Answer:
paragraph proof
Step-by-step explanation:
20x+ 5y = 15
Move 20x to the other side. Sign changes from +20x to -20x
20x-20x+5y=-20x+15
5y=-20x+15
Divide both sides by 5
5y/5=y ( Cross out 5 and 5, divide by 5, 1*1*y=y)
-20/5=-4x
15/5=3
y=-4x+3 or y=3-4x
Answer: y=-4x+3 or y=3-4x
0 = 0
Simplifying
7x + -11 = 5(x + -2) + 2x + -1
Reorder the terms:
-11 + 7x = 5(x + -2) + 2x + -1
Reorder the terms:
-11 + 7x = 5(-2 + x) + 2x + -1
-11 + 7x = (-2 * 5 + x * 5) + 2x + -1
-11 + 7x = (-10 + 5x) + 2x + -1
Reorder the terms:
-11 + 7x = -10 + -1 + 5x + 2x
Combine like terms: -10 + -1 = -11
-11 + 7x = -11 + 5x + 2x
Combine like terms: 5x + 2x = 7x
-11 + 7x = -11 + 7x
Add '11' to each side of the equation.
-11 + 11 + 7x = -11 + 11 + 7x
Combine like terms: -11 + 11 = 0
0 + 7x = -11 + 11 + 7x
7x = -11 + 11 + 7x
Combine like terms: -11 + 11 = 0
7x = 0 + 7x
7x = 7x
Add '-7x' to each side of the equation.
7x + -7x = 7x + -7x
Combine like terms: 7x + -7x = 0
0 = 7x + -7x
Combine like terms: 7x + -7x = 0
0 = 0
Solving
0 = 0
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
