Question

Write P(x) = x3 + x2 − 17x + 15 as a product of two factors, using x − 3 as one factor.

Answer 1

To write the polynomial P(x) = x^3 + x^2 - 17x + 15 as a product of two factors, one factor can be (x - 3). The factored form of P(x) is (x - 3)(x^2 + 4x - 5).

Step-by-step explanation:

To write the polynomial P(x) = x^3 + x^2 - 17x + 15 as a product of two factors, we can use (x - 3) as one factor.

To do this, we need to divide P(x) by (x - 3) using polynomial long division.

Performing the polynomial division, we get:

(x^3 + x^2 - 17x + 15) ÷ (x - 3) = x^2 + 4x - 5

Therefore, P(x) = (x - 3)(x^2 + 4x - 5) is the factored form of P(x).

Answer 2

Answer: (x-1)(x-3)(x+5)

Step-by-step explanation:

Use the rational root theorem

Constant term = 15, Coefficient of leading term = 1

Factors of 15: 1, 3 , 5, 15

Factors of 1: 1

Therefore, (x-1) is a factor

`\begin{array}{l}=(\left(x-1\right)(x^3+x^2-17x+15)/(x-1))/(x-3)\\\\=(\left(x-1\right)\left(x^2+2x-15\right))/(\left(x-3\right))\\\\=(\left(x-1\right)\left(x-3\right)\left(x+5\right))/(x-3)\\\\=\left(x-1\right)\left(x+5\right)\end{array}`

Cubic equations must have 3 factors to get to the third degree, therefore (x-1)(x-3)(x+5)