How do you factor 12v^2-25v-7?
what does the variables mean maybe i can help you if i knew what the number was that the variable replaces
well, it's gonna be
(3v-)(4v+) or (6v-)(2v+) or something like that
Since 25 is relatively large, I'd try the 6/2 combination, except that 7 has no factors, so
(4v+1)(3v-7)
seems to work, since -25 = -28+3
good answer steve!!
To factor the quadratic expression 12v^2 - 25v - 7, we need to find two binomial factors that multiply together to give us the original expression.
Step 1: Multiply the coefficient of the quadratic term (12) by the constant term (-7). In this case, 12 * -7 = -84.
Step 2: Look for two numbers that multiply to give us -84 and add up to the coefficient of the linear term (-25). In this case, the numbers are -28 and 3, because -28 * 3 = -84 and -28 + 3 = -25.
Step 3: Split the middle term using these two numbers. Rewrite the original expression as follows:
12v^2 - 28v + 3v - 7
Step 4: Factor by grouping. Group the first two terms together and the last two terms together:
(12v^2 - 28v) + (3v - 7)
Step 5: Factor out the common factor from each group:
4v(3v - 7) + 1(3v - 7)
Step 6: Notice that we have a common binomial factor, (3v - 7), in both terms. Factor it out:
(3v - 7)(4v + 1)
Therefore, the factored form of the quadratic expression 12v^2 - 25v - 7 is (3v - 7)(4v + 1).