Divide 6x^6+5x^5+2x^4-9x^3+7x^2-10x+2 by 3x + 1 by using long division. Show all work and steps work. Then explain if 3x + 1 is
a factor of the dividend.
1 answer:
A) First, write all the terms of the polynomial separated; then follow these steps:
1) take the term of the highest degree of the dividend and divide it by the term of the highest degree of the divisor (6x⁶ ÷ 3x = 2x⁵) and write the result on the proper part of the division;
2) multiply the monomial obtained times the divisor (2x⁵ × 3x+1 = 6x⁶ + <span>2x</span>⁵), write the result under the polynomial, under the colum of the same degree;
3) subtract the result obtained from the polynomial (all the terms of the polynomial!!);
4) repeat step 1-3 with the new polynomial obtained.
Complete work is shown on the picture attached.
The result is: 6x⁶ + 5x⁵ + 2x⁴ - 9x³ + 7x² -10x + 2 = (3x + 1) · (2x⁵ + x⁴ + 1/3 x³ - 28/9 x² + 91/27 x - 361/81) + 523/81
B) (3x + 1) is not a factor of the dividend because the division has a remainder not equal to zero.
1) take the term of the highest degree of the dividend and divide it by the term of the highest degree of the divisor (6x⁶ ÷ 3x = 2x⁵) and write the result on the proper part of the division;
2) multiply the monomial obtained times the divisor (2x⁵ × 3x+1 = 6x⁶ + <span>2x</span>⁵), write the result under the polynomial, under the colum of the same degree;
3) subtract the result obtained from the polynomial (all the terms of the polynomial!!);
4) repeat step 1-3 with the new polynomial obtained.
Complete work is shown on the picture attached.
The result is: 6x⁶ + 5x⁵ + 2x⁴ - 9x³ + 7x² -10x + 2 = (3x + 1) · (2x⁵ + x⁴ + 1/3 x³ - 28/9 x² + 91/27 x - 361/81) + 523/81
B) (3x + 1) is not a factor of the dividend because the division has a remainder not equal to zero.
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