5x⁴ - 3x³ + 6x) - (3x³ + 11x² - 8x)<span>
</span>Expand the second bracket by multiplying throughout by -1
5x⁴ - 3x³ + 6x - <span>3x³ - 11x² + 8x
</span>
Group like terms and simplify
5x⁴ - 3x³ - 3x³ - 11x² + 6x <span>+ 8x
</span>5x⁴ - 6x³ - <span>11x² + 14x</span>
All rectangles are parallelograms. Hope this helps.
Answer: y=-2x+6
Step-by-step explanation:
So 
. We can substitute (0, 6) to get:
6 = 2(0)+b
b=6.
Meaning y=-2x+6.
Simple, 7/12 is greater than 1/3 because 7/12=0.58333 and 1/3=0.333, 0.58333 is greater than 0.333. That is how I know that 7/12 is greater than 1/3. I know that 1/3 is less than 2/3 because 1/3=0.333 and 2/3=0.666, 0.333 is less than 0.666
<h3>
Answer: n = -11</h3>
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Explanation:
Since x-2 is a factor of f(x), this means f(2) = 0.
More generally, if x-k is a factor of p(x), then p(k) = 0. This is a special case of the remainder theorem.
So if we plugged x = 2 into f(x), we'd get
f(x) = x^3+x^2+nx+10
f(2) = 2^3+2^2+n(2)+10
f(2) = 8+4+2n+10
f(2) = 2n+22
Set this equal to 0 and solve for n
2n+22 = 0
2n = -22
n = -22/2
n = -11 is the answer
Therefore, x-2 is a factor of f(x) = x^3+x^2-11x+10
Plug x = 2 into that updated f(x) function to find....
f(x) = x^3+x^2-11x+10
f(2) = 2^3+2^2-11(2)+10
f(2) = 8+4-22+10
f(2) = 0
Which confirms our answer.
