By Jerry Pallotta

How lengthy is a foot? what's the metric approach? What weighs extra, a ton of feathers or a ton of Hershey's sweet? writer and educator Jerry Pallotta solutions those and many different questions as in simple terms he can--using Hershey's Kisses, Twizzlers goodies, Hershey's chocolate bars, and extra to coach weights and measurements. Rob Bolster's comical clowns show the concepts.

This is the 8th booklet within the sequence through Pallotta and Bolster, who've taught children counting by way of fives, addition, subtraction, fractions, multiplication, percents, shapes, and patterns.

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**Additional info for Hershey's Weights and Measures **

**Example text**

This technique, called factoring by grouping, is illustrated in the next example. 38 CHAPTER 1 FUNDAMENTAL CONCEPTS OF ALGEBRA EXAMPLE 10 Factoring by grouping Factor: (a) 4ac ϩ 2bc Ϫ 2ad Ϫ bd (b) 3x 3 ϩ 2x 2 Ϫ 12x Ϫ 8 (c) x 2 Ϫ 16y 2 ϩ 10x ϩ 25 SOLUTION (a) We group the first two terms and the last two terms and then proceed as follows: 4ac ϩ 2bc Ϫ 2ad Ϫ bd ϭ ͑4ac ϩ 2bc͒ Ϫ ͑2ad ϩ bd͒ ϭ 2c͑2a ϩ b͒ Ϫ d͑2a ϩ b͒ At this stage we have not factored the given expression because the right-hand side has the form 2ck Ϫ dk with k ϭ 2a ϩ b.

ILLUS TRATION The Notation can 5 и 23 ϭ 5 и 8 ϭ 40 Ϫ5 и 23 ϭ Ϫ5 и 8 ϭ Ϫ40 Ϫ24 ϭ Ϫ͑24͒ ϭ Ϫ16 3͑Ϫ2͒3 ϭ 3͑Ϫ2͒͑Ϫ2͒͑Ϫ2͒ ϭ 3͑Ϫ8͒ ϭ Ϫ24 We next extend the definition of an to nonpositive exponents. 2 Exponents and Radicals 17 If m and n are positive integers, then m factors of a ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ ⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ aman ϭ a и a и a и и и и и a и a и a и a и и и и и a. n factors of a Since the total number of factors of a on the right is m ϩ n, this expression is equal to amϩn; that is, aman ϭ amϩn. We can extend this formula to m Յ 0 or n Յ 0 by using the definitions of the zero exponent and negative exponents.

For example, x 2 Ϫ 2 is irreducible over the rational numbers, since it cannot be expressed as a product of two polynomials of positive degree that have rational coefficients. However, x 2 Ϫ 2 is not irreducible over the real numbers, since we can write x 2 Ϫ 2 ϭ ͑ x ϩ 22͒͑ x Ϫ 22͒. 4, not over the complex numbers. Every polynomial ax ϩ b of degree 1 is irreducible. Before we factor a polynomial, we must specify the number system (or set) from which the coefficients of the factors are to be chosen.