Classify a. acute b. obtuse c. right d. straight
1 answer:
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Answer:
f(x) = 2x³ - 5x² + 7x - 7
Step-by-step explanation:
In the division statement: m ÷ n = q +
- m is the dividend
- n is the divisor
- q is the quotient
- r is the remainder
- m = q × n + r
Let us use the fact above to solve the question
∵ f(x) is divided by (2x - 3), the quotient is x² - x + 2 and the remainder is -1
∴ f(x) is the dividend ⇒ m
∴ (2x - 3) is the divisor ⇒ n
∴ (x² - x + 2) is the quotient ⇒ q
∴ -1 is the remainder ⇒ r
→ Use the rule above to find f(x)
∵ f(x) = (x² - x + 2) × (2x - 3) + -1
∴ f(x) = (x² - x + 2)(2x - 3) - 1
→ Multiply the 2 brackets at first
∵ (x² - x + 2)(2x - 3) = x²(2x) + x²(-3) + -x(2x) + -x(-3) + 2(2x) + 2(-3)
∴ (x² - x + 2)(2x - 3) = 2x³ - 3x² - 2x² + 3x + 4x - 6
→ Add the like terms
∴ (x² - x + 2)(2x - 3) = 2x³ + (-3x² - 2x²) + (3x + 4x) - 6
∴ (x² - x + 2)(2x - 3) = 2x³ + (-5x²) + 7x - 6
∴ (x² - x + 2)(2x - 3) = 2x³ - 5x² + 7x - 6
→ Substitute it in f(x)
∴ f(x) = 2x³ - 5x² + 7x - 6 - 1
→ Add the like term
∵ f(x) = 2x³ - 5x² + 7x + (- 6 - 1)
∴ f(x) = 2x³ - 5x² + 7x + (-7)
∴ f(x) = 2x³ - 5x² + 7x - 7
Answer:
Step-by-step explanation:
Given the quadratic equation , you need to factor it.
In order to find the form asked of the given equation, you need to factor out the common factor of the terms.
You can observe that the common factor of the terms of the equation is:
Now, knowing this, you must factor out . Then you get the following form:
Therefore, the factored fom of the equation is: