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Chapter 0: Problem 30

Factor each trinomial, or state that the trinomial is prime. $$8 x^{2}+33 x+4$$

Short Answer

Expert verified
The factors of the trinomial \(8x^{2}+33x+4\) are \(8x+4\) and \(x+1\).

Step by step solution

01

Identify the Trinomial

The given expression is \(8 x^{2}+33 x+4\), which is a trinomial, meaning it has three terms.
02

Factoring

To factorize the quadratic trinomial, we need to find two numbers which add up to 33 (the coefficient of x) and multiply to \(8 \times 4 = 32\) (the product of the coefficient of \(x^2\) and the constant term). The numbers that fit the above condition are 29 and 4.
03

Write the Factors

Once the aforementioned conditions are met, the original trinomial can be written as a product of two binomials. Therefore, the factors of the given trinomial will be \(8x^{2}+33x+4 = (8x+4)(x+1)\)

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Most popular questions from this chapter

What does it mean to solve a formula for a variable?

Perform the indicated operations. $$\frac{1}{x^{n}-1}-\frac{1}{x^{n}+1}-\frac{1}{x^{2 n}-1}$$

Exercises \(142-144\) will help you prepare for the material covered in the next section. Use the distributive property to multiply: $$ 2 x^{4}\left(8 x^{4}+3 x\right) $$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I subtracted \(\frac{3 x-5}{x-1}\) from \(\frac{x-3}{x-1}\) and obtained a constant.

Exercises \(142-144\) will help you prepare for the material covered in the next section. Simplify and express the answer in descending powers of \(x\) : $$ 2 x\left(x^{2}+4 x+5\right)+3\left(x^{2}+4 x+5\right) $$
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