When 2x^{2}-7+9 is divided by a polynomial, the quotient is 2x - 3 and the remainder is 3. Find the polynomial?

Josalynn

Josalynn

Answered question

2021-05-18

When 2x27+9 is divided by a polynomial, the quotient is 2x - 3 and the remainder is 3. Find the polynomial?

Answer & Explanation

cyhuddwyr9

cyhuddwyr9

Skilled2021-05-19Added 90 answers

Step 1
We know that
Dividend = (Divisor) (Quotient) + Remainder
Step 2
Given that
Dividend=2x27x+9
Quotient =2x−3
Remainder=3
Step 3
Simplification:
Dividend = (Divisor) (Quotient) + Remainder
2x27x+9=d(x)(2x3)+3 (Let Divisior = d(x))
2x27x+93=d(x)(2x3)
2x27x+6=d(x)(2x3)
d(x)=2x27x+6(2x3)
d(x)=2x24x3x+6(2x3)
d(x)=2x(x2)3(x2)(2x3)
d(x)=(x2)(2x3)(2x3)
d(x)=(x-2)
Step 4
Hence the divisor polynomial is (x-2).

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