







The remainder theorem 
20160327 

From Pratyasha: A quadratic polynomial when divide by x+2 leaves a remainder of 1 and when divided by x1 leaves a remainder of 4. What will be the remainder if it is divided by (x+2)(x1)? Answered by Penny Nom. 





A limit of a rational function 
20160116 

From selvamani: F (x) = x^3+3x^29x2 / x^3x6 and limit x tends to 2, f (x) exist then limit x tends to 2, f (x) is equal to ? How to answer this problem. Answered by Penny Nom. 





The zeros of a fourth degree polynomial 
20130123 

From Dakota: My problem has multiple steps and I have done everything but the last one. 8The original problem is f(x)=x^45x^3+7x^2+3x10 and I have to find the zeros of the equation. I used synthetic substitution like my teacher taught us to get the equation of x^33x^2+x+5=0 but now I don't know how to get the zeros of that equation, or solve it. Answered by Penny Nom. 





A cubic inequality 
20120325 

From Victoria: The flight path of a bumblebee above the ground can be modelled by the function f(x)= 2x^3 17x^2+ 11x + 130. Where x is the time in seconds and f(x) represents the height in inches above the ground. The entrance to the bee's hive is located 100 inches above the ground. Determine when the bumblebee's height is greater than 100 inches. The bee's height was monitored from 0 to 25 seconds inclusive. (over the domain 0 Answered by Penny Nom. 





4x^3  6x + 2 = 0 
20080528 

From paul: 4x^3  6x + 2 = 0 Answered by Janice Cotcher. 





The factor theorem 
20080506 

From Nomaan: factorise
x³2x²x+2
using factor theorem Answered by Penny Nom. 





Factor 2x^3 + 3x^2  32x + 15 
20080402 

From sarah: I have a course review I'm working on and I'm not sure how I'm supposed to factor the following
2x^3 + 3x^2  32x + 15. Answered by Penny Nom. 





(x+2) is a factor of x^3+bx^214x+24. Find the value of b? 
20070311 

From victoria: hi my names victoria and i have been stuck on this question for ages can you please help me! (x+2) is a factor of x^3+bx^214x+24. Find the value of b? Answered by Penny Nom. 





The factor theorem 
20070304 

From Sophia: hi this is sophia, 10th grade from the philippines. im really having a hard time in factor theorem im just asking if you could help me solve these problems because i really dont have an idea on how to do solve these.. please
find the values of A and B so that (x+3) (x2) are both factors of x^3+Ax^2+Bx12
and
find the values of A, B, and C so that (x3) (x+1)and (x2) factors of P(x)=x^4+Ax^3+Bx^2+Cx+12
please help me.. i really do not understand these problems Answered by Penny Nom. 





When kx^2+3x+1 divided by (x2) the remainder is 3 
20061109 

From Brianna: For the dividend, find the value of k if the remainder is 3. (kx^2+3x+1) divided by (x2) Answered by Penny Nom. 





X^1/3X^1/9=60 
20060926 

From Harini: I need the answer for
The value of X in X^1/3X^1/9=60. Answered by Penny Nom. 





f(x) is a polynomial of degree 3. 
20060313 

From Meadow: f(x) is a polynomial of degree 3. It leaves a remainder of 10 and 4 when divided by
x + 1 and x  2 respectively. Given also that f(1) = f(2) = 0, find the remainder when
f(x) is divided by x  3. Answered by Penny Nom. 





Factors of a cubic 
20060308 

From Skye: Show that (x+2) is a factor of f(x) where:
f(x) = px^{3} + (4p+2)x^{2} + (5p+4)x + 2p
Find the range of values for which the equation f(x) = 0 has 3 distinct real roots Answered by Penny Nom. 





The remainder theorem 
20051007 

From Ron: If f(x) is divided by (x3), the remainder is 5, and if it is divided by (x+1), the remainder is 3. Find the remainder when f(x)is divided by (x3)(x+1). Answered by Chris Fisher. 





An algebraic remainder 
20050622 

From Raymond: Given that 4x^{3}  kx is divisible by 2x+1, find the remainder when the expression is divided by 4  x^{2}. Answered by Penny Nom. 





The factor theorem 
20040308 

From LisaMarie:
Hi, I have a career link question from gr.12 advanced functions
and intro. calculus. The equations is:
R(t) = 5(t^{4}  4t^{3} +
19/4 t^{2}  3/2 t)
The question is to apply the factor theorem
and quadratic formula to determine the times it crosses the t axis. The
only method i know of for using the factor theorem is when the last number
does not have a variable beside it so i'm not sure how you would even
use the factor theorem for this? We haven't dealt with any that have 0 as
the last number with no variable so i'm a little confused! please help!
Thank you
Answered by Penny Nom. 





Factoring 
20030204 

From Marcin: I am having a really hard time with the factor theorem. Can you please help me with the following? (a'3 means a to the exponent 3)
a)8a'3+64b'3c'6 b)8x'412x'344x'2+24x c)x'421x'2100
Answered by Penny Nom. 





Factoring a cubic 
20021205 

From Dorota: I got a problem with factorise the expression 2x^{3}+11x^{2}5x50. Answered by Penny Nom. 





The factor theorem 
20020910 

From Yael: Prove (x  a  b) is a factor of x^{3}  a^{3}  b^{3}  3ab (a + b) Answered by Penny Nom. 





A limit 
20020903 

From Circe:
Lim 3x^{ 3}+ax+a+3 /(x^{ 2}+x2), X>2 Answered by Penny Nom. 





A degree 5 polynomial 
20020217 

From Carla: Write an equation for a polynomial of degree 5 given the following zeros: 7+3i, 2+sqrt(13), 6 Answered by Penny Nom. 





Factoring by graphing 
20000111 

From Dylan Kirkwood: How can you factor a quadratic equation by graphing it? Answered by Penny Nom. 





Solving a cubic equation 
19991230 

From Natalia: How can I solve: 2 x^{3}  x^{2} + x  2 = 0 ??? Answered by Penny Nom. 





Two algebra problems 
19991217 

From Michael Standfest: If x+4 is a factor of 2x^{4}+kx^{3}3kx^{2}+6x40, find k and Prove that n^{2}n is even for all n, using the proof of contradiction Answered by Penny Nom. 





Factoring 
19990330 

From Maggie Stephens: I don't know anything about factoring would you plese help me. 3x^{4}  48 54x^{6} + 16y^{3} 1258x^{3} 12x^{2}  36x + 27 9  81x^{2} a^{3} + b^{3}c^{3} I would greatly appreciate any help you can give me thanks. Answered by Jack LeSage. 





Factoring polynomials 
19990329 

From Karen: I have been unable to factorise a polynomial equation and was wondering if you could please help. It is level (1012) maths. The polynomial is x^{3} + x^{2}  24x + 36 I have tried a few factorisation methods such as foctorisation by grouping but it won't work this polynomial. Please help. Answered by Jeff Walters and Jack LeSage. 





The Factor Theorem 
19980118 

From Dhruv Bansal: Hi, I'm a ninth grade student doing a math project for school. I'm trying to learn about various ways of solving 3rd and 4th degree polynomial equations using the remainder theorem, the factor theorem, and synthetic division. The books I have all mention x  r, which I know nothing about, not even how to get it. I would really appreciate any information on this. Thanks. Dhruv Bansal Answered by Penny Nom. 

