answer this question
Answers
Answer:
To be done :
We are asked to check whether (3x - 7) is a factor of the Polynomial 6x³ + x² - 26x - 25
Let us make (3x - 7) = 0, in order to find the value of x.
\longrightarrow{ \sf{3x - 7 = 0}}⟶3x−7=0
\longrightarrow{ \sf{3x = 7}}⟶3x=7
\longrightarrow{ \boxed{ \sf{x = \dfrac{7}{3} }}}⟶
x=
3
7
Now let's substitute the value of x in the given Polynomial,
\longrightarrow{ \sf{ {6x}^{3} + {x}^{2} - 26x - 25}}⟶6x
3
+x
2
−26x−25
\longrightarrow{ \sf{6( { \dfrac{7}{3}) }^{3} + {( \dfrac{7}{3}) }^{2} - 26 \times \dfrac{7}{3} - 25}}⟶6(
3
7
)
3
+(
3
7
)
2
−26×
3
7
−25
Uff, how scary this looks -.-
Let's make it simpler by simplifying it! xD xD
\longrightarrow{ \sf{6 \times \dfrac{343}{27} + \dfrac{49}{9} - 26 \times \dfrac{7}{3} - 25}}⟶6×
27
343
+
9
49
−26×
3
7
−25
\longrightarrow{ \sf{ \dfrac{686}{9} + \dfrac{49}{9} - \dfrac{182}{3} - 25}}⟶
9
686
+
9
49
−
3
182
−25
Let's take the LCM ;)
\longrightarrow{ \sf{ \dfrac{686 + 49 - 546 - 225}{9} }}⟶
9
686+49−546−225
It looks easy now, doesn't it? xD
\longrightarrow{ \sf{ \dfrac{ - 36}{ 4} }}⟶
4
−36
\longrightarrow{ \sf{ - 4}}⟶−4
If (3x - 7) was a factor of the given Polynomial, then by substituting the value of x in the Polynomial we should get 0. But here, we didn't.
Hence, (3x - 7) is not the factor of 6x³ + x² - 26x - 25.
_____________________
Itna kuch krne ke baad we realised that it isn't the factor, I be like : Mehnat Barbaad, huh! xD xD
But who knows agar ye question 3 marks ka aa jaye :grin: xD
For now, let's not predict the future. All the best! :D
Best of luck
If (3x - 7) was a factor of the given Polynomial, then by substituting the value of x in the Polynomial we should get 0. But here, we didn't. Hence, (3x - 7) is not the factor of 6x³ + x² - 26x - 25
Answer:
3x-7 is not factor
Step-by-step explanation:
because remainder is not equal to zero so 3x-7 is not factor of p(x)
