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GaryK [48]
2 years ago
11

F(x)=15x³+22x²-15x+2 Write f(x) as a product of linear factors.

Mathematics
1 answer:
Goryan [66]2 years ago
3 0

Answer:

(5x  - 1)(3x - 1)(x + 2)

Step-by-step explanation:

(15 {x}^{3}  + 22 {x}^{2}  - 15x + 2)

Apply Rational Root Theorem, our possible roots will be

plus or minus( 2/15, 2/5,2/3,2, 1/15,1/5,1/3,1).

I

I tried root -2 and it work so

If we apply synthetic dividon, we would be left with

15 {x}^{2}  - 8x + 1

We can factor this regularly.

Apply AC method that a number

AC will multiply to 15 but add to -8.

The answer are -5 and -3 so we write this as

15 {x}^{2}  - 5x - 3x + 1

Factor by grouping

(15x {}^{2}  - 5x) - (3x + 1)

5x(3x - 1) - 1(3x - 1)

So our factor are

(5x - 1)(3x - 1)(x + 2)

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