Final answer:
The quadratic expression b² - 19b + 90 can be factored into (b - 10)(b - 9), by finding two numbers that multiply to 90 and add up to -19.
Step-by-step explanation:
The student's question pertains to factoring the quadratic expression b² - 19b + 90. This is a standard problem in algebra where the goal is to express the quadratic in the form of (b - m)(b - n), where m and n are numbers such that m*n = c (the constant term in the original quadratic) and m + n = -b (the coefficient of the linear term in the original quadratic).
To factor the given quadratic expression, we need to find two numbers whose product is 90 (the constant term) and whose sum is -19 (the coefficient of the middle term). The numbers that satisfy these conditions are -10 and -9, as (-10) * (-9) = 90 and (-10) + (-9) = -19. Therefore, the factored form of the quadratic expression is (b - 10)(b - 9).