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Mathematics Clinic => Calculus => Topic started by: Lobcity on May 26, 2021

Title: Factor x4 + 4x3 + 4x2 - 9 into a product of linear factors and quadratic factors having no real roots.
Post by: Lobcity on May 26, 2021

Question 1

Factor the polynomial  x4 - x3 - x2 + x  into a product of linear factors and quadratic factors having no real roots.
◦ x(x - 1)(x2 - 1)
◦ x(x + 1)(x - 1)2
◦ x(x - 1)(x + 1)2
◦ x(x + 1)(x + 1)2
◦ (x2 + 1)(x - 1)2

Question 2

Factor  x4 + 4x3 + 4x2 - 9  into a product of linear factors and quadratic factors having no real roots.
◦ (x2 - 2x + 3)(x2 + 2x + 3)
◦ (x2 - x + 9)(x2 + x + 1)
◦ (x - 1)(x + 3)(x2 + 2x + 3)
◦ (x - 1)2 (x + 3)2
◦ (x - 1)(x + 3)(x + 1)(x - 3)

Title: Factor x4 + 4x3 + 4x2 - 9 into a product of linear factors and quadratic factors having no real roots.
Post by: cat123 on May 26, 2021

Answer 1

x(x + 1)(x - 1)2

Answer 2

(x - 1)(x + 3)(x2 + 2x + 3)