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Using factorization, the expression x² + x - 20 = ?
- a)(x + 4) (x + 5)
- b)(x + 4)(x - 5)
- c)(x - 4) (x + 5)
- d)(x -4) (x -5)
Correct answer is option 'C'. Can you explain this answer?
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Using factorization, the expression x² + x - 20 = ?a)(x + 4) (x +...
To factorize the expression x^2 - 20, we need to find two binomials whose product is equal to this expression.
1. Identify the common factors:
The expression x^2 - 20 does not have any common factors, so we move on to the next step.
2. Determine the sum and product of the factors:
We are looking for two numbers whose product is -20 and whose sum is 0 (since there is no coefficient of x^2). The numbers that satisfy these conditions are -4 and 5.
3. Write the expression in factored form:
Using the numbers -4 and 5, we can write the expression as:
x^2 - 20 = (x - 4)(x + 5)
Explanation of the factored form:
The factored form of the expression x^2 - 20 is (x - 4)(x + 5). Let's break it down:
1. (x - 4):
This factor represents one of the solutions to the equation x^2 - 20 = 0. When x = 4, this factor becomes zero, satisfying the equation.
2. (x + 5):
This factor represents the other solution to the equation x^2 - 20 = 0. When x = -5, this factor becomes zero, satisfying the equation.
Together, the factors (x - 4)(x + 5) represent all possible solutions to the equation x^2 - 20 = 0.
Conclusion:
The correct factored form of the expression x^2 - 20 is (x - 4)(x + 5), which corresponds to option (c) (x - 4)(x + 5) in the given options.
1. Identify the common factors:
The expression x^2 - 20 does not have any common factors, so we move on to the next step.
2. Determine the sum and product of the factors:
We are looking for two numbers whose product is -20 and whose sum is 0 (since there is no coefficient of x^2). The numbers that satisfy these conditions are -4 and 5.
3. Write the expression in factored form:
Using the numbers -4 and 5, we can write the expression as:
x^2 - 20 = (x - 4)(x + 5)
Explanation of the factored form:
The factored form of the expression x^2 - 20 is (x - 4)(x + 5). Let's break it down:
1. (x - 4):
This factor represents one of the solutions to the equation x^2 - 20 = 0. When x = 4, this factor becomes zero, satisfying the equation.
2. (x + 5):
This factor represents the other solution to the equation x^2 - 20 = 0. When x = -5, this factor becomes zero, satisfying the equation.
Together, the factors (x - 4)(x + 5) represent all possible solutions to the equation x^2 - 20 = 0.
Conclusion:
The correct factored form of the expression x^2 - 20 is (x - 4)(x + 5), which corresponds to option (c) (x - 4)(x + 5) in the given options.
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Community Answer
Using factorization, the expression x² + x - 20 = ?a)(x + 4) (x +...
Since the sum is in positive the greater should have the positive sign. And product is in negative -4 is multipiled
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Using factorization, the expression x² + x - 20 = ?a)(x + 4) (x + 5)b)(x + 4)(x - 5)c)(x - 4) (x + 5)d)(x -4) (x -5)Correct answer is option 'C'. Can you explain this answer?
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