The expression y² - 10y + 24 has a factor of y - 4. What is another factor of y² - 10y + 24?

Solution:

Let us factorize the polynomial using the middle term.

Step 1: Factorize by splitting the middle term.

y² - 10y + 24

The middle term can be split into the factors of 24 as -6 and -4 which on multiplying give the third term and on adding give the second term.

y² - 6y - 4y + 24

Step 2: Take out the common factors from the first two terms and from the last two terms separately.

y² - 6y - 4y + 24

y(y - 6) - 4(y - 6)

(y - 4)(y - 6)

Thus if one factor is (y-4), the other factor is (y-6)

The expression y² - 10y + 24 has a factor of y - 4. What is another factor of y² - 10y + 24?

Summary:

Thus, the other factor for the expression y² - 10y + 24 is y - 6.