how to factor this equation algebraically?
2a^2-84a+70
Thank you for helping me and any help given will be greatly appreciated.
And to solve this you probably have to use the factor theorem.
2(35 + -42a + a2)
use algebrahelp(dot)com/calculators/expression/factoring/
but sub the dot for a period
To factor the equation 2a^2 - 84a + 70 algebraically, you can follow these steps:
Step 1: Check if there is a common factor among the coefficients of the terms. In this case, the coefficient 2 is a common factor, which we can factor out:
2(a^2 - 42a + 35)
Step 2: Factor the quadratic expression inside the parentheses. To do this, look for two numbers that multiply to give the constant term (35) and add up to give the coefficient of the middle term (-42). In this case, -5 and -7 satisfy these conditions:
2(a^2 - 5a - 7a + 35)
Step 3: Group the terms into two pairs:
2[(a^2 - 5a) + (-7a + 35)]
Step 4: Factor the common factor out of each pair:
2[a(a - 5) - 7(a - 5)]
Step 5: Notice that (a - 5) is a common factor. Factor it out:
2(a - 5)(a - 7)
Therefore, the factored form of the equation 2a^2 - 84a + 70 is 2(a - 5)(a - 7).
Regarding your mention of the factor theorem, the factor theorem is typically used to determine whether or not a given polynomial has a certain factor. In this case, we simply factored the expression algebraically without using the factor theorem.