Question

Verify if 1 and -3 are zeroes of the polynomial 3x³+5x²-11x+3. If yes, then factorize the polynomial.

Answer 1

Hola Mate !!

Here's your answer :-

$p(x) = 3 {x}^{3} + 5 {x}^{2} - 11x + 3$

Now, verifying :

$p(1) = 3 \times {1}^{3} + 5 \times {1}^{2} - 11 \times x + 3 \\ = 3 +5 - 11 + 3 \\ = 11 - 11 \\ = 0$

$p( - 3) = 3 \times { - 3}^{3} + 5 \times { - 3}^{2} - 11 \times - 3 + 3 \\ = 3 \times - 27 + 5 \times 9 + 33 + 3 \\ = - 81 + 45 + 36 \\ = - 81 + 81 \\ = 0$

Factorising ⤴