Question

Divide 3x2 – 11x – 4 by x – 4.

Answer 1

Answer:

The answer is $(3x+1)$

Step-by-step explanation:

we have

$\frac{3x^{2}-11x-4}{x-4}$

Convert the numerator in factored form

$3x^{2}-11x-4=0$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$3x^{2}-11x=4$

Factor the leading coefficient

$3(x^{2}-11x/3)=4$

Complete the square. Remember to balance the equation by adding the same constants to each side.

$3(x^{2}-11x/3+(121/36))=4+(121/12)$

$3(x^{2}-11x/3+(121/36))=(169/12)$

$(x^{2}-11x/3+(121/36))=(169/36)$

Rewrite as perfect squares

$(x-(11/6))^{2}=(169/36)$

Square root both sides

$x-\frac{11}{6}=(+/-)\frac{13}{6}$

$x=\frac{11}{6}(+/-)\frac{13}{6}$

$x=\frac{11}{6}+\frac{13}{6}=4$

$x=\frac{11}{6}-\frac{13}{6}=-\frac{1}{3}$

therefore

$3x^{2}-11x-4=3(x-4)(x+\frac{1}{3})=(x-4)(3x+1)$

Substitute

$\frac{3x^{2}-11x-4}{x-4}=\frac{(x-4)(3x+1)}{x-4}=(3x+1)$

Answer 2

I hope this helps you




3x²-11x-4
_________

(x-4)


(3x+1)(x-4)
_________
(x-4)



3x+1