Using factor theorem, show that (x – 5) is a factor of the polynomia

1.	Using factor theorem, show that (x – 5) is a factor of the polynomial 2x3 – 5x2 – 28x + 15
Answer» Let P(x) = 2x³ – 5x² – 28x + 15 By factor theorem, (x – 5) is a factor of P(x), if P(5) = 0 P(5) = 2(5)³ – 5(5)² – 28(5) + 15 = 2 x 125 – 5 x 25 – 140 + 15 = 250 – 125 – 140 + 15 = 265 – 265 = 0 ∴ (x – 5) is a factor of 2x³ – 5x²– 28x + 15

Using factor theorem, show that (x – 5) is a factor of the polynomial 2x3 – 5x2 – 28x + 15

Answer»

Let P(x) = 2x³ – 5x² – 28x + 15

By factor theorem, (x – 5) is a factor of P(x), if P(5) = 0

P(5) = 2(5)³ – 5(5)² – 28(5) + 15

= 2 x 125 – 5 x 25 – 140 + 15

= 250 – 125 – 140 + 15 = 265 – 265 = 0

∴ (x – 5) is a factor of 2x³ – 5x²– 28x + 15