Questions: Factor. x^2 + 7x - 18

Factor. x^2 + 7x - 18
Transcript text: Factor. \[ x^{2}+7 x-18 \]
failed

Solution

failed
failed

Solution Steps

To factor the quadratic expression \(x^2 + 7x - 18\), we need to find two numbers that multiply to the constant term (-18) and add up to the linear coefficient (7). Once these numbers are identified, we can express the quadratic as a product of two binomials.

Step 1: Identify the Quadratic Expression

We are given the quadratic expression \(x^2 + 7x - 18\). Our goal is to factor this expression into a product of two binomials.

Step 2: Find Two Numbers

To factor the quadratic expression, we need to find two numbers that multiply to the constant term \(-18\) and add up to the linear coefficient \(7\).

Step 3: Factor the Expression

The two numbers that satisfy these conditions are \(9\) and \(-2\) because:

  • \(9 \times (-2) = -18\)
  • \(9 + (-2) = 7\)

Thus, the quadratic expression can be factored as: \[ x^2 + 7x - 18 = (x - 2)(x + 9) \]

Final Answer

The factored form of the quadratic expression is \(\boxed{(x - 2)(x + 9)}\).

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Nervous tissue consists of cells called which pass information, and cells that support them, called. a. Axons, microtubules b. Cerebrospinal nerves, neuroglia c. Neurons, neuroglia d. Nuclei, dendrites
failedAnswered
The names and chemical formulae of some chemical compounds are written in the first two columns of the table below. Each compound is soluble in water. Imagine that a few tenths of a mole of each compound is dissolved in a liter of water. Then, write down in the third column of the table the chemical formula of the major chemical species that will be present in this solution. For example, you know water itself will be present, so you can begin each list with the chemical formula for water (H2O). Note: "major" chemical species are those present in concentrations greater than 10^-6 mol / L. compound formula major species present when dissolved in water --------- methanol CH3OH propylene glycol C3H6(OH)2 glycerol C3H8O3
failedAnswered
True or False Question Thinking about how your body is reacting to a particular situation may help you determine which emotion you are experiencing. True False
failedAnswered
B. Periodic table 1. Write the elemental symbols and atomic numbers from Procedure A in the proper boxes on the blank periodic table in the report sheet. Write the group numbers on the top of the representative element vertical columns using both numbering systems. Write the period numbers for each of the horizontal rows. Draw a heavy line to separate the metals and nonmetals. 2. Six of the fourteen actinides were named for scientists. Write the elemental symbols and atomic numbers in the proper boxes on the blank periodic table in the report sheet for the elements named for the following famous scientists: Marie Curie (known for her pioneering work on radioactivity), Albert Einstein (developed the theory of general relativity), Dmitri Mendeleev (created the periodic table), and Alfred Nobel (inventor of dynamite and sponsor of the Nobel prizes). 3. Use colored pencils to label and shade the columns that contain the alkali metals, alkaline earth metals, halogens, and noble gases.
failedAnswered
Karen deposits 10,000 into an account that pays simple interest at a rate of 2% per year. David deposits 10,000 into an account that also pays 2% interest per year. But it is compounded annually. Find the interest Karen and David earn during each of the first three years. Then decide who earns more interest for each year. Assume there are no withdrawals and no additional deposits.