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Chapter 6: Problem 7

Use the method of your choice to factor each trinomial, or state that the trinomial is prime. Check each factorization using FOIL multiplication. $$5 y^{2}-16 y+3$$

Short Answer

Expert verified
The trinomial is prime and cannot be factored over the integers.

Step by step solution

01

Compute ac Value and Find Its Factors

In the trinomial, \(5y^{2}-16y+3\), a=5, b=-16, and c=3. Start by finding ac, which is \(5*3 = 15\). Identify the pairs of factors of 15 and find a pair that can sum up to -16, the value of b. Since none of the pairs of factors of 15 can sum up to -16, this trinomial is prime.
02

Break the Middle Term (Not Applicable for Prime Trinomials)

This step is not applicable here as the trinomial is prime and cannot be factored about any integers.
03

Factorization (Not Applicable for Prime Trinomials)

The trinomial is prime and cannot be factored about any integers.
04

FOIL multiplication (Not Applicable for Prime Trinomials)

There is no need for FOIL multiplication here because no factorization could be performed in the previous steps.

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Most popular questions from this chapter

Use the \(x\)-intercepts for the graph in \(a[-10,10,1]\) by \([-13,10,1]\) viewing rectangle to solve the quadratic equation. Check by substitution. Use the graph of \(y=x^{2}+3 x-4\) to solve \(x^{2}+3 x-4=0\).

In Exercises \(130-133,\) use the \([\mathrm{GRAPH}]\) or \([\mathrm{TABLE}]\) feature of a graphing utility to determine if the polynomial on the left side of each equation has been correctly factored. If the graphs of \(y_{1}\) and \(y_{2}\) coincide, or if their corresponding table values are equal, this means that the polynomial on the left side has been correctly factored. If not, factor the polynomial correctly and then use your graphing utility to verify the factorization. $$4 x^{2}-9=(4 x+3)(4 x-3)$$

Solve equation and check your solutions. \((x-3)^{2}+2(x-3)-8=0\)

Use factoring to solve quadratic equation. Check by substitution or by using a graphing utility and identifying \(x\)-intercepts. \(4 x(x+1)=15\)

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