Answer:
see explanation
Step-by-step explanation:
(a)
Given
2k - 6k² + 4k³ ← factor out 2k from each term
= 2k(1 - 3k + 2k²)
To factor the quadratic
Consider the factors of the product of the constant term ( 1) and the coefficient of the k² term (+ 2) which sum to give the coefficient of the k- term (- 3)
The factors are - 1 and - 2
Use these factors to split the k- term
1 - k - 2k + 2k² ( factor the first/second and third/fourth terms )
1(1 - k) - 2k(1 - k) ← factor out (1 - k) from each term
= (1 - k)(1 - 2k)
1 - 3k + 2k² = (1 - k)(1 - 2k) and
2k - 6k² + 4k³ = 2k(1 - k)(1 - 2k)
(b)
Given
2ax - 4ay + 3bx - 6by ( factor the first/second and third/fourth terms )
= 2a(x - 2y) + 3b(x - 2y) ← factor out (x - 2y) from each term
= (x - 2y)(2a + 3b)
Answer:
Step-by-step explanation:
80 divided by 7 is 11 with a remainder of 3.
x + 1
__________
3x+2 I 3x² +5x -3
3x² +2x
----------
3x -3
3x+2
--------
-5 is the remainder
Since there are 16 oz in a pound, it would be 1/16
If the position at time <em>t</em> is
<em>s(t)</em> = (1 m/s³) <em>t</em> ³
then the average velocity over <em>t</em> = 2 s and <em>t</em> = 2.001 s is
<em>v</em> (ave) = (<em>s</em> (2.001 s) - <em>s</em> (2 s)) / (2.001 s - 2 s)
<em>v</em> (ave) = ((1 m/s³) (2.001 s)³ - (1 m/s³) (2 s)³) / (2.001 s - 2 s)
<em>v</em> (ave) ≈ (8.01201 m - 8 m) / (0.001 s)
<em>v</em> (ave) ≈ 12.006 m/s
