Answer:
(2c^2+3)(2c-1)(2c+1)
Step-by-step explanation:
8c^4+10c^2-3
8c^4+12c^2-2c^2-3
4c^2(2c^2+3)-(2c^2+3)
(2c^2+3)(4c^2-1)
(2c^2+3)(2c-1)(2c+1)
Given polynomial in the question,
8c⁴ + 10c² - 3
Coefficient of c⁴ = 8
Coefficient of c² = 10
Constant term = -3
Steps to factorize the given polynomial,
Multiplication of 8 and (-3) = 8(-3) = -24
Split (-24) into two numbers such that sum of these numbers is equal to coefficient of c².
(-24) = (12)(-2)
Addition of 12 and -2 = 12 - 2 = 10
Therefore, 8c⁴ + 10c² - 3 = 8c⁴ + 12c² - 2c² - 3
= 4c²(2c² + 3) - 1(2c² + 3)
= (4c²- 1)(2c² + 3)
= (2c - 1)(2c + 1)(2c² + 3) [a² - b² = (a - b)(a + b)]
Therefore, factored form of the given polynomial is (2c - 1)(2c + 1)(2c² + 3).
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