Step-by-step explanation:
<u>Given</u>
- f(x) = 4x³ + 3x² - 2x - 1
<u>Divide it by the following:</u>
<u>(a) 2x + 1</u>
- 4x³ + 3x² - 2x - 1 =
- (4x³ + 2x²) + (x² + 1/2x) - (5/2x + 5/4) + 1/4 =
- 2x²(2x+1) + 1/2x(2x + 1) - 5/4(2x + 1) + 1/4 =
- (2x + 1)(2x² + 1/2x - 5/4) + 1/4
Quotient = 2x² + 1/2x - 5/4
Remainder = 1/4
<u>(b) 2x - 3</u>
- 4x³ + 3x² - 2x - 1 =
- (4x³ - 6x²) + (9x² - 13.5x) + (11.5x - 17.25) + 16.25 =
- (2x -3)(2x² + 4.5x + 5.75) + 16.25
Quotient = 2x² + 4.5x + 5.75
Remainder = 16.25
<u>(c) 4x - 1</u>
- 4x³ + 3x² - 2x - 1 =
- (4x³ - x²) + (4x² - x) - (2x - 1/2) - 3/2 =
- (4x - 1)(x² + x - 1/2) - 3/2
Quotient = x² + x - 1/2
Remainder = - 3/2
<u>(d) x + 2</u>
- 4x³ + 3x² - 2x - 1 =
- (4x³ + 8x²) - (5x² + 10x) + (8x + 16) - 17 =
- (x + 2)(4x² - 5x + 8) - 17
Quotient = 4x² - 5x + 8
Remainder = - 17
The answer is 8.1
.........................
Answer: C) 10x + 25
<u>Step-by-step explanation:</u>
f(x) = <u> 2x + 5 </u>, g(x) = <u> 5 </u>
(fg)(x) = (2x + 5) * 5
= 10x + 25
Given the equation: (km / 3) - 2x = 4, it is essential to isolate x to obtain the expression to solve it. This is done below:
(km / 3<span>) - 2x = 4
</span>
Adding 2x to both sides:
(km / 3<span>) - 2x + 2x = 4 + 2x
</span>(km / 3<span>) = 4 + 2x
</span>
Subtracting 4 from both sides:
(km / 3<span>) - 4 = 4 + 2x - 4
</span>(km / 3<span>) - 4 = 2x
</span>
Dividing 2 from both sides:
[(km / 3<span>) - 4] /2 = 2x /2
</span>[(km / 3<span>) - 4] /2 = x
</span>x = (km / 6) - 2
Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. We are given the slope of -3, but we need the y-intercept. We will sub in the x coordinate for x in the equation and the y coordinate for y in the equation, along with the slope and solve for b. -2 = -3(0) + b and -2 = b. Rewriting the equation, we have y = -3x - 2.
