Question

X 25. Given polynomials: P(x) = 2x4- 3x3 - x2 + 4x 6 : Q(x) = x4 - 2x3 + 7x - 2; Calculate : a) P(x) + Q(x) b) Q(x) - P(x)
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Answer 1

Answer:

Step-by-step explanation:

Given that,.

P ( x ) = 2x⁴ - 3x³ - x² + 4x + 6 and Q ( x ) = x⁴ - 2x³ + 7x - 2

a) P ( x ) + Q ( x )

= 2x⁴ - 3x³ - x² + 4x + 6 + x⁴ - 2x³ + 7x - 2

= ( 2x⁴ + x⁴ ) + ( - 3x³ - 2x³ ) + ( - x² ) + ( 4x + 7x ) + ( 6 - 2 ) (∵adding like terms )

= 3x⁴ + ( - 5x³ ) - x² + 11x + 4 (∵ + × - = - )

= 3x⁴ - 5x³ - x² + 11x + 4 is the answer.

b ) Q ( x ) - P ( x )

= ( x⁴ - 2x³ + 7x - 2 ) - ( 2x⁴ - 3x³ - x² + 4x + 6 )

= x⁴ - 2x³ + 7x - 2 - 2x⁴ + 3x³ + x² - 4x - 6 (∵ - × + = - ; - × - = + )

= ( x⁴ - 2x⁴ ) + ( - 2x³ + 3x³ ) + x² + ( 7x - 4x ) + ( - 2 - 6 ) (∵like terms )

= - x⁴ + x³ + x² + 3x + ( - 8 )

= - x⁴ + x³ + x² + 3x - 8 is the answer.