Quotient of 3x²+17x+10 by x+5

To find the quotient of (3x²+17x+10) ÷ (x+5), we can follow the steps given below.

These steps make the polynomial division process simple.

Step 1: Set up the division, writing the dividend 3x²+17x+10 and the divisor x+5.

Step 2: Divide the first term of the dividend (3x²) by the first term of the divisor (x), which gives 3x.

Step 3: Multiply the entire divisor (x+5) by this result (3x), which gives 3x²+15x.

Step 4: Subtract this product from the original dividend: (3x²+17x+10) - (3x²+15x) = 2x+10.

Step 5: Repeat the process with the new dividend (2x+10). Divide the first term (2x) by the first term of the divisor (x), giving 2.

Step 6: Multiply the entire divisor by this result (2), which gives 2x+10.

Step 7: Subtract this product from the current dividend: (2x+10) - (2x+10) = 0. So, the quotient is 3x+2 with a remainder of 0.

• Quotient: The result we get after dividing one polynomial by another.

• Polynomial: An expression consisting of variables and coefficients, that involves the operations of addition, subtraction, multiplication, and non-negative integer exponents.

• Dividend: The polynomial that is being divided.

• Divisor: The polynomial by which the dividend is divided.

• Remainder: The part of the dividend that is left over after division, which is zero in this case.