Polynomial Vocabulary
What is the degree of
5x^4 - 3x^2 + 7?
4
Simplify:
(3x² + 2x - 5) + (2x² - x + 4)
5x² + x - 1
Solve:
5x + 7 = 27
x = 4
Solve: x² = 49
x = 7 or x = -7
Use technology to solve x³ - 4x = 0.
x = -2, 0, 2
For -2x⁵ + 4x³ - x + 9, state the leading coefficient and constant.
Leading coefficient -2; constant 9
Simplify:
(7x² - 3x + 2) - (4x² + 5x - 6)
3x² - 8x + 8
Solve:
3(x - 2) = 18
x = 8
Solve by factoring:
x² - 7x + 12 = 0
x = 3, 4
Use technology to solve x³ - 4x - 1 = 0. Give answers to 3 decimal places.
x = -1.861, -0.254, 2.115
Write
6x - 4 + 3x⁴ - x²
in standard form.
3x⁴ - x² + 6x - 4
Multiply and write in standard form:
(x + 4)(x - 6)
x² - 2x - 24
Solve:
4(2x - 3) + 5 = 3x + 18
x=5
Solve by factoring:
x² + 2x - 15 = 0
x = 3, -5
Use technology to solve x³ + x² - 4x - 2 = 0. Give answers to 3 decimal places.
x = -2.343, -0.471, 1.814
Write one possible 4th-degree trinomial with leading coefficient -3 and constant 5.
-3x⁴ + 2x + 5
Divide and simplify:
(24x⁵ - 18x³ + 12x²) / (6x²)
4x³ - 3x + 2
Solve or classify:
3(x + 2) = 3x + 6
Infinitely many solutions
Solve:
2x² - 7x + 3 = 0
x = 3, 1/2
Use technology to solve x³ - 2x² - 5x + 3 = 0. Give answers to 3 decimal places.
Answer: x = -1.773, 0.520, 3.253
For -4x⁵ + 7x³ - 2x + 9, state the degree, leading coefficient, constant, number of terms, and coefficient of the x⁴ term.
Degree 5; leading coefficient -4; constant 9; 4 terms; coefficient of x⁴ is 0
Multiply and write in standard form:
(2x - 3)(x² + 4x - 5)
2x³ + 5x² - 22x + 15
Solve:
4(3x - 2) - 5 = 2(2x + 7) + 9
Answer: x = 4.5 or x = 9/2
Use the quadratic formula to solve
2x² + 3x - 7 = 0
x = 1.27, -2.77
Use technology to solve x⁴ - 5x² + 2 = 0. Give all real solutions to 3 decimal places.
Answer: x = -2.136, -0.662, 0.662, 2.136