What is the complete factorization of x2 + 2x − 63? A. (x + 21)(x − 3) B. (x − 9)(x + 7) C. (x + 9)(x − 7) D. (x − 21)(x + 3)
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Answer:
(x + 9)(x - 7)
Step-by-step explanation:
We want to factorize
We need to find two numbers such that their product is -63 and they add up to +2. The two numbers are +9 and -7:
The complete factorization is (x + 9)(x - 7)
The factored form of the expression x² + 2x - 63 is (x + 9)(x - 7).
What is the factored form of the expression?
Given the expression in the question:
x² + 2x - 63
To determine the complete factorization of the quadratic expression x² + 2x - 63, we aim to break it down into its simplest factors.
This is achieved through factoring, a process of identifying the expressions that, when multiplied, result in the original quadratic expression.
x² + 2x - 63
Now, find a pair of integers whose sum equals 2,
and whose product equals -63.
We use integers 9 and -7.
Next, rewrite the quadratic expression using these factors:
(x + 9)(x - 7)
Therefore, the complete factorization of x² + 2x - 63 is (x + 9)(x - 7).
Option C) (x + 9)(x - 7) is the correct answer.
Learn more about factorization here: brainly.com/question/20293447
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4*4 = 16
4+4= 8
16/8 =2
Another possibility is 3 and 6
3*6 =18
3+6 =9
18/9=2
There are many other possibilities. Basically the question is saying that if you multiply two numbers, the number you get is twice as large as if you were to add the two numbers.
[42 ÷ (2 + 3 • 2)] + [4 • (36 – 52)]
I really need help!!!
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other side 36 - 52 = 16 * 4 = 64 now add 4.2 + 64 = 68.2
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Part B: Explain in words how to graph the solution to the inequality on a number line. (4 points)
Part C: Find two values that would make the inequality true. Explain how you know the values are solutions to the inequality. (4 points)
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Answer: Sure, I can help you with that!
Part A: To solve the inequality −6(x − 3) > 42, we first need to distribute the -6 to the expression inside the parentheses:
-6(x - 3) > 42 -6x + 18 > 42
Next, we’ll subtract 18 from both sides:
-6x > 24
Finally, we’ll divide both sides by -6. Since we’re dividing by a negative number, we need to flip the inequality sign:
x < -4
Therefore, the solution to the inequality is x < -4.
Part B: To graph the solution to this inequality on a number line, we’ll start by drawing an open circle at -4 (since x is not equal to -4). Then, we’ll draw an arrow pointing to the left of -4 to indicate that all values less than -4 are solutions to the inequality.
Part C: To find two values that would make the inequality true, we can choose any two values less than -4 and substitute them into the original inequality. For example, if we choose x = -5, then:
-6(-5 - 3) > 42 -6(-8) > 42 48 > 42
Since 48 is greater than 42, this confirms that x = -5 is a solution to the inequality. Similarly, if we choose x = -10, then:
-6(-10 - 3) > 42 -6(-13) > 42 78 > 42
Since 78 is also greater than 42, this confirms that x = -10 is also a solution to the inequality.
I hope this helps!