find the value of p and q if x-1 andx+2 are factor of polynomial 2x^3+px^2+qx-14
Answers
Answer:
First, multiply out the two factors:
(x - 1)(x + 2) = x^2 + x - 2
Now, divide the original polynomial by that expression. This has to be done by long division which is very difficult to format in a text-based medium but let’s see what I can do:
2x + (p - 2)
x^2 + x - 2 ) 2x^3 + px^2 + qx - 14
-2x^3 - 2x^2 + 2x
(p - 2)x^2 + (q + 2)x - 14
-(p - 2)x^2 - (p - 2)x + 2(p - 2)
(q + 2 - p + 2)x - 14 + 2(p - 2)
That last bit (q + 2 - p + 2)x - 14 + 2(p - 2) is the remainder and, if your two expressions are factors, has to equal 0 since they have to divide the original polynomial evenly. That means we have to have
-14 + 2(p - 2) = 0
2(p - 2) = 14
p - 2 = 7
p = 9
and
q - p + 4 = 0
q - 9 + 4 = 0
q-5=0
q=5
Step-by-step explanation:
Answer:
hope this helps see if the answer comes
