The area of a rectangular painting is given by the trinomial x^2+2x-15. What are the possible dimensions of the painting? Use factoring.
( x + 5 ) and ( x - 3 )
( x + 5 ) and ( x + 3 )
( x - 5 ) and ( x - 3 )
( x - 5 ) and ( x + 3 )
since there is a -15 at the end and a +2x in the center, you want two factors of 15 which differ by 2. Those are 5 and 3. Now, you want one + and one -, so +5-3 = +2
(x+5)(x-3) = x^2+2x-15
Ohhhhh thanks SO MUCH Steve!
do anybody got the whole final test?
if you got the answers to the whole test or already took the test please post them.
why the got me tho
Lol I like how these are only posted in May. Thx for te answers btw!
To find the possible dimensions of the painting, we need to factor the trinomial x^2 + 2x - 15.
Step 1: Multiply the coefficient of x^2 and the constant term: 1 * -15 = -15.
Step 2: Find two numbers that multiply to -15 and add up to the coefficient of x, which is 2. In this case, the numbers are 5 and -3 since 5 * -3 = -15 and 5 + (-3) = 2.
Step 3: Rewrite the trinomial using these two numbers: x^2 + 5x - 3x - 15.
Step 4: Group the terms and factor by grouping: (x^2 + 5x) + (-3x - 15) = x(x + 5) - 3(x + 5).
Step 5: Factor out the common factor (x + 5): (x + 5)(x - 3).
Therefore, the possible dimensions of the painting are (x + 5) and (x - 3).
Option 1: (x + 5) and (x - 3) - This is the correct answer since it matches the factored form obtained above.
Option 2: (x + 5) and (x + 3) - This is not correct because the signs are incorrect for one of the factors.
Option 3: (x - 5) and (x - 3) - This is not correct because the signs are incorrect for one of the factors.
Option 4: (x - 5) and (x + 3) - This is not correct because the signs are incorrect for one of the factors.