To find the quotient of the polynomial division of 3x³ + 11x² + 26x + 30 by x + 5, we can use polynomial long division.
Step 1: Divide the leading term of the dividend (3x³) by the leading term of the divisor (x). This gives us 3x².
Step 2: Multiply the entire divisor by 3x²:
(x + 5)(3x²) = 3x³ + 15x².
Step 3: Subtract this from the original polynomial:
(3x³ + 11x² + 26x + 30) – (3x³ + 15x²) results in -4x² + 26x + 30.
Step 4: Now, divide the leading term of the result (-4x²) by the leading term of the divisor (x), which gives us -4x.
Step 5: Multiply the entire divisor by -4x:
(x + 5)(-4x) = -4x² – 20x.
Step 6: Subtract this from the previous result:
(-4x² + 26x + 30) – (-4x² – 20x) results in 46x + 30.
Step 7: Next, divide the leading term (46x) by the leading term of the divisor (x), giving us 46.
Step 8: Multiply the entire divisor by 46:
(x + 5)(46) = 46x + 230.
Step 9: Subtract this from the previous result:
(46x + 30) – (46x + 230) results in -200.
Putting this all together, the quotient of the division is:
3x² – 4x + 46 with a remainder of -200.
Therefore, the final answer can be stated as:
Quotient: 3x² – 4x + 46
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