Question

5x3 + 14x2 + 9x
help

Answer 1

Answer: x(x+1)(5x+9)

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Work Shown:

5x^3 + 14x^2 + 9x

x( 5x^2 + 14x + 9 )

To factor 5x^2 + 14x + 9, we could use the AC method and guess and check our way to getting the correct result.

A better way in my opinion is to solve 5x^2 + 14x + 9 = 0 through the quadratic formula

`x = (-b\pm√(b^2-4ac))/(2a)\\\\x = (-(14)\pm√((14)^2-4(5)(9)))/(2(5))\\\\x = (-14\pm√(16))/(10)\\\\x = (-14\pm4)/(10)\\\\x = (-14+4)/(10) \ \text{ or } \ x = (-14-4)/(10)\\\\x = (-10)/(10) \ \text{ or } \ x = (-18)/(10)\\\\x = -1 \ \text{ or } \ x = (-9)/(5)\\\\`

Then use those two solutions to find the factorization

x = -1 or x = -9/5

x+1 = 0 or 5x = -9

x+1 = 0 or 5x+9 = 0

(x+1)(5x+9) = 0

So we have shown that 5x^2 + 14x + 9 factors to (x+1)(5x+9)

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Overall,

5x^3 + 14x^2 + 9x

factors to

x(x+1)(5x+9)