Answer to Question #240909 in Calculus for CCW

Question

Factoring Polynomials Practice:

Use synthetic division to divide polynomials by possible roots

5x³ + 29x + 19x - 5

P= Q=

Answer 1

One of the possible root of the polynomial is $(x+1)$. since, when -1 is substituted into the polynomial it is zero. Now, to the synthetic division steps.

STEP 1: Write the polynomial being divided in descending order. Then, write only it's coefficient and constant, using 0 for any missing terms.

$5x^3+29x^2+19x-5\\ 5~~~~~~~~~29~~~~~~~~~19~~-5$

STEP 2: Write the constant, a, of the divisor $x-a$ , to the left. $a=-1.$

$-1|5~~~~~~~~~29~~~~~~~~~19~~~~~~~~~-5$

STEP 3: Bring down the first coefficient as shown below.

STEP 4: Multiply the first coefficients by the divisor or, - 1. Then write this product under the second coefficient. Add the second coefficient with the products and write the sum as shown below

STEP 5: Continue this process of multiplying and adding until there is a sum for the last column.

The number along the bottom row are the coefficient of the quotient with powers of x in descending order. The last coefficient is the remainder. The first power is 1 less than the highest power of the polynomial that was been divided.

The division answer is;

$5x^2+24x-5$