To find the values of a and b, we can expand the right side of the equation and compare it to the given equation.
(x+a)(x+b) = x^2 + (a+b)x + ab
Now, we know that the equation x^2 - 13x + 42 is equivalent to the expanded form x^2 + (a+b)x + ab. By comparing the coefficients of x and the constant term on both sides, we can determine the values of a and b.
From the equation x^2 - 13x + 42 = x^2 + (a+b)x + ab, we can see that a + b = -1 ab = 42
Now, we need to find two numbers that multiply to 42 and add up to -13. These two numbers are -6 and -7.
To find the values of a and b, we can expand the right side of the equation and compare it to the given equation.
(x+a)(x+b) = x^2 + (a+b)x + ab
Now, we know that the equation x^2 - 13x + 42 is equivalent to the expanded form x^2 + (a+b)x + ab. By comparing the coefficients of x and the constant term on both sides, we can determine the values of a and b.
From the equation x^2 - 13x + 42 = x^2 + (a+b)x + ab, we can see that
a + b = -1
ab = 42
Now, we need to find two numbers that multiply to 42 and add up to -13. These two numbers are -6 and -7.
Therefore, a = -6 and b = -7.
So, x^2 - 13x + 42 = (x-6)(x-7).