Question

The hcf of 8x4-16x3-40x2+48x and 16x5+64x4+80x3+32x2

Answer 1

We have to find 8x⁴ - 16x³ - 40x² + 48x and 16x^5 + 64x⁴ + 80x³ + 32x²

solution : factors of 8x⁴ - 16x³ - 40x² + 48x = 8x(x³ - 2x² - 5x + 6)

= 8x{x³ - x² - x² + x - 6x + 6}

= 8x{x²(x - 1) - x(x - 1) - 6(x - 1)}

= 8x(x - 1)(x² - x - 6)

= 8x(x - 1)(x - 3)(x + 2)

factors of 16x^5 + 64x⁴ + 80x³ + 32x² = 8x²{2x³ + 8x² + 10x + 4}

= 8x²{2x³ + 2x² + 6x² + 6x + 4x + 4}

= 8x²{2x²(x + 1) + 6x(x + 1) + 4(x + 1)}

= 8x²(x + 1)(2x² + 6x + 4)

= 8x²(x + 1)(2x² + 2x + 4x + 4)

= 8x²(x + 1)(2x + 4)(x + 1)

= 16x²(x + 1)²(x + 2)

now common factors = HCF = 8 × x × (x + 2)

= 8x(x + 2)

Therefore the hcf of given expressions is 8x(x + 2)

Answer 2

Answer:

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