Help with factoring polynomials?
I need help with these problems, any help would be appreciated. a- complete factoring. the terms of the polynomial is z^3 - 4 x(z^3 - 4) + 8y(z^3 - 4) = (z^3 - 4) (???????) b- factor this. x(3x - yz) + 2yz(3x - yz) c- factor by grouping. 8xy - 10y + 36x - 45 (?????)(?????) d- factor by grouping. 6ab - 21 + 14a - 9b
Help factoring polynomials?
2x^2 - 4xy - 7x + 14y Regroup: 2x^2 - 7x + 14y - 4xy Factor: x * (2x - 7) + 2y (7 - 2x) Rearrange Based on (7 - 2x) = - (2x - 7): x * (2x - 7) - 2y * (2x - 7) Factor: (2x - 7) * (x - 2y)
Factoring polynomials:?
x^2-64 (x-8)(x+8) 2x^2y-4xy-30y 2y(x^2-2x-15) 2y(x-5)(x+3)
Factoring polynomials with tiles?
0 = 2X^2 + 8X + 6 0 = X^2 + 4X + 3 0 = (X + 1)(X + 3) X = -3 X = -1
What is the purpose of factoring polynomials?
To find roots: One can factorise a polynomial, [math]f(x)[/math] say, to find the roots - ie the values of [math]x[/math] where [math]f(x)=0[/math]. Why do this? It may be useful to graph a polynomial and this finds the [math]x[/math]-intercepts.To simplify expressions/equations: A factored polynomial will almost always be nicer and neater to look at than an unfactored, wholly expanded polynomial. Which is beneficial because it will be easier to understand what it is being said and/or it may be easier to manipulate.An interesting question: Factorising polynomials is a useful tool, and it follows naturally from the practise of decomposing integers. Can you take it for granted though that you can even find a factorisation?
Factoring polynomials completely?
Hi, a. -5p^4+2000 Take out a GCF of -5. Then factor as the difference of perfect squares -5(p^4 - 400) -5(p^2 - 20)(p^2 + 20) <== answer b. -36x^4+25x^2-4 Factor out a GCF of -1. -1(36x^4 - 25x^2 + 4) -1(9x^2 - 4)(4x^2 - 1) Both binomials are the difference of perfect squares, so factor both of them again. -1(3x - 2)(3x + 2)((2x - 1)(2x + 1) <== answer c. x^4-18x^2+81 (x^2 - 9)(x^2 - 9) Again both binomials are the difference of perfect squares, so factor both of them again. (x - 3)(x + 3)(x - 3)(x + 3) or (x - 3)²(x + 3)² <== answer Notice since the factors repeat you can write them with exponents outside the parentheses if you choose, but either way is correct. d. 60x^2-64xy-60y^2 Factor out a GCF of 4. 4(15x^2 - 16xy - 15y^2) 4(3x - 5y)(5x + 3y) <== answer I hope that helps!! :-)
How can I get better at factor polynomials?
That you are interested in learning this for math competitions suggests that you already have a reasonable foundation in factoring the sort of expressions that are commonly encountered in school math. Familiarizing yourself with general cases for factoring higher order polynomials could be helpful. You might also want to think about learning modulo arithmetic, which will help you better understand divisibility and the relation between numbers.