Polynomial Conjugates & Difference of Squares
Read this topicExplanations 2
- Factoring: Product of a Sum and Difference Whenever you see a polynomial in the form of a2−b2a^2 - b^2a2−b2, where aaa and bbb are perfect squares, its factored form is (a+b)(a−…
By Vinitha Ranganeni, Naomi Burgess, Alex Federspiel, Sarah Walker, Anusha Rahman
- (Video) Factoring Sum and Difference of Cubes by mathman1024 Here's a video by mathman1024 showing you how to factor polynomials with the sum or difference of cubes. The formula…
By Alex Federspiel, Anusha Rahman
Problems 14
- If x9−xx^9-xx9−x is factored completely into a product of terms with integer coefficients, how many terms are there?
- If aaa and bbb are nonzero real numbers such that ∣a∣≠∣b∣\left| a \right| \ne \left| b \right|∣a∣=∣b∣, compute the value of the expression (b2a2+a2b2−2)×(a+bb−a+b−aa+b)×(1a2+1b…
- How many terms are there in the expansion of (a+b)(a2+b2)(a4+b4)⋯(a64+b64)?(a + b)(a^2+b^2)(a^4+b^4)\cdots (a^{64}+b^{64})?(a+b)(a2+b2)(a4+b4)⋯(a64+b64)?
- Does the product of any four consecutive natural numbers plus one need to be a perfect square?
- What is the prime factorization of 24x4y324x^4y^324x4y3?
- If aaa and bbb are two consecutive whole numbers, and a2=b2−99a^2=b^2-99a2=b2−99, what is aaa?
- If x2+4y2=4yxx^2 + 4y^2 = 4yxx2+4y2=4yx and y≠0y\neq0y=0, find xy\frac{x}{y}yx.
- Factorize: 4(2a−3)2−3(2a−3)(a−1)−(a−1)24( 2a-3)^2-3(2a-3)(a-1) - ( a-1 )^24(2a−3)2−3(2a−3)(a−1)−(a−1)2.
- Write the following fraction in simplest form x4−y4x+y.\frac{x^4-y^4}{x+y}.x+yx4−y4.
- Is x2−y2x^2-y^2x2−y2 divisible by x−yx-yx−y? If so, find the quotient.
- Factor x3+3x2+3x+9.x^3 + 3x^2 + 3x + 9.x3+3x2+3x+9.
- Find the LCM of 2x2+2x2x^2 + 2x2x2+2x and 2x4+2x3.2x^4 + 2x^3.2x4+2x3.
- Find the LCM of xy2xy^2xy2 and xy(y+1).xy(y + 1).xy(y+1).
- Find the LCM of 12(x5+y5)2(x2+y2)512(x^5 + y^5)^2(x^2 + y^2)^512(x5+y5)2(x2+y2)5 and 12(x5+y5)5(x2+y2)2.12(x^5 + y^5)^5(x^2 + y^2)^2.12(x5+y5)5(x2+y2)2.