The value of the remainder is -5.
A division is a process of splitting a specific amount into equal parts. The number to be divided by another number is called the dividend. The number by which we divide another number (dividend) into equal parts is called the divisor. The result of division is called a quotient. The leftover number after division is called the remainder.
For the given situation,
Fiona divided 3x^2 + 5x – 3 by 3x +2.
Here the dividend is [tex]3x^2 + 5x - 3[/tex]
The divisor is [tex]3x+2[/tex]
The quotient is [tex]x+1[/tex]
The remainder can be calculated as
Step 1: when multiplied by x with the divisor, r = 3x
⇒ [tex]\frac{3x^2 + 5x - 3}{3x+2}, q= x, r = 3x[/tex]
Step 2: when multiplied by x+1 with the divisor, r = -5
⇒ [tex]\frac{3x^2 + 5x - 3}{3x+2}, q= x+1, r = -5[/tex]
Hence we can conclude that the value of the remainder is -5.
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