If polynomial Ax3 + 4x2 + Bx +5 leaves same remainder, when divided by x - 1 and x + 2
respectively then value of 3A + B is equal to
Answers
Concept:
Polynomials are the type of algebraic expressions that contains both variables and coefficients. Variables are those terms that can have different values and coefficients are those terms which are written with the variable.
In an polynomial, the expression does not have a negative exponent. Also the polynomial only involves the basic operation of mathematics that is addition, subtraction, multiplication and division.
Given:
A x³ + 4 x² + B x +5 leaves same remainder, when divided by x - 1 and x + 2
Find:
We need to find the value of 3A + B.
Solution:
For x-1:
Put x=1 in the polynomial:
A (1)³ + 4 (1)² + B (1) +5
=A+4+B+5
=A+B+9
For x+2:
Put x=-2 in the polynomial:
A (-2)³ + 4 (-2)² + B (-2) +5
=-8A+16-2B+5
=21-8A-2B
Now ATQ:
A+B+9=21-8A-2B
A+8A+B+2B=21-9
9A+3B=12
3A+B=4
Therefore, the value of 3A+B is equal to 4.
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