Jenny wanted to solve the quadratic equation x2 - 11x +18 = 0 by factoring. Which of the following equations would lead her to solve the given equation?
Factor pair :
( - 2 , - 9 )
So :
x ^ 2 - 11 x + 18 = ( x - 2 ) ( x - 9 ) = 0
To solve the quadratic equation x^2 - 11x + 18 = 0 by factoring, we need to find two numbers whose product is 18 and whose sum is -11 (the coefficient of x).
Let's list the factors of 18:
1, 2, 3, 6, 9, 18
Now we need to find two numbers whose sum is -11:
-3 + -6 = -9 ≠ -11
-2 + -9 = -11
Therefore, the equation that would lead Jenny to solve the given quadratic equation is:
(x - 2)(x - 9) = 0
To solve the quadratic equation x^2 - 11x + 18 = 0 by factoring, we need to find two numbers that multiply to give 18 and add up to give -11 (the coefficient of x).
The factors of 18 are:
1, 18
2, 9
3, 6
From these factor pairs, we can test which pair satisfies the condition of adding up to -11.
The pair that satisfies this condition is 2 and 9.
So, to solve the given equation by factoring, we can rewrite it as (x - 2)(x - 9) = 0.
Therefore, the equation that would lead Jenny to solve the given equation is (x - 2)(x - 9) = 0.