Warm Up Feb. 19th 1. Solve x4 – 6x2 = 27

2. State the zeros of x(x + 2)(3x – 7)2

3. Write a polynomial in standard form with zeros at 0, 2 and 3i.

Homework Questions??

Finding All Zeros of Any PolynomialLONG & SYNTHETIC DIVISION

4th Grade Review – No Calc.1. 1424 ÷ 8 2. 9706 ÷ 4

Long Division Divide x2 – 5x – 24 by x + 3.

(9b2 + 9b – 10) ÷ (3b – 2)

(6x3 + 2x2 – 11x – 12) ÷ (3x + 4)

Synthetic Division Rules: Divisor must be a linear binomial with a leading coefficient of 1. (x + 4) or (x – 9)

Dividend must be in standard form with “place holders” for missing terms

943 2 xxx 125472 23 xxxx

624 35 xxx

Examples (2x3 – 7x2 – 8x + 16) ÷ (x – 4)

)3()4253( 23 xxxx

Examples)2()20( 4 zz

Remainder TheoremIs (x – 3) a factor of 6x3 – 19x2 + x + 6?

Remainder TheoremGiven: f(x)=x4 – 16x3 – 37x2 + 18x + 13. Evaluate f(18) without a calculator.

Warm Up Feb. 20th 1. The volume of a rectangular prism is given by V(x) = x3 + 3x2 – 36x + 32. The length is given by x – 4. Find the missing measures.

2. Find the value of k so that the remainder is 3 for (x2 + 5x + 7) ÷ (x + k)

Homework Answers & Questions

Finding All Zeros For f(x) = 2x3 + x2 + 1, x = -1 is a zero. Find the others.

For f(x) = x4 – 3x2 – 4, x = 2 and x = -2 are zeros. Find the others.

Rational Root Theorem Find all zeros for x3 – 5x2 + 5x – 4.

Find all zeros for x4 – 20x2 + 24x – 5.

Test Review Topics:

◦ Solving Quadratics, Radicals and Complex Numbers from Last Unit

◦ Polynomials Graphs – end behavior, domain and range, extrema (max and mins), zeros, increasing/decreasing, regression (best fit model) applications and optimization word problems◦ KNOW YOUR CALC. STEPS!!

◦ Writing Polynomials – turning zeros into factors and multiply

◦ Solving Polynomials – by factoring (perfect cubes and special quartics), long/synthetic division, remainder theorem, rational root theorem