Question

If p(x) = 3x2 - 5x+7, then
(a) What number is p(2) ?
(b) Write the polynomial got by subtracting p(2) from p(x).
(c) Write P(x) - P(2) as the product of two first degree polynomials.​

Answer 1

Step-by-step explanation:

Given:-

P(x) = 3x^2 - 5x+7

To find:-

a) What number is p(2) ?

(b) Write the polynomial got by subtracting p(2) from p(x) ?

(c) Write P(x) - P(2) as the product of two first degree Polynomials ?

Solution:-

Given quadratic polynomial is P(x)=3x^2 - 5x+7

a) If x = 2 then

P(2) = 3(2)^2-5(2)+7

=> P(2) = 3(4)-10+7

=> P(2) = 12-10+7

=> P(2) = 19-10

P(2) = 9

b) On Subtracting P(2) from P(x)

=> P(x) - P(2)

=> 3x^2 - 5x+7 -9

=> 3x^2-5x-2

P(x) - P(2) = 3x^2-5x-2

c)

P(x) - P(2) = 3x^2 - 5x - 2

=> 3x^2 - 6x + x - 2

=> 3x ( x - 2 ) +1 ( x - 2 )

=> ( x - 2 ) (3x + 1)

P(x) - P(2) = ( x - 2 ) (3x + 1)

Answer:-

a) The value of P(2) = 9

b) The Pilynomial got by subtracting P(2) from P(x)

= P(x) - P(2) = 3x^2-5x-2

c) The product of two first degree polynomial of

P(x) - P(2) = ( x - 2 ) (3x + 1)