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If (x5) is a factor of x34x211x+30, fin...

If (x5) is a factor of x34x211x+30, find the remaining factors.

A.

(x+3)and(x2)

B.

(x3)and(x+2)

C.

(x3)and(x2)

D.

(x+3)and(x+2)

Correct answer is A

(x - 5) is a factor of x34x211x+30. To find the remaining factors, let's draw out (x5) from the parent expression.

x34x211x+30=x35x2+x25x6x+30

=x2(x5)+x(x5)6(x5)=(x5)(x2+x6)

∴ To find the remaining factors, we factorize (x2+x6)

x2+x6=x2+3x2x6

=x(x+3)2(x+3)=(x+3)(x2)

∴ The other two factors are (x+3)and(x2)

ALTERNATIVELY
∴ x^2 + x - 6 = (x + 3) and (x - 2)