Since (3x + 2) and (x - 1) are factors of the polynomial p(x), we can set the polynomial equal to zero and solve for x.
Setting p(x) = 0, we have:
(3x + 2)(x - 1) = 0
Expanding this expression, we get:
3x^2 - 3x + 2x - 2 = 0
Combining like terms, we have:
3x^2 - x - 2 = 0
Comparing this equation to the given polynomial p(x) = 3x^3 + hx^2 - 5x + k, we can equate the corresponding coefficients:
h = -1 (coefficient of x^2 term)
k = -2 (constant term)
Therefore, the values of h and k are -1 and -2, respectively.
To factorize the polynomial completely, we use the values of h and k to rewrite p(x) as:
p(x) = 3x^3 - x^2 - 5x - 2
Now we can see that p(x) has a common factor of (x - 1) and (3x + 2). Factoring out these common factors, we have:
p(x) = (x - 1)(3x + 2)(x + 2)
Hence, the polynomial is completely factorized as (x - 1)(3x + 2)(x + 2).
The polynomial 3x3 + hx2 - 5x + k is denoted by p(x). Given that (3x + 2) and (x- 1)
are factors of p(x), find the values of h and ofk. Hence factorise the polyomial completely.
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