Factor completely
8c2 - 26c + 15
by inspection
(4c-3)(2c-5)
To factor the given quadratic expression completely, we need to find two binomials that, when multiplied together, would yield the original quadratic expression.
To factor the quadratic expression 8c^2 - 26c + 15, we first look at the coefficient of the squared term (8) and the constant term (15).
The factors of 8 are 1, 2, 4, and 8.
The factors of 15 are 1, 3, 5, and 15.
Now we need to find a combination of these factors that would give us the coefficient of the linear term (-26).
The possible combinations are:
- (1, 15) which gives us 1 + 15 = 16 (not -26)
- (3, 5) which gives us 3 + 5 = 8 (not -26)
- (1, 3) which gives us 1 + 3 = 4 (not -26)
- (3, 15) which gives us 3 + 15 = 18 (not -26)
- (5, 15) which gives us 5 + 15 = 20 (not -26)
- (1, 5) which gives us 1 + 5 = 6 (not -26)
None of the combinations seem to be yielding -26.
To factor the quadratic expression completely, we can use a different approach called factoring by grouping.
We group the first two terms (8c^2 and -26c) and look for a common factor. In this case, the common factor is 2c:
2c(4c - 13)
Next, we group the last two terms (-26c and 15) and look for a common factor. In this case, the common factor is -1:
2c(4c - 13) - 1(4c - 13)
Now, we can see that we have a common binomial factor of (4c - 13). We factor it out:
(2c - 1)(4c - 13)
So, the quadratic expression 8c^2 - 26c + 15 is factored completely as (2c - 1)(4c - 13).