Question

divide (8x²+6x-35) by (4x-7)​

Answer 1

$\begin{gathered}\\ \sf\longmapsto (8x^{2}+6x-35)÷(4x-7)\end{gathered}$

$\begin{gathered}\\ \sf\longmapsto \frac{8x^{2}+6x-35}{4x-7}\end{gathered}$

$\begin{gathered}\\ \sf\longmapsto \frac{8x^{2}+20x-14x-35}{4x-7}\end{gathered}$

$\begin{gathered}\\ \sf\longmapsto \frac{4x(2x+5)-7(2x+5)}{4x+7}\end{gathered}$

$\begin{gathered}\\ \sf\longmapsto \frac{(2x+5)(4x-7)}{4x-7}\end{gathered}$

$\begin{gathered}\\ \sf\longmapsto 2x+5\end{gathered}$

Answer 2

Answer:

$2x + 5$

Step-by-step explanation:

STEP 1 : Equation at the end of step 1

STEP 2 : 8x2 + 6x - 35

Simplify —————————————

4x - 7

Step 3 : Trying to factor by splitting the middle term

Factoring 8x2 + 6x - 35

The first term is, 8x2 its coefficient is 8 .

The middle term is, +6x its coefficient is 6 .

The last term, "the constant", is -35

(Step-1 ): Multiply the coefficient of the first term by the constant 8 • -35 = -280

(Step-2) : Find two factors of -280 whose sum equals the coefficient of the middle term, which is 6 .

-280 + 1 = -279

-140 + 2 = -138

-70 + 4 = -66

-56 + 5 = -51

-40 + 7 = -33

-35 + 8 = -27

-28 + 10 = -18

-20 + 14 = -6

-14 + 20 = 6 That's it

(Step-3) : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -14 and 20

8x2 - 14x + 20x - 35

(Step-4) : Add up the first 2 terms, pulling out like factors :

2x • (4x-7)

Add up the last 2 terms, pulling out common factors :

5 • (4x-7)

(Step-5) : Add up the four terms of step 4 :

(2x+5) • (4x-7)

Which is the desired factorization

Canceling Out : Cancel out (4x-7) which appears on both sides of the fraction line.

Final result : 2x + 5

munishsharma32

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