GIVING BRAINLIEST!!!Show that(Factor it) 4x^4-12x^3+22x^2-24x+26=(x-1)^2[(2x-1)^2+9]

Mathematics

1 answer:

-BARSIC- [3]2 years ago

3 0

Answer:

See below

Step-by-step explanation:

Given equation:

4x⁴ - 12x³ + 22x² - 24x + 26 = (x-1)²[(2x-1)² + 9]

Expand the right side and compare with left side:

(x - 1)²[(2x - 1)² + 9] =
(x² - 2x + 1)(4x² - 4x + 1 + 9) =
(x² - 2x + 1)(4x² - 4x + 10) =
x²(4x² - 4x + 10) - 2x(4x² - 4x + 10) + (4x² - 4x + 10) =
4x⁴ - 4x³ + 10x² - 8x³ + 8x² - 20x + 4x² - 4x + 10 =
4x⁴ - 12x³ + 22x² - 24x + 10

As we see LHS is different from RHS and the difference is 26 ≠ 10, all the other terms are equal

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