Final answer:
The student's question is about factoring the quadratic expression 12k^2 - 26k + 12. If it can be factored, the goal is to rewrite it as the product of two binomials. If the expression cannot be factored easily, the quadratic formula is used.
Step-by-step explanation:
The student's question involves factoring quadratics, specifically the quadratic expression 12k^2 - 26k + 12. To factor this, we need to find two binomials that multiply to get the original expression. The process of factoring breaks down the expression into a product of simpler expressions.
In general, a quadratic equation of the form at² + bt + c = 0 can often be factored if there are two numbers that multiply to ac (the product of the coefficient of t² and the constant term) and add up to b (the coefficient of t). However, if it is not factorable, one can use the quadratic formula to find the roots:
Quadratic formula: x = −(b ± √(b² - 4ac))/(2a)
In the case of the student's expression, one would seek factors of 12∗(+12) that sum to −26. If such factors are found, we can then write the expression as a product of two binomials. If not, the quadratic formula is the alternative method to solve for the variable k.