1) The product of a number and 1 less than the number is 42. Find the number

2) write a polynomial equation that has three solutions of 5,3, and - 8

a) x^3 - 49x + 120 = 0

b) x^3 - 120x - 49=0

c) x^3 - 49^2 + 120=0

d) x^3 - 49x - 120=0

1) Answer

One set = (7, 6)

Second set = (-6, - 7)

Step by step explanation

Let "x" be a number.

The other number = x - 1

The product of the two number is 42

Therefore, x (x - 1) = 42

x^2 - x = 42

x^2 - x - 42 = 0

Now we have to factorize the equation.

(x - 7) (x + 6) = 0

x = 7 and x = - 6

Take x = 7, and the other number = x - 1

The number is = 7 - 1 = 6

One set of number is (7, 6)

The other set is when x = - 6

The other number is = x - 1

= - 6 - 1

= - 7

The other set is (-6, - 7)

2) Answer

a) x^3 - 49x + 120 = 0

Step by step explanation

Here the solution are 5, 3 and - 8

Therefore, the factors are (x - 5) (x - 3) and (x + 8)

Multiplying the factors we get the equation.

(x - 5) (x - 3) (x + 8) = 0

(x^2 - 5x - 3x + 15) (x + 8) = 0

(x^2 - 8x + 15) (x + 8) = 0

x^3 - 8x^2 + 15x + 8x^2 - 64x + 120 = 0

x^3 - 49x + 120 = 0