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Polynomial p(x) = 2x3 + x2 + ax + b, where a
and b are real integer constants, has a factor
of (x - 1). If the remainder of the division of
p(x) by (x + 3) is -36, what is the value of
2a-5b?
-6
-3
3
6

Polynomial px 2x3 x2 ax b where a and b are real integer constants has a factor of x 1 If the remainder of the division of px by x 3 is 36 what is the value of class=

Respuesta :

nathanbowman

Answer:

-6

Step-by-step explanation:

asuwafohjames

The value of 2a-5b is -6.

 

Given:

  • P(x) = 2x³+x²+ax+b

Where:

  • a and b = constant.

If the polynomial p(x) has a factor of (x-1)

Therefore,

  • P(1) = 0.
  • P(1) =  2(1³)+1²+a(1)+b = 0
  • 2+1+a+b = 0
  • a+b+3 = 0
  • a+b = -3 ................ Equation 1

Also,

When P(x) is divided by (x+3) the remainder is -36

  • P(-3) = -36
  • 2(-3³)+(-3²)+(-3×a)+b = -36
  • -54+9-3a+b = -36
  • -45-3a+b = -36
  • b-3a = -36+45
  • b-3a = 9................... Equation 2

Solving equation 1 and equation 2 simultaneously,

make "a" the subject of equation 1

  • a+b = -3
  • a = -3-b.................. Equation 3

Substitute the value of "a" in equation 3 into equation 2

  • b-3(-3-b) = 9
  • b+9+3b = 9
  • 4b = 9-9
  • 4b = 0
  • b = 0/4
  • b = 0.

Substitute the value of b into equation 3.

  • a = -3-0
  • a = -3.

Thefore,

  • 2a-5b = 2(-3)+5(0)
  • 2a-5b = -6.

Hence, The value of 2a-5b is -6

Learn more about polynomial here: https://brainly.com/question/2833285

 

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