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:

x+13x+4=x23x2+7x+41+3x2+7x+41x+\frac{1}{3}x+4=x^2\frac{3x^2+7x+4}{1}+\frac{3x^2+7x+4}{1}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Factor by groupingright chevron icon

Full solution

Q. x+13x+4=x23x2+7x+41+3x2+7x+41x+\frac{1}{3}x+4=x^2\frac{3x^2+7x+4}{1}+\frac{3x^2+7x+4}{1}
  1. Multiply by LCD: Multiply both sides of the equation by the least common denominator (LCD), which is (3x+4)(3x2+7x+4)(3x + 4)(3x^2 + 7x + 4), to clear the fractions.\newline(x+13x+4)×(3x+4)(3x2+7x+4)=(x2+13x2+7x+4)×(3x+4)(3x2+7x+4)(x + \frac{1}{3x + 4}) \times (3x + 4)(3x^2 + 7x + 4) = \left(\frac{x^2 + 1}{3x^2 + 7x + 4}\right) \times (3x + 4)(3x^2 + 7x + 4)
  2. Simplify after distribution: Simplify both sides of the equation after distributing the LCD. \newlinex(3x+4)(3x2+7x+4)+(3x2+7x+4)=(x2+1)(3x+4)x(3x + 4)(3x^2 + 7x + 4) + (3x^2 + 7x + 4) = (x^2 + 1)(3x + 4)
  3. Distribute xx and simplify: Distribute xx into (3x+4)(3x2+7x+4)(3x + 4)(3x^2 + 7x + 4) and simplify the left side of the equation.\newline3x3+4x2+7x2+28x+16x+3x2+7x+4=(x2+1)(3x+4)3x^3 + 4x^2 + 7x^2 + 28x + 16x + 3x^2 + 7x + 4 = (x^2 + 1)(3x + 4)
  4. Combine like terms: Combine like terms on the left side of the equation.\newline3x3+14x2+51x+4=(x2+1)(3x+4)3x^3 + 14x^2 + 51x + 4 = (x^2 + 1)(3x + 4)
  5. Distribute and simplify: Distribute (x2+1)(x^2 + 1) into (3x+4)(3x + 4) on the right side of the equation.\newline3x3+14x2+51x+4=3x3+4x2+3x+43x^3 + 14x^2 + 51x + 4 = 3x^3 + 4x^2 + 3x + 4
  6. Subtract and set to zero: Subtract 3x33x^3, 4x24x^2, 3x3x, and 44 from both sides of the equation to get all terms on one side and set the equation to zero.\newline3x3+14x2+51x+4−(3x3+4x2+3x+4)=03x^3 + 14x^2 + 51x + 4 - (3x^3 + 4x^2 + 3x + 4) = 0
  7. Combine like terms: Combine like terms after subtraction.\newline14x2+51x+4−4x2−3x−4=014x^2 + 51x + 4 - 4x^2 - 3x - 4 = 0\newline10x2+48x=010x^2 + 48x = 0

More problems from Factor by grouping

Question
Find the greatest common factor.\newline9v3,6v39v^3, 6v^3\newline\newlineWrite your answer as a constant times a product of single variables raised to exponents.\newline‾\underline{\hspace{1cm}}
Get tutor helpright-arrow

Posted 1 month ago

Question
Factor out the greatest common factor. If the greatest common factor is 11, just retype the polynomial.\newline6x3+9x26x^3 + 9x^2\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
Factor.\newlinek2+9k+18k^2 + 9k + 18\newline______
Get tutor helpright-arrow

Posted 1 month ago

Question
Factor.\newline9j2−169j^2 - 16\newline______
Get tutor helpright-arrow

Posted 1 month ago

Question
Factor.\newlinej3+2j2+5j+10j^3 + 2j^2 + 5j + 10
Get tutor helpright-arrow

Posted 2 months ago

Question
Factor x4+6x2+9x^4 + 6x^2 + 9 completely.\newlineAll factors in your answer should have integer coefficients.\newline______
Get tutor helpright-arrow

Posted 2 months ago

Question
Factor.\newlinez2+13z+22z^2 + 13z + 22\newline______
Get tutor helpright-arrow

Posted 1 month ago

Question
Simplify the expression: \newline5x+9x−4x−2x5x + 9x - 4x - 2x \newline______
Get tutor helpright-arrow

Posted 3 months ago

Question
3−323 - 3^2
Get tutor helpright-arrow

Posted 3 months ago

Question
5−525 - 5^2
Get tutor helpright-arrow

Posted 1 month ago

View all (50)