Question

question from polynomial

please solve it​

Answer 1

Answer:

file attached

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

p(x) = 3x³+16x²+15x-18

p(2/3) = 0

⇒x = 2/3

⇒3x = 2

⇒3x-2 = 0

∴ (3x-2) is a factor of p(x).

On dividing p(x) by (3x-2), we get

3x-2 ) 3x³+16x²+15x-18 ( x²+6x+9

3x³- 2x²

- +

18x²+15x-18

18x²- 12x

- +

27x-18

27x-18

- +

×

∴ p(x) = (3x-2) (x²+6x+9)

∴ the other zeros of p(x) are given by (x²+6x+9).

Now, x²+6x+9 = 0 ⇒x²+3x+3x+9 = 0

⇒x(x+3)+3(x+3) = 0

⇒(x+3) (x+3) = 0

⇒x+3 = 0 or x+3 = 0

⇒x = -3 or x = -3

Hence, the other zeros of p(x) are -3 & -3.