Question

answer fast guys plz I knew so easy question but I forgot some steps how to solve

x⁴+2x³-2x²+2x-3 is divisible by
x²+2x-3.​

Answer 1

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$\huge{\mathbb\colorbox{blue}{x^4+2x^3-2x^2+2x-3 ÷ x^2+2x-3.}}$

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Answer:

Dividing (x⁴+2x³-2x²+2x-3) by (x²+2x-3)

SOLUTION:

$2-3$

$1-6x^2+2x-3$

$2-6$

$x^2+1$

$x^4+2x^3$

$(-) x^4(-) +2x^3$

Now,

Now finding other factors,

x² + 2x - 3

x² + 3x - 1x - 3

x(x+3) -1(x+3)

(x - 1)(x+3)

Hence,

Factors are (x - 1), (x+3), and zeroes are (1) and (-3)

Verification:

P(x) = x⁴ + 2x³ - 2x² + 2x - 3

P(1) = (1)⁴ + 2(1)³ - 2(1)²+ 2(1) - 3

P(1) = 1 + 2 - 2 + 2 - 3

P(1) = 5 - 5

P(1) = 0

So, x = 1 is a zero

Now,

P(x) = x⁴ + 2x³ - 2x² + 2x - 3

P(-3) = (-3)⁴ + 2(-3)³ + 2(-3)²+ 2(-3) - 3

P(-3) = 81 + 2(-27) + 2(-9)+ 2(-3) - 3

P(-3) = 81 - 54 - 18 - 6 - 3

P(-3) = 81 - 81

P(-3) = 0

So, x = (-3) is a zero

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