Check whether (x + 6) is a factor of
[tex] {x}^{2} [/tex]
– x – 42 or not.
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Check whether (x + 6) is a factor of
[tex] {x}^{2} [/tex]
– x – 42 or not.
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Answer:
To check that x−2 is the factor of x
3
−2x
2
−5x+4:
The value of x−2=0 ⟹ x=2.
So, put x=2 in expression, we get,
f(x)=x
3
−2x
2
−5x+4
f(2)=(2)
3
−2(2)
2
−5(2)+4
⇒f(2)=8−2×4−5×2+4
⇒f(2)=8−8−10+4
⇒f(2)=−6.
Remainder is not 0, when x−2 divides the polynomial x
3
−2x
2
−5x+4.
Thus x−2 is not a factor of polynomial x
3
−2x
2
−5x+4.