Adding, Subtracting, Multiplying Polynomials
Add:
(3x² + 2x − 5) + (x² − 4x + 7)
4x² − 2x + 2
When setting up synthetic division to divide by (x − 4), what number do you write in the box/divisor spot?
4
What is i² equal to?
−1
Find the slope of the line through (2, 3) and (6, 11)
m = 2
Factor: 12x2 + 18x
6x(2x + 3)
Subtract:
(5x³ − 2x + 1) − (2x³ + x − 4)
3x³ − 3x + 5
Use synthetic division: x2 - 5x +6 /(x − 2)
x − 3 (remainder 0)
Simplify: √−16
4i
Write the equation of a line with slope −3 and y-intercept 5 in slope-intercept form
y = −3x + 5
Factor: x² − 49
(x − 7)(x + 7)
Multiply:
(x + 3)(x − 5)
x² − 2x − 15
Use the Remainder Theorem to find the remainder when f(x) = x² + 3x − 5 is divided by (x − 1)
f(1) = 1 + 3 − 5 = −1, so remainder is −1
Add: (3 + 2i) + (−5 + 6i)
−2 + 8i
Write the equation of the line that passes through (4, −1) with slope 2 in point-slope form
y + 1 = 2(x - 4)
Factor: x² + 2x − 24
(x + 6)(x − 4)
Simplify:
3(2x² − x + 4) − 2(x² + 5x − 1)
4x² − 13x + 14
Is (x + 3) a factor of
f(x) = x² + x − 6?
Use the Factor Theorem to justify.
Yes — f(−3) = 9 − 3 − 6 = 0, so (x + 3) is a factor
Multiply: (2 + 3i)(1 − 4i)
14 − 5i
What is the slope of a line perpendicular to
y = (2/3)x − 1?
-3 / 2
Factor by grouping:
x³ + 2x² + 3x + 6
(x + 2)(x² + 3)
Expand and simplify:
(x + 2)²
x² + 4x + 4
Use synthetic division to divide x³ − 8 by (x − 2)
x² + 2x + 4, remainder 0
Divide (5 + i) / (2i)
(1 / 2) - (5 / 2)i
A cell phone plan costs $30 plus $0.10 per text message. Find the total cost of the plan if 150 text messages are sent.
$45
Factor completely by grouping:
2x³ − 3x² − 8x + 12
(2x − 3)(x − 2)(x + 2)