Math, asked by shalinikansalemail, 5 months ago

(x²+x-1)(x+2)+(-3)
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Answers

Answered by Mehak890
1

Answer:

step 1

((x2)-x)-(1/2)((x-3)+3x2))

Step 2

((x2) - x) - (1/2 • (3x2 + x - 3))

Step 3

Trying to factor by splitting the middle term

Factoring 3x2+x-3

The first term is, 3x2 its coefficient is 3 .

The middle term is, +x its coefficient is 1 .

The last term, "the constant", is -3

Step-1 : Multiply the coefficient of the first term by the constant 3 • -3 = -9

Step-2 : Find two factors of -9 whose sum equals the coefficient of the middle term, which is 1 .

-9 + 1 = -8

-3 + 3 = 0

-1 + 9 = 8

Conclusion : Trinomial can not be factored

Equation at the end of step 3 :

(3x2 + x - 3)

((x2) - x) - —————————————

2

Step 4 :

Rewriting the whole as an Equivalent Fraction :

4.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using 2 as the denominator :

x2 - x (x2 - x) • 2

x2 - x = —————— = ————————————

1 2

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Step 5 :

Pulling out like terms :

5.1 Pull out like factors :

x2 - x = x • (x - 1)

Adding fractions that have a common denominator :

5.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x • (x-1) • 2 - ((3x2+x-3)) -x2 - 3x + 3

2 2

Step 6 :

Pulling out like terms :

6.1 Pull out like factors :

-x2 - 3x + 3 = -1 • (x2 + 3x - 3)

Trying to factor by splitting the middle term

6.2 Factoring x2 + 3x - 3

The first term is, x2 its coefficient is 1 .

The middle term is, +3x its coefficient is 3 .

The last term, "the constant", is -3

Step-1 : Multiply the coefficient of the first term by the constant 1 • -3 = -3

Step-2 : Find two factors of -3 whose sum equals the coefficient of the middle term, which is 3 .

-3 + 1 = -2

-1 + 3 = 2

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Final result :

-x2 - 3x + 3

————————————

2

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