Question

4) Factor the following Basic Trinomials: a) x - 20x+36 b) x² +6x-40

Answer 1

`x^2-20x+36`

this polynomial has the form:

`ax^2+bx+c`

which is factored as:

`a(x-x_1)(x-x_2)`

where x1 and x2 are the zeros of the polynomial.

Using the quadratic formula to find the zeros:

`\begin{gathered} x_(1,2)=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x_(1,2)=\frac{20\pm\sqrt[]{(-20)^2-4\cdot1\cdot36}}{2\cdot1} \\ x_(1,2)=\frac{20\pm\sqrt[]{256}}{2} \\ x_1=(20+16)/(2)=18 \\ x_2=(20-16)/(2)=2 \end{gathered}`

Therefore, the factored expression is (x - 18)(x - 2)