Question

Need help factoring this polynomial: 10x² - 11x - 6

Answer 1

Let's identify first the terms in the polynomial

10x² → leading term

-11x → middle term

-6 → constant term

Let's find the factors of the polynomial using Slide and Divide Method.

1. Slide the leading coefficient 10 to the constant term by multiplying it by the constant term. The polynomial becomes:

`x^2-11x-60`

2. Find the factors of -60 that sums up to the middle coefficient which is -11.

a. 2 and -30 → sum is -28.

b. 3 and -20 → sum is -17

c. 4 and -15 → sum is -11

Therefore, the factors of -60 that sums up to -11 are 4 and -15.

3. Divide each factor by 10 and simplify.

`(4)/(10)\Rightarrow(2)/(5)`
`-(15)/(10)\Rightarrow-(3)/(2)`

4. Add each simplified fraction to "x" and multiply the formed binomial.

`(x+(2)/(5))(x-(3)/(2))`

5. Slide each denominator to every "x" by multiplying it by x. The factor becomes:

`(5x+2)(2x-3)`

Answer:

The factors of the given polynomial 10x² - 11x - 6 are (5x + 2) and (2x - 3).