Example 1A LCM of Monomials and Polynomials A. Find the LCM of 15a 2 bc 3, 16b 5 c 2, and 20a 3 c 6....
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LCM of Monomials and Polynomials A. Find the LCM of 15a 2 bc 3 , 16b 5 c 2 , and 20a 3 c 6 . 15a 2 bc 3 = 3 ● 5 ● a 2 ● b ● c 3 Factor the first monomial. 16b 5 c 2 = 2 4 ● b 5 ● c 2 Factor the second monomial. 20a 3 c 6 = 2 2 ● 5 ● a 3 ● c 6 Factor the third monomial. LCM = 3 ● 5 ● 2 4 ● a 3 ● b 5 ● c 6 Use each factor the greatest number of times it appears.
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Transcript of Example 1A LCM of Monomials and Polynomials A. Find the LCM of 15a 2 bc 3, 16b 5 c 2, and 20a 3 c 6....
LCM of Monomials and Polynomials
A. Find the LCM of 15a2bc3, 16b5c2, and 20a3c6.
15a2bc3 = 3 ● 5 ● a2 ● b ● c3 Factor the first monomial.
16b5c2 = 24 ● b5 ● c2 Factor the secondmonomial.
20a3c6 = 22 ● 5 ● a3 ● c6 Factor the third monomial.
LCM = 3 ● 5 ● 24● a3
● b5 ● c6 Use each factor thegreatest number of timesit appears.
LCM of Monomials and Polynomials
Answer: 240a3b5c6
= 240a3b5c6 Simplify.
LCM of Monomials and Polynomials
B. Find the LCM of x3 – x2 – 2x and x2 – 4x + 4.
LCM = x(x + 1)(x – 2)2
Use each factor the greatest number of times it appears as a factor.
x3 – x2 – 2x = x(x + 1)(x – 2) Factor the firstpolynomial.
x2 – 4x + 4 = (x – 2)2 Factor the secondpolynomial.
Answer: x(x + 1)(x – 2)2
Monomial Denominators
The LCD is 42a2b2.
Simplify .
Simplify each numerator and denominator.
Add the numerators.
Monomial Denominators
Answer:
Polynomial Denominators
Factor the denominators.
Simplify .
Subtract the numerators.
The LCD
is 6(x – 5).
Polynomial Denominators
Distributive Property
Combine like terms.
Simplify.
Simplify.Answer:
Complex Fractions with Different LCDs
The LCD of the numerator is ab. The LCD of the denominator is b.
Simplify .
Complex Fractions with Different LCDs
Write as a division expression.
Simplify the numerator and denominator.
Multiply by the reciprocal of the divisor.
Simplify.
Complex Fractions with Different LCDs
Answer:
Complex Fractions with Same LCD
The LCD of all of the
denominators is xy.
Multiply by
Simplify
Distribute xy.
Complex Fractions with Same LCD
Answer:
