Answer:
So the solutions to the equation x² + 9x - 10 = 0 are x = 0 and x = -9.
To find the missing numbers in the factorized form (x − _)(x + —), we need to determine the numbers that, when multiplied, give -10 and, when added, give 9. In this case, the numbers are -10 and 1, since -10 * 1 = -10 and -10 + 1 = 9. Therefore, the factorized form is:
(x − 1)(x + 10)
Explanation:
A) To factorize the expression x² + 9x, we can look for common factors. In this case, both terms have an x, so we can factor out an x:
x(x + 9)
B) Now, let's use the answer from part A to solve the equation x² + 9x - 10 = 0. We can rewrite the equation as:
x(x + 9) - 10 = 0
Expanding the expression, we get:
x² + 9x - 10 = 0
Since we already have the expression in factored form, we can set each factor equal to zero:
x = 0
x + 9 = 0
Solving for x in each equation, we find:
x = 0
x = -9
So the solutions to the equation x² + 9x - 10 = 0 are x = 0 and x = -9.
To find the missing numbers in the factorized form (x − _)(x + —), we need to determine the numbers that, when multiplied, give -10 and, when added, give 9. In this case, the numbers are -10 and 1, since -10 * 1 = -10 and -10 + 1 = 9. Therefore, the factorized form is:
(x − 1)(x + 10)