When a polynomial f(x) is divided by 2x-3,the quotient is x^2-x+2 and the remainder is -1. Find the f(x)
1 answer:
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
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Answer:
a. 11/5 pi; -9/5 pi
Step-by-step explanation:
Coterminal angles are those which have a common terminal side. For example 30° is coterminal with −330° and 390° (see figure).
From the example we can see that the following expressions must be fulfilled:
positive angle - reference angle = 360°
reference angle - negative angle = 360°
where positive angle is 390°, reference angle is 30° and negative angle is -330°. In this problem reference angle is pi/5. Also, we have to change 360° for its equivalent in radians, i. e., 2 pi. So,
positive angle - pi/5 = 2 pi
positive angle = 2 pi + pi/5
positive angle = 11/5 pi
pi/5 - negative angle = 2 pi
negative angle = pi/5 - 2 pi
negative angle = -9/5 pi
