4.4 and 4.5 Can you see the end?

2 common mishaps 2(3-4x+2) What do I do first? Distribute? x-4(5+2x) = x – 20 – 8x Parenthesis go away

Exponents & Scientific Notation Dividing Monomials Note: When you multiply monomials, you add the exponents. When you divide monomials, you subtract the exponents!!!!!! x5/x2 a7/a3 (r8*t6)/(r7t) p7/z4

Those crazy zeros x4/x4 (12a3)0 where a doesn’t equal 0 -(4x3y7)0 Note: a variable in the denominator cannot equal zero because that would make the problem undefined!

The negative Exponent Def1: x-n = 1/xn Def2: 1/x-n = xn x4/x6 Evaluate and Simplify 2-4 3n-5 2/(5a-4)

Exponents + Fractions = Mess If you have a fraction and it has an exponent, multiply each exponent in the quotient by the outside exponent (a3/b2)4 Negative Exponent Method 1 (same as above) (x2/y3)-2 Method 2 (do the reciprocal) (t4/r2)-3

Tricky things Evaluate: 5-2/5 (3ab-4)(-2a-3b7) [6m2n3/8m7n2]-3 Note: 6*6*6 =216 and 8*8*8 = 512 and 216/512 = 27/64 4a-2b5/6a5b2

Scientific Notation How to write really really big numbers or really really small numbers Usually used in the natural sciences. Big numbers – Distances in Space, electrical forces like volts, my ego. 240,000 93,000,000 Small numbers – Microscopic Things, Biology, Chemistry. 0.0003 0.0000832

Going the other way Positive exponents 3.45 x 106 2.3 x 108 Negative exponents 8.1 x 10-3 6.34 x 10-7

You Try It (-2x2)(x-3y-4)-2 (6a-2b3)-1/(4a3b-2)-2 [6r3s-3/9r3s-1]-2 Write 0.000000961 in scientific notation now! Write the number 7.329 x 106 in decimal notation

Answers -2x8y8 8a8/3b7 9s4/4 9.61x10-7 7,329,000

Homework for 4.4 Section 4.4 HW 1-123 every other odd 2, 8, 20, 36, 60, 74, 92, 104, 110, 118, 128

Section 4.5 – Division of Polynomials

Divide Divide Divide! Polynomial by a monomial It’s the opposite of distribution Let me show you how: (6x3 – 3x2 +9x) / 3x Have another (12x2y – 6xy + 4x2) / 2xy

Divide by polynomials Long division…because you love it (x2-5x+8) / (x-3) What if a term is missing? Put a zero in for the missing term (6x+26-2x3) / (2+x) Note: remainder gets put over the divisor

Check it out How do you check? All you gots to do is multiply your answer by the divisor and add your remainder. DON’T FORGET THE REMAINDER!!!!! Another example: (x^2-1)/(x+1)

Now You do it (2x3 +x2 -8x -3) / (2x-3) (x3 – 2x +1)/ (x-1)

Soln’s X2 + 2x -1 – 6/(2x-3) X2 +x -1

homework Section 4.5 HW 1-55 eoo 2, 12, 20, 32, 40, 50