High School

What polynomial, when divided by [tex]2x^2[/tex], yields [tex]7x^6 - 6x^4 + 8x^2[/tex] as a quotient?

Answer :

Answer:

14x⁸ - 12x⁶ + 16x⁴

Step-by-step explanation:

To find the required polynomial, multiply 2x² and the quotient.

Multiply each term of (7x⁶ - 6x⁴ + 8x²) by 2x².

2x² * 7x⁶ = (2*7) *x²⁺⁶ = 14x⁸

Required polynomial =2x² *(7x⁶ - 6x⁴ + 8x²)

= (2x²*7x⁶) - (2x²*6x⁴) + (2x²*8x²)

= 14x⁸ - 12x⁶ + 16x⁴

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