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Chapter 7: Q. 296 (page 878)

In the following exercises, factor completely.

3n2+30n+72

Short Answer

Expert verified

The factored form of the polynomial is3n2+30n+72=3(n+4)(n+6).

Step by step solution

01

Step 1. Given Information.  

The given Polynomial is3n2+30n+72.

02

Step 2. Factoring by Reverse foil.

Polynomial have a common factor3.

3n2+30n+72=3(n2+10n+24)

In the parentheses, it is a trinomial with a leading coefficient1.

So factorize it by reverse foil.

3n2+30n+72=3(n2+10n+24)3n2+30n+72=3(n2+6n+4n+24)3n2+30n+72=3(n(n+6)+4(n+6))3n2+30n+72=3(n+4)(n+6)

Now the polynomial cannot be factored further.

So factored form islocalid="1647946235208" 3n2+30n+72=3(n+4)(n+6).

03

Step 3. Verification.  

Check whether the expanded form of the factored polynomial is equal to the original polynomial or not.

3n2+30n+72=?3(n+4)(n+6)3n2+30n+72=?3(n2+6n+4n+24)3n2+30n+72=?3(n2+10n+24)3n2+30n+72=3n2+30n+72

The left-hand side is equal to the right-hand side so factored form is correct.

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Most popular questions from this chapter

A rectangular sign has an area of 30square feet. The length of the sign is one foot more than the width. Find the length and width of the sign.

The difference of squares y4-625can be factored as y2-25y2+25.But it is not completely factored. What more must be done to completely factor it?

Solve:y-6y+9=0.

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.

Factor:8nn-4+5n-4
See all solutions

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