Resolve in factors. I) x⁴+x²+1

let a = x² (a ≥ 0), we have the equation:

a² + a + 1 = 0

⇔ a² + 2.1/2.a + 1/4 + 3/4 = 0

⇔ (a + 1/2)² = -3/4 (unreasonable)

=> no solutions

Step-by-step explanation:

(x2−x+1)(x2+x+1)

Step-by-step explanation:

Let’s multiply by x2−1

(x4+x2+1)(x2–1)=x6+x4+x2−x4−x2−1=x6−1

So x4+x2+1=x6−1x2−1 .

Now, let’s factorize x6−1 differently: x6−1=(x3+1)(x3−1) . Also x2−1=(x+1)(x−1) .

So x4+x2+1=(x3+1)(x3−1)(x+1)(x−1)=x3+1x+1⋅x3−1x−1 .

Now, I can factorize x3+1=(x+1)(x2−x+1) and x3−1=(x−1)(x2+x+1) .

So. x4+x2+1=(x2−x+1)(x2+x+1) .

total amount of money that he should pay if he has not used his duty free exemption is $98

step-by-step explanation:

given a united states citizen returning to the states declares the following items at the customs office: 3 shirts at $8.50 each 2 dresses at $27.50 each 1 pair of gold cuff links at $17.50 per pair. we have to find how much he pay

cost of 3 shirts if one cost at $8.50 is

cost of 2 dresses if one cost at $27.50 is  

cost of 1 pair of gold cuff at $17.50

so, total amount of money that he should pay if he has not used his duty free exemption is   $25.5+$55+$17.50=$98

answer: the distance

step-by-step explanation:

to calculate the distance d of a line segment with endpoints (x1, y1) and (x2, y2) use the formula d (x2 x1)2 (y2 y1)2. to calculate the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) use the formula