Question

2x−3 must be subtracted from f (x), so that result is exactly divisible by x2−4x+3.
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Answer 1

Answer:

We know that dividend = Quotient × Divisor + Remainder

Dividend- Remainder = Quotient × Divisor

Therefore, right hand side is divisible by Divisor

Thus, if we subtract reminder from dividend, then it will exactly divisible by the Divisor

Dividing x⁴ + 2x³ - 13 x² - 12x +21 by x² - 4x + 3

After Dividing ( Division is given in attachment)

We get Quotient = x² + 6x + 8 and Remainder = 2x-3

Thus if we subtract reminder 2x - 3 from x⁴ + 2x³ - 13x² + 21

It will be divisible by x²- 4x + 3

Explanation:

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Answer 2

The given expression is

The given expression isx

The given expression isx 4

The given expression isx 4 +2x

The given expression isx 4 +2x 3

The given expression isx 4 +2x 3 −2x

The given expression isx 4 +2x 3 −2x 2

The given expression isx 4 +2x 3 −2x 2 +4x+6

The given expression isx 4 +2x 3 −2x 2 +4x+6The divisor is

The given expression isx 4 +2x 3 −2x 2 +4x+6The divisor is x

The given expression isx 4 +2x 3 −2x 2 +4x+6The divisor is x 2

The given expression isx 4 +2x 3 −2x 2 +4x+6The divisor is x 2 +2x−3

The given expression isx 4 +2x 3 −2x 2 +4x+6The divisor is x 2 +2x−3Use long division method to divide the given expression by

The given expression isx 4 +2x 3 −2x 2 +4x+6The divisor is x 2 +2x−3Use long division method to divide the given expression by x

The given expression isx 4 +2x 3 −2x 2 +4x+6The divisor is x 2 +2x−3Use long division method to divide the given expression by x 2

The given expression isx 4 +2x 3 −2x 2 +4x+6The divisor is x 2 +2x−3Use long division method to divide the given expression by x 2 +2x−3

The given expression isx 4 +2x 3 −2x 2 +4x+6The divisor is x 2 +2x−3Use long division method to divide the given expression by x 2 +2x−3x

The given expression isx 4 +2x 3 −2x 2 +4x+6The divisor is x 2 +2x−3Use long division method to divide the given expression by x 2 +2x−3x 4

The given expression isx 4 +2x 3 −2x 2 +4x+6The divisor is x 2 +2x−3Use long division method to divide the given expression by x 2 +2x−3x 4 +2x

The given expression isx 4 +2x 3 −2x 2 +4x+6The divisor is x 2 +2x−3Use long division method to divide the given expression by x 2 +2x−3x 4 +2x 3

The given expression isx 4 +2x 3 −2x 2 +4x+6The divisor is x 2 +2x−3Use long division method to divide the given expression by x 2 +2x−3x 4 +2x 3 −2x

The given expression isx 4 +2x 3 −2x 2 +4x+6The divisor is x 2 +2x−3Use long division method to divide the given expression by x 2 +2x−3x 4 +2x 3 −2x 2

The given expression isx 4 +2x 3 −2x 2 +4x+6The divisor is x 2 +2x−3Use long division method to divide the given expression by x 2 +2x−3x 4 +2x 3 −2x 2 +4x+6=x

The given expression isx 4 +2x 3 −2x 2 +4x+6The divisor is x 2 +2x−3Use long division method to divide the given expression by x 2 +2x−3x 4 +2x 3 −2x 2 +4x+6=x 2

The given expression isx 4 +2x 3 −2x 2 +4x+6The divisor is x 2 +2x−3Use long division method to divide the given expression by x 2 +2x−3x 4 +2x 3 −2x 2 +4x+6=x 2 +1+

The given expression isx 4 +2x 3 −2x 2 +4x+6The divisor is x 2 +2x−3Use long division method to divide the given expression by x 2 +2x−3x 4 +2x 3 −2x 2 +4x+6=x 2 +1+ x

The given expression isx 4 +2x 3 −2x 2 +4x+6The divisor is x 2 +2x−3Use long division method to divide the given expression by x 2 +2x−3x 4 +2x 3 −2x 2 +4x+6=x 2 +1+ x 2

The given expression isx 4 +2x 3 −2x 2 +4x+6The divisor is x 2 +2x−3Use long division method to divide the given expression by x 2 +2x−3x 4 +2x 3 −2x 2 +4x+6=x 2 +1+ x 2 +2x−3

The given expression isx 4 +2x 3 −2x 2 +4x+6The divisor is x 2 +2x−3Use long division method to divide the given expression by x 2 +2x−3x 4 +2x 3 −2x 2 +4x+6=x 2 +1+ x 2 +2x−32x+9

The given expression isx 4 +2x 3 −2x 2 +4x+6The divisor is x 2 +2x−3Use long division method to divide the given expression by x 2 +2x−3x 4 +2x 3 −2x 2 +4x+6=x 2 +1+ x 2 +2x−32x+9

The given expression isx 4 +2x 3 −2x 2 +4x+6The divisor is x 2 +2x−3Use long division method to divide the given expression by x 2 +2x−3x 4 +2x 3 −2x 2 +4x+6=x 2 +1+ x 2 +2x−32x+9

The given expression isx 4 +2x 3 −2x 2 +4x+6The divisor is x 2 +2x−3Use long division method to divide the given expression by x 2 +2x−3x 4 +2x 3 −2x 2 +4x+6=x 2 +1+ x 2 +2x−32x+9 The remainder is 2x+9. It means if we subtract (2x+9) from given expression, then it is exactly divisible by x

The given expression isx 4 +2x 3 −2x 2 +4x+6The divisor is x 2 +2x−3Use long division method to divide the given expression by x 2 +2x−3x 4 +2x 3 −2x 2 +4x+6=x 2 +1+ x 2 +2x−32x+9 The remainder is 2x+9. It means if we subtract (2x+9) from given expression, then it is exactly divisible by x 2

The given expression isx 4 +2x 3 −2x 2 +4x+6The divisor is x 2 +2x−3Use long division method to divide the given expression by x 2 +2x−3x 4 +2x 3 −2x 2 +4x+6=x 2 +1+ x 2 +2x−32x+9 The remainder is 2x+9. It means if we subtract (2x+9) from given expression, then it is exactly divisible by x 2 +2x−3.

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