Final answer:
To factorize 7x^2-45x+28, we can use the AC method or the box method. The expression can be factored as (7x - 4)(x - 7).
Step-by-step explanation:
To factorize the expression 7x^2-45x+28, we need to find two binomial expressions that, when multiplied together, give us the original expression. To do this, we can use a factoring method called the AC method or the box method.
First, we need to multiply the coefficient of the quadratic term (7) and the constant term (28), which gives us 196. We then need to find two numbers that multiply to 196 and add up to the coefficient of the linear term (-45). After trying different combinations, we find that the numbers are -4 and -49.
Next, we split the linear term (-45x) into two terms (-4x and -49x). We can now group the terms and factor by grouping. So the given expression can be factored as (7x - 4)(x - 7).