2x^2 + 7x + 2 does not factor using rational numbers.
Here is how I know
Multiply the first times the last ---> 2(2) = 4
Are there two numbers which when multiplied will give you 4 and which added will give you 7 ?
Nope!
I think your problem is meant to say:
(x^2-7x-18)/(x^2-6x-27) * (2x^2+7x+2)/(2x^2+5x+2)
HUGE difference from what you wrote
= (x-9)(x+2)/((x-9)(x+3) * (2x^2 + 7x + 2)/((2x+1)(x+2))
= (2x^2 + 7x + 2)/((x+3)(2x+1))
notice that if we expand the bottom we get
2x^2 + 7x + 3
are you sure you don't have a typo in the top and that 2 is not a 3 ????
If not, the book probably has that typo.
Yes it was a typo it was a 3! Thanks for the help this does make scense.
To factor the expression 2x^2 + 7x + 2, we need to find two binomials in the form (ax + b)(cx + d) that multiply together to give us the original expression. Here's how you can do that:
Step 1: Find the factors of 2 and the factors of 2x^2 (the coefficient of x^2), such that the sum of the products of the outer and inner terms of both binomials adds up to the middle term (7x).
The factors of 2 are: 1 and 2.
The factors of 2x^2 are: 1x and 2x.
Step 2: Now, we need to determine which combination of these factors will give us the middle term (7x) when multiplied. We can try different combinations:
Using the factors of 2 (1 and 2) and the factors of 2x^2 (1x and 2x), we can try:
(1x + 2)(2x + 1) or (2x + 2)(1x + 1).
Step 3: Simplify the expressions we got in Step 2 to check which one factors correctly.
(1x + 2)(2x + 1) = 2x^2 + (1x)(2) + (2)(2x) + 2 = 2x^2 + 2x + 4x + 2 = 2x^2 + 6x + 2, which is not equal to the original expression.
(2x + 2)(1x + 1) = 2x^2 + (1x)(2) + (2)(1x) + 2 = 2x^2 + 2x + 2x + 2 = 2x^2 + 4x + 2, which is also not equal to the original expression.
Since neither of these expressions matches the original expression, it seems that 2x^2 + 7x + 2 cannot be factored further using integer coefficients.
If you need to compute the given problem and write the final result in the lowest terms, you'll need to provide the entire expression.