Linked Comprehensive type
$A = 5 x^{2} - 16 x - 21$
$B = 3 (x + 2)^{2} - 5 (x + 2) + 2$
Sum of the factors of $A$ and $B$ are

(x + 1) (8 x + 17)

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(x + 1) (8 x - 17)

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(x + 1) (5 x - 17)

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(x + 1) (8 x - 25)

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Solution

The correct option is B $(x + 1) (8 x - 17)$
$A = 5 x^{2} - 16 x - 21$
$B = 3 (x + 2)^{2} - 5 (x + 2) + 2$
factor of A.
$5 x^{2} - 16 x - 21$
$\Rightarrow 5 x^{2} - 21 x + 5 x - 21$
$\Rightarrow x (5 x - 21) + 1 (5 x - 21)$
$\Rightarrow (5 x - 21) (x + 1)$ Ans
factor of B.
$\Rightarrow 3 (x + 2)^{2} - 5 (x + 2) + 2$
$\Rightarrow 3 (x^{2} + 4 + 4 x) - 5 x - 10 + 2$
$\Rightarrow 3 x^{2} + 12 x + 12 - 5 x - 8$
$\Rightarrow 3 x^{2} + 7 x + 4$
$\Rightarrow 3 x^{2} + 4 x + 3 x + 4$
$x (3 x + 4) (x + 1)$ Ans
Sum of factors of A & B.
$\Rightarrow (5 x - 21) (x + 1) + (3 x + 4) (x + 1)$
$\Rightarrow (x + 1) {5 x - 21 + 3 x + 4} = (x + 1) {8 x - 17}$ Ans

Suggest Corrections

Similar questions

A = 5 x^{2} - 16 x - 21

B = 3 (x + 2)^{2} - 5 (x + 2) + 2

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