8 Preparing for Synthetic Division, cont. Polynomials need to be written in expanded, standard polynomial form.Translation: If you’re missing terms, then you need to write them out as 0 times (*) the variable.
13 Step 12Write the constant value of the divisor (c) here.
14 Step 22Write all the coefficients of the expanded dividend here.
15 Step 323“Drop” the 1st coefficient underneath the line.
16 Step 4263Multiply “c” by the last value underneath the line. Write their product just underneath the next coefficient.
17 Step 526Add together the numbers in that column and write their sum underneath the line.
18 Step 62Multiply “c” by the last value underneath the line. Write their product just underneath the next coefficient.
19 Step 72Repeat steps 5 and 6 until a number appears in the box underneath the last column.
20 Step 8 – Naming the Quotient 2In the last row are the coefficients of the quotient in decreasing order. The quotient is one degree less than the dividend.
21 Step 8 – Naming the Quotient The number in the box is the remainder.3x3 + 6x2 + 4x – 3 Remainder -5
22 Your TurnOn the Synthetic Division – Guided Notes handout, solve for the quotient of problems 11 – 14 using synthetic division
23 Synthetic Division and the Factor Theorem Conclusions:
24 Your Turn:Using problems 1 – 12 on the Synthetic Division Practice handout (last night’s hmwk), identify which problems represent division by a factor/root and which problems represent division by NOT a factor root.
25 So What’s Next?* To get the remaining roots, set the expression equal to 0, factor, and solve.
26 Your Turn:On the Synthetic Division Practice handout, solve for the remaining roots for problems – 4 and 10 – 12
27 Rewriting the Original Polynomial We can use the roots and linear factors to rewrite the polynomialThis form is called the product of linear factorsIf you multiplied all the linear factors together, then you’d get the original polynomial
29 Product of Linear Factors Product = MultiplyProduct of linear factors = Multiply all the linear factorsTranslation: Rewrite all the linear factors with parentheses around each factorHelpful format for graphing polynomialsProduct of Linear Factors