The expression 4x^3-bx^3+x-c leaves a remainder 0 and 30 when divided by (x+1) and (2x-3) respectively. Calculate the values a and b and hence factorise the expression completely.
asked Feb 6, 2017 in Algebra 1 Answers by Paula

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

Assuming -b^3 should be -bx^2:

Use synthetic division for dividing x+1:

-1 | 4 -b           1       -c

      4 -4       4+b -(5+b)

      4 -(4+b) 5+b | 0

So -c-5-b=0 and c=-5-b.

Suppose f(x) is a function of x (polynomial with degree 2) such that:


Let f(x)=px^2+qx+r then

(2x-3)(px^2+qx+r)+30=4x^3-bx^2+x-c, because of the remainder 30.


We can equate coefficients of like terms:

x^3: 2p=4 so p=2

x^2: -3p+2q=-b, but p=2 so q=(6-b)/2

x: -3q+2r=1, but q=(6-b)/2 so 2r=1+3(6-b)/2=(2+18-3b)/2=(20-3b)/2 and r=(20-3b)/4.

Constant: -3r=-c-30, -3(20-3b)/4=-c-30, -60+9b=-4c-120, 9b+4c=-60.

But c=-5-b, so 9b-20-4b=-60, 5b=-40, b=-8 and c=-5+8=3.

The expression is 4x^3+8x^2+x-3.

The two numbers are therefore -8 and 3.

The result of dividing by x+1 is therefore 4x^2+4x-3=(2x-1)(2x+3).

The complete factorisation is (x+1)(2x-1)(2x+3).

Let's see if this is correct. 4x^3+4x^2-3x+4x^2+4x-3=4x^3+8x^2+x-3. This appears to be correct for x+1.

Now 2x-3: if we subtract 30 from the expression, 2x-3 should exactly divide into it:


Substituting in f(x) we have f(x)=2x^2+7x+11 (putting in values for p, q and r).



answered Feb 8, 2017 by Rod Top Rated User (560,000 points)

Related questions

1 answer
asked May 19, 2014 in Algebra 1 Answers by Safal Das Biswas Level 4 User (7,940 points) | 240 views
1 answer
asked Apr 6, 2013 in Algebra 2 Answers by unknown (140 points) | 98 views
1 answer
asked Nov 4, 2012 in Algebra 2 Answers by aaminahanif Level 1 User (540 points) | 309 views
1 answer
asked May 9, 2013 in Algebra 1 Answers by anonymous | 56 views
1 answer
asked Mar 10, 2013 in Factors of a number by anonymous | 115 views
2 answers
asked Mar 10, 2013 in Factors of a number by anonymous | 358 views
Welcome to, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
81,280 questions
85,416 answers
68,898 users