Factoring by Grouping
Read this topicProblems 18
- Factorize (ab+cd)2+(ac−bd)2(ab+cd)^2+(ac-bd)^2(ab+cd)2+(ac−bd)2. Check all that are correct.
- Factorize a2+b2+c2+2ab+2ac+2bca^2+b^2+c^2+2ab+2ac+2bca2+b2+c2+2ab+2ac+2bc.
- Simplify y4−xy3−x3y+x2y2x2+y2\dfrac{y^4-xy^3 -x^3y+x^2y^2}{x^2+y^2}x2+y2y4−xy3−x3y+x2y2, where x,yx,yx,y are positive real numbers.
- x3+4x2+3x−2x^3 + 4x^2 + 3x - 2x3+4x2+3x−2 has a factor of the form x+nx+nx+n, where nnn is an integer. Find nnn.
- When 4096x3+64x2−64x−14096x^3 + 64x^2 -64x - 14096x3+64x2−64x−1 is fully factored, how many linear terms are there?
- For how many integers nnn is 1+nx1+nx1+nx a factor of 36x3+9x2−4x−136x^3 + 9x^2 -4x - 136x3+9x2−4x−1?
- The polynomial 2x3+6x2+8x+242x^3 + 6x^2 +8x + 242x3+6x2+8x+24 factors as (x+n)Q(x)(x+n)Q(x)(x+n)Q(x), where nnn is an integer and QQQ is quadratic. What is Q(1)Q(1)Q(1)?
- The polynomial x3+3x2−x−3x^3 + 3x^2 - x -3x3+3x2−x−3 can be written in the form (x+a)(x+b)(x+c)(x+a)(x+b)(x+c)(x+a)(x+b)(x+c) for integers a,b,ca,b,ca,b,c. What is ∣(a−b)(b−c)(c…
- What is the quantity one wishes to find for each group in factoring by grouping?
- The product of the ages (in years) of Cindy, George, and Lucy is P(5)P(5)P(5), where P(x)=x3−6x2+5x+12P(x) = x^3 - 6x^2 +5x + 12P(x)=x3−6x2+5x+12. Cindy is older than George and…
- Janet wants to calculate the average of her Algebra exam grades. Unfortunately, Janet's teacher never returned the exams (she is a tough teacher!) and Janet doesn't know her gra…
- How many distinct positive real roots does the equation log10(x6)=(log10x)3\log_{10}(x^6) = (\log_{10}x)^3log10(x6)=(log10x)3 have?
- How many distinct positive real roots does the equation (log10(x6))2=(log10x)3(\log_{10}(x^6))^2 = (\log_{10}x)^3(log10(x6))2=(log10x)3 have?
- Find the value of xxx such that 6xy−4y+3x−2=06xy - 4y + 3x - 2 = 06xy−4y+3x−2=0 is true for all values of yyy.
- Evaluate the expression 121(113−117)+169(117−111)+289(111−113)11(113−117)+13(117−111)+17(111−113)\frac{121\left(\frac{1}{13}-\frac{1}{17}\right)+169\left(\frac{1}{17}-\frac{1}{1…
- Find all solutions on the interval [0,2π)[0,2\pi)[0,2π) for 2sin(x)cos(x)−sin(x)+2cos(x)−1=0.\\2\sin(x)\cos(x)-\sin(x)+2\cos(x)-1=0.2sin(x)cos(x)−sin(x)+2cos(x)−1=0.
- Simplify: x2+2x2y−2xy+2xy2−3y2x+y\frac{x^2+2x^2y-2xy+2xy^2-3y^2}{x+y}x+yx2+2x2y−2xy+2xy2−3y2
- Which of the following is not a factor of: x3−x2−24x−36x^3-x^2-24x-36x3−x2−24x−36