Question

By using long division, Prove that f(x)= 2x⁴+x³-12x²+11x-3 is a multiple of 2x-3​

Answer 1

Answer:

p(x) = 2x⁴ + 3x³ - 26x² - 5x + 6

g(x) = x - 3

After dividing we obtained :

• Quotient = 2x³ + 9x² + x - 2

• Remainder = 0

Refer to the attachment!

Verification :

★ Dividend = Divisor × Quotient + Remainder

→ 2x⁴ + 3x³ - 26x² - 5x + 6 = (x - 3) × 2x³ + 9x² + x - 2 + 0

→ 2x⁴ + 3x³ - 26x² - 5x + 6 = x(2x³ + 9x² + x - 2) - 3(2x³ + 9x² + x - 2) + 0

→ 2x⁴ + 3x³ - 26x² - 5x + 6 = (2x⁴ + 9x³ + x² - 2x) - (6x³ + 27x² + 3x - 6) + 0

→ 2x⁴ + 3x³ - 26x² - 5x + 6 = 2x⁴ + 9x³ + x² - 2x - 6x³ - 27x² - 3x + 6

→ 2x⁴ + 3x³ - 26x² - 5x + 6 = 2x⁴ + 9x³ - 6x³ - 27x² + x² - 2x - 3x + 6

→ 2x⁴ + 3x³ - 26x² - 5x + 6 = 2x⁴ + 3x³ - 26x² - 5x + 6

\therefore∴ (x-3) is factor of the polynomial 2x⁴ + 3x³ - 26x² - 5x + 6

Answer 2

Answer:

By using long division, prove that 2x +x3-120c²² + 1/oc-3 is multiple of 2x - 3