Question

factor theorem

Answer 1

Use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial.

x - 5; 3x2 + 5x + 50

Answer 2

if yes, that would mean that ... is a zero. just check if ... is indeed a zero.

Answer 3

3(0)^2+5(0)+50
0+0+50
50 so no?

Answer 4

don't replace \(x\) by \(0\). replace \(x\) by \(5\)

Answer 5

in any case, \(5\) cannot be a zero of \( 3x^2 + 5x + 50
\) because all the coefficients are positive

Answer 6

okay... so 3(5)^2+5(5)+50
75+25+50=150

Answer 7

the factor theorem basically says

if

(x -5) is a factor

then x = 5 is a zero

so you need to find

f(5)

if f(5) = 0 then you know (x -5) is a factor

Answer 8

we arnt trying to find 0's though....

Answer 9

that is clear right? if all the coefficients are positive, and you replace \(x\) by a positive number, then everything is positive, so it cannot be zero
zeros mean
\[f(x)=0\] not \(f(0)\)

Answer 10

for example the zeros of \(x^2-4\) are \(2\) and \(-2\) not \(0^2-4=-4\)

Answer 11

in any event \( f(x)=3x^2 + 5x + 50\) lives entirely above the \(x\) axis and has no zeros
does not factor with real numbers

Answer 12

according to the thm:
(x-5) is a factor of the polynomial
IFF
5 is a zero of the polynomial.

5 is not a zero => x-5 is not a factor of the polynomial.

Answer 13

ok...

so given a polynomial

e.g

\[y = x^2 + 5x + 6 \]

then

it factors to

\[y = (x + 2)(x + 3)\]

to find the values of x that may y = 0 you need to solve

\[x + 2 = 0... and.... x + 3 = 0\]

so the solutions are

x = -2, and x = -3

substitute these values into the original equation and you'll find

f(-2) = 0....... and f (-3) = 0

so therefore (x +2) and (x + 3) are factors...

Answer 14

lol okay thanks you guys