Final answer:
To factor the quadratic equation, we find two numbers that multiply to get the product of the coefficient of 'a^2' (6) and the constant term (252), and add up to the coefficient of 'a' (-78). Upon finding that -42 and -36 meet these conditions, we rewrite, group, and factor the equation to get (3a - 18)(2a - 14), which matches answer option B.
Step-by-step explanation:
To factor the quadratic equation №6a^2 - 78a + 252№, we will first look for two numbers that multiply to give the product of the coefficient of №a^2№ (which is 6) and the constant term (which is 252), and at the same time, add up to -78, the coefficient of the linear term №a№. In this case, the product is 6 * 252 = 1512. We are looking for factors of 1512 that add up to -78.
After checking the factors of 1512, we find that -42 and -36 are the numbers we are looking for because (-42) * (-36) = 1512 and -42 + -36 = -78. So we can write -78a as -42a - 36a.
The equation 6a^2 - 78a + 252 can be rewritten as:
6a^2 - 42a - 36a + 252
By grouping, we get:
(6a^2 - 42a) + (-36a + 252)
Factoring out the common factors, we get:
6a(a - 7) - 36(a - 7)
Now we can factor out (a - 7), giving us:
(3a - 18)(2a - 14), which matches with answer choice B.