Question

Please help me with this problem:Factor completely.x^2+3x−18Enter your answer in the boxes.x^2+3x−18= (___ ) (___ )

Answer 1

To factor the quadratic equation, use the quadratic formula.

To a quadratic equation ax² + bx + c = 0, the quadratic formula is:

`x=(-b\pm√(b^2-4ac))/(2a)`

Given the quadratic equation x² + 3x - 18 = 0, the coefficients are:

a = 1

b = 3

c = -18

Substituting the coefficients and solving the equation:

`\begin{gathered} x=(-3\pm√(3^2-4*1*(-18)))/(2*1) \\ x=(-3\pm√(9+72))/(2) \\ x=(-3\pm√(81))/(2) \\ x=(-3\pm9)/(2) \\ x_1=(-3-9)/(2)=-(12)/(2)=-6 \\ x_2=(-3+9)/(2)=(6)/(2)=3 \end{gathered}`

So, the roots are: -6 and 3.

If a quadratic equation has roots x₁ and x₂, then the equation in the factored form is (x - x₁)(x - x₂).

So,

x² + 3x - 18 = (x - 3)(x + 6).

Answer: (x - 3)(x + 6).