Form a third-degree polynomial function with real coefficients, with leading coefficient 1, such that - 2 + i and 7 are zeros.

In standard form, this third-order polynomial - call it p(x) - has real coefficients a, b, c, d so that it is written as

p(x) = a x ³ + b x ² + c x + d

We're told the leading coefficient is a = 1, so

p(x) = x ³ + b x ² + c x + d

Since the coefficients are all real, any complex roots with non-zero imaginary part occurs alongside its complex conjugate, so the fact that -2 + i is a root means that its conjugate, -2 - i is also a root.

Then by the factor theorem, we can write p(x) as the product of linear terms involving its roots:

p(x) = (x - (-2 + i )) (x - (-2 - i )) (x - 7)

Now just expand this to get

p(x) = x ³ - 3 x ² - 23 x - 35

step-by-step explanation:

always plug in x. in this case, x equals 4.

i'm going to first solve 4(2+3x)

1) 4(2+3(4)) use pemdas to solve.

i'm going to multiply whats in the parenthesis first, so 3 times 4=12.

2)4 (2+12) i'm then going to multiply 4 by both numbers in the parenthesis (because multiplying comes before adding)

4 times 2= 8.   4 times 12= 48

4) (8+48)= 56 (answer)

i'm then going to solve 8+12x and plug in 4 for x.

1) 8 +12(4)

multiplying comes before adding, so i'm gonna multiply 12 and 4.

12 times 4= 48.

2) 8+48=56

both equal the same!

175

step-by-step explanation:

2 inches x 10 miles = 200 miles - 3 inches = 175