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If (2x+1) is a factor of (2x³+x²-6x-3), then zero of (2x+1) will also be a zero of (2x³+x²-6x-3). zero of (2x+1) can be found by equating it to 0. 2x+1 = 0 ⇒2x = -1 ⇒x = -1/2

Put x=-1/2 in (2x³+x²-6x-3). we get (2x³+x²-6x-3) = 2(-1/2)³ + (-1/2)² - 6(-1/2) - 3 = 2(-1/8) + (1/4) - 6(-1/2) - 3 = -2/8 + 1/4 + 6/2 - 3 = -1/4 + 1/4 + 3 - 3 = 0 Since -1/2 is also a zero of (2x³+x²-6x-3), (2x+1) is a factor of (2x³+x²-6x-3).