Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find factors of the quadratic expression: 6x2−3x−96x^{2}-3x-9\newline(?x+?)(x+?)(?x+?)(x+?)

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Evaluate integers raised to rational exponentsright chevron icon

Full solution

Q. Find factors of the quadratic expression: 6x2−3x−96x^{2}-3x-9\newline(?x+?)(x+?)(?x+?)(x+?)
  1. Identify Factors: We need to factor the quadratic expression 6x2−3x−96x^2 - 3x - 9. To do this, we look for two numbers that multiply to give the product of the coefficient of x2x^2 (which is 66) and the constant term (which is −9-9), and add up to the coefficient of xx (which is −3-3).
  2. Calculate Product: The product of the coefficient of x2x^2 and the constant term is 6×−9=−546 \times -9 = -54. We need to find two numbers that multiply to −54-54 and add up to −3-3.
  3. Find Suitable Numbers: The two numbers that satisfy these conditions are −9-9 and 66, because −9×6=−54-9 \times 6 = -54 and −9+6=−3-9 + 6 = -3.
  4. Perform Decomposition: Now we rewrite the middle term of the quadratic expression using the two numbers we found. This is known as decomposition. \newline6x2−3x−96x^2 - 3x - 9 becomes 6x2−9x+6x−96x^2 - 9x + 6x - 9.
  5. Factor by Grouping: Next, we factor by grouping. We group the terms as follows: 6x2−9x6x^2 - 9x + 6x−96x - 9.
  6. Factor out Common Factor: We factor out the common factor from each group. From the first group, we can factor out 3x3x, and from the second group, we can factor out 33. This gives us: 3x(2x−3)+3(2x−3)3x(2x - 3) + 3(2x - 3).
  7. Factor out Common Factor: We notice that (2x−3)(2x - 3) is a common factor in both terms, so we can factor it out.\newlineThe expression becomes (2x−3)(3x+3)(2x - 3)(3x + 3).
  8. Simplify Second Term: We can simplify the second term (3x+3)(3x + 3) by factoring out the common factor of 33, which gives us 3(x+1)3(x + 1).\newlineSo the final factored form of the expression is (2x−3)(3)(x+1)(2x - 3)(3)(x + 1).
  9. Write Final Answer: Since we are looking for factors in the form of ax+b)(cx+d)\, we can write the final answer as \(\(2x - 33)(33x + 33)\.

More problems from Evaluate integers raised to rational exponents

Question
Simplify.\newline811281^{\frac{1}{2}}\newline_____________
Get tutor helpright-arrow

Posted 9 months ago

Question
Simplify.\newline(−32)1/5(-32)^{1/5}\newline______
Get tutor helpright-arrow

Posted 9 months ago

Question
Simplify. Assume all variables are positive.\newlinew43w73\frac{w^{\frac{4}{3}}}{w^{\frac{7}{3}}}\newlineWrite your answer in the form AA or AB\frac{A}{B}, where AA and BB are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.\newline______
Get tutor helpright-arrow

Posted 5 months ago

Question
Simplify. Assume all variables are positive.\newline(2r13)8(2r^{\frac{1}{3}})^8\newline\newlineWrite your answer in the form AA or AB\frac{A}{B}, where AA and BB are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.\newline______
Get tutor helpright-arrow

Posted 5 months ago

Question
Simplify. Assume all variables are positive.\newlinev74⋅v94v^{\frac{7}{4}} \cdot v^{\frac{9}{4}}\newline\newlineWrite your answer in the form AA or AB\frac{A}{B}, where AA and BB are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.\newline______\newline
Get tutor helpright-arrow

Posted 5 months ago

Question
Simplify.\newline114⋅1141^{\frac{1}{4}} \cdot 1^{\frac{1}{4}}\newline______
Get tutor helpright-arrow

Posted 5 months ago

Question
Simplify. \newline32(−1/5)32^{(-1/5)}
Get tutor helpright-arrow

Posted 7 months ago

Question
Simplify. Assume all variables are positive.\newlinew32w52\frac{w^{\frac{3}{2}}}{w^{\frac{5}{2}}}\newline\newlineWrite your answer in the form AA or AB\frac{A}{B}, where AA and BB are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.\newline______\newline
Get tutor helpright-arrow

Posted 9 months ago

Question
Simplify. Assume all variables are positive.\newline(27x)23(27x)^{\frac{2}{3}}\newline\newlineWrite your answer in the form AA or AB\frac{A}{B}, where AA and BB are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.\newline______
Get tutor helpright-arrow

Posted 8 months ago

Question
Simplify. Assume all variables are positive.\newlinex14x114\frac{x^{\frac{1}{4}}}{x^{\frac{11}{4}}}\newline\newlineWrite your answer in the form AA or AB\frac{A}{B}, where AA and BB are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.\newline______\newline
Get tutor helpright-arrow

Posted 7 months ago

View all (95)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant