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Answer:
4(k - 3)(3k + 5)
Step-by-step explanation:
Given
12k² - 16k - 60 ← factor out 4 from each term
= 4(3k² - 4k - 15) ← factor the quadratic
Consider the factors of the product of the coefficient of the k² term and the constant term which sum to give the coefficient of the k term
product = 3 × - 15 = - 45 , sum = - 4
Factors are - 9 and + 5
Use these factors to split the middle term
3k² - 9k + 5k - 15 → ( factor the first/second and third/fourth terms
= 3k(k - 3) + 5(k - 3) ← factor out (k - 3)
= (k - 3)(3k + 5)
Hence
12k² - 16k - 60 = 4(k - 3)(3k + 5) ← in factored form
See the attached picture for the solution:
