could i get a step by step explanation for factoring this trinomial?
i don't seem to understand how to get the final answer as i always get 2x(x+2)+x+2
2x^2+5x+2
you do kind of a reverse FOILing
to get 2x^2 ... 2x and x
to get 2 ... 2 and 1
now pair them up to get 5x as the center term
(2x + 1) (x + 2) ... FOILing ... 2x^2 + 4x + x + 2
Of course! I can help you with factoring the trinomial 2x^2 + 5x + 2 step by step.
Step 1: Identify the coefficient of the x^2 term, which is 2, and write it down.
- We'll start by writing down 2x^2.
Step 2: Identify the constant term at the end of the trinomial, which is 2, and write it down.
- We'll add + 2 at the end.
Step 3: Find the factors of the coefficient of the x^2 term, which is 2.
- The factors of 2 are 1 and 2.
Step 4: Find the factors of the constant term, which is also 2.
- The factors of 2 are 1 and 2.
Step 5: Look for a combination of the factors found in Step 3 and Step 4 that can be added or subtracted to give the coefficient of the x term, which is 5.
- In this case, the factors are 1 and 2, and adding them together gives us 3, not 5. Since we don't have a combination that satisfies this condition, we'll need to use a different method.
Step 6: Multiply the coefficient of the x^2 term, which is 2, by the constant term, which is 2.
- 2 * 2 = 4
Step 7: Look for the factors of the product found in Step 6, which is 4. These factors should also be able to be added or subtracted to give the coefficient of the x term, which is 5.
- The factors of 4 are 1 and 4, and if we add them together, we get 5.
Step 8: Rewrite the middle term, which is 5x, using the factors found in Step 7 and separate it into two parts.
- We rewrite 5x as (1x + 4x).
Step 9: Rewrite the original trinomial, replacing the middle term, 5x, with the two parts obtained in Step 8.
- 2x^2 + 1x + 4x + 2
Step 10: Group the first two terms together and the last two terms together.
- (2x^2 + 1x) + (4x + 2)
Step 11: Factor out the greatest common factor from each group.
- x(2x + 1) + 2(2x + 1)
Step 12: Notice that there is now a common binomial term, (2x + 1), in both groups.
- Combine the individual terms with the common binomial term.
- (x + 2)(2x + 1)
And there you have it! The factored form of the trinomial 2x^2 + 5x + 2 is (x + 2)(2x + 1).
It should be of form
(ax+b)(cx+d)
we need two numbers for bc and ad that add to 5, like 1 and 4
try
(2 x + 1)(x+2) = 2 x^2 + 1 x + 4 x + 2
which is
2 x^2 + 5 x + 2 whew !
by the way
2x(x+2)+x+2
is
2x(x+2 ) + 1(x+2)
which is
(2x+1)(x+2)
so you almost had it right