Final answer:
The student is attempting to factor a quadratic equation using the decomposition method, but there appears to be a typo in the equation. Proper factoring requires a correct quadratic form and confirmation of the middle term before proceeding.
Step-by-step explanation:
The student is asking about a process in Algebra called factoring by decomposition, which is used to factor quadratic equations. However, it seems there could be a typo in the original question, as s2 + 78 + 6 does not appear to be a typical format for a quadratic equation (which generally is in the form ax2 + bx + c).
Assuming the question meant to express s2 + 78s + 6, we can proceed with the decomposition method which involves breaking up the middle term (78s in this case) into two terms that multiply to give the product of the first and last coefficients (s2 and 6).
To find such terms, we might look for factors of 6s2 that sum to 78s. Once we identify these two numbers, we would rewrite the middle term, split the quadratic into two binomials, and then factor by grouping. Unfortunately, with the information provided, we cannot continue as there seems to be a mistake with the initial expression.
The complete question is: Match each step with the correct expression to factor s2 + 78 + 6 by using the decomposition method. is: