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

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step-by-step explanation: