If x3 - 3x2 - 3xf -7 - x - 1 ax2 -bx - c- hten a - b -c - 103412

The correct option is C 4 x^3 3x^2 + 3x +7 = (x+ 1) (ax^2 + bx + c) = ax^3 + bx^2 + cx+ ax^2 + bx +c x^3 3x^2 + 3x 7 = ax^3 + (b +a ) x^2 + (c + b ...

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Byju's Answer

Standard IX

Mathematics

Algebraic Identities

If x3 - 3x2 +...

Question

If $x^{3} - 3 x^{2} + 3 x f - 7 = (x + 1) (a x^{2} + b x + c), h t e n a + b + c =$

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Solution

The correct option is A
4

$x^{3} - 3 x^{2} + 3 x + 7 = (x + 1) (a x^{2} + b x + c) = a x^{3} + b x^{2} + c x + a x^{2} + b x + c x^{3} - 3 x^{2} + 3 x - 7 = a x^{3} + (b + a) x^{2} + (c + b) x + c$
Comparing the coefficient,
$a = 1 b + a = - 3 \Rightarrow b + 1 = - 3 \Rightarrow b = o o - 3 - 1 = - 4 c + b = 3 \Rightarrow c - 4 = 3 \Rightarrow c = 3 + 4 = 7 a + b + c = 1 - 4 + 7 = 8 - 4 = 4$

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If x3−3x2+3xf−7=(x+1)(ax2+bx+c),htena+b+c=

The correct option is A 4 x3−3x2+3x+7=(x+1)(ax2+bx+c)=ax3+bx2+cx+ax2+bx+cx3−3x2+3x−7=ax3+(b+a)x2+(c+b)x+c Comparing the coefficient, a=1b+a=−3⇒b+1=−3⇒b=oo−3−1=−4c+b=3⇒c−4=3⇒c=3+4=7a+b+c=1−4+7=8−4=4

If $x^{3} - 3 x^{2} + 3 x f - 7 = (x + 1) (a x^{2} + b x + c), h t e n a + b + c =$