factor the expression:
10a^2-19a+7
ok I no how to start of which would be
(10a- )(a+ )
but i don't no how to factor it from here
If you are in a class-room situation, then you should have been taught some kind of "method" to do these, just plain guessing works only up to a point.
there are actually two choices for the first terms
(10x..)(x...) or (5x....)(2x....)
at the back it would have to be
(..-7)(...-1) or (...+7)(...+1)
remember, after you make your choice, expand to see if you get the original.
ok i get it now i just didn't no what to do with the middle number
To factor the expression 10a^2 - 19a + 7 completely, follow these steps:
Step 1: Look for two numbers whose product is equal to the product of the coefficient of the quadratic term (10) and the constant term (7), which is 70. Additionally, these two numbers must add up to the coefficient of the linear term (-19). The two numbers in this case are -10 and -7, because (-10) * (-7) = 70, and (-10) + (-7) = -17.
Step 2: Rewrite the middle term (-19a) using these numbers. Split the middle term by replacing it with -10a - 7a.
10a^2 - 19a + 7 becomes: 10a^2 - 10a - 7a + 7
Step 3: Factor by grouping. Group the first two terms and the last two terms separately, and factor out the common terms from each group.
10a^2 - 10a - 7a + 7 becomes: 10a(a - 1) - 7(a - 1)
Step 4: Notice how (a - 1) is common in both groups. Factor it out.
10a(a - 1) - 7(a - 1) becomes: (10a - 7)(a - 1)
Therefore, the factored form of the expression 10a^2 - 19a + 7 is (10a - 7)(a - 1).