Factor each trinomials.
1.m^2-mv-56v^2. Thanks
To factor the trinomial m^2 - mv - 56v^2, we need to find two binomials whose product is equal to the given expression.
First, we look for two numbers that, when multiplied, give us the product of the coefficient of the squared term (m^2) and the constant term (-56v^2). In this case, the product of these two terms is -56m^2v^2.
Next, we need to find two numbers whose sum is equal to the coefficient of the linear term (-mv). In this case, the coefficient is -1m. Considering the sign, we need to find two numbers whose sum is -1. Let's call the two numbers p and q.
Now, we need to split the linear term -mv into two terms using p and q. So, we rewrite the original trinomial as:
m^2 + (p - q)mv - 56v^2
By comparing the above expression with the original trinomial, we can conclude that:
p - q = -1 (Equation 1)
Now, we also know that the product of the two numbers p and q should be -56. So, we have:
p * q = -56 (Equation 2)
To find the values of p and q, we need to solve Equations 1 and 2 simultaneously.
By trial and error, we can find that p = 7 and q = -8 satisfy both equations.
Now, we rewrite the trinomial by splitting the linear term using p = 7 and q = -8:
m^2 + 7mv - 8mv - 56v^2
Next, we group the terms:
(m^2 + 7mv) - (8mv + 56v^2)
Then, we factor out the greatest common factor (GCF) from each group:
m(m + 7v) - 8v(m + 7v)
Finally, we can factor the trinomial by factoring out the common binomial factor (m + 7v):
(m - 8v)(m + 7v)
So, the factored form of the trinomial m^2 - mv - 56v^2 is (m - 8v)(m + 7v).