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Chapter 7: Q 274 (page 868)

Home repair The height a twelve-foot ladder can

reach up the side of a building if the ladder鈥檚 base

is b feet from the building is the square root of the

binomial 144-b2Factor the binomial.

Short Answer

Expert verified

The factorization of the binomial is(12+b)(12-b)

Step by step solution

01

Step 1. Given information

Given expression is144-b2

02

Step 2. Write the expression as the difference of square.

144-b2=(12)2-(b)2

03

Step 3. Use formula a2-b2=(a+b)(a-b)

(12)2-(b)2=(12+b)(12-b)

04

Step 4. Check

(12+b)(12-b)=144+12b-12b-b2=144-b2

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Pumpkin drop A fall tradition at the University of California San Diego is the Pumpkin Drop, where a pumpkin is dropped from the eleventh story of Tioga Hall.

(a) The binomial -16t2+128 gives the height of the pumpkin t seconds after it is dropped. Factor the greatest common factor from this binomial.

(b) If the pumpkin is thrown down with initial velocity 32 feet per second, its height after t seconds is given by the trinomial -16t2-32t+128.Completely factor this trinomial.
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