Question

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Answer 1

Answer:

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Step-by-step explanation:

3x3-5x2-6x+10

Final result :

(x2 - 2) • (3x - 5)

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2" was replaced by "x^2". 1 more similar replacement(s).

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(((3 • (x3)) - 5x2) - 6x) + 10

Step 2 :

Equation at the end of step 2 :

((3x3 - 5x2) - 6x) + 10

Step 3 :

Checking for a perfect cube :

3.1 3x3-5x2-6x+10 is not a perfect cube

Trying to factor by pulling out :

3.2 Factoring: 3x3-5x2-6x+10

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: -6x+10

Group 2: 3x3-5x2

Pull out from each group separately :

Group 1: (3x-5) • (-2)

Group 2: (3x-5) • (x2)

-------------------

Add up the two groups :

(3x-5) • (x2-2)

Answer 2

Qᴜᴇsᴛɪᴏɴ :-

what should be added to 3x³ - 5x² + 6x so that, when resulting Polynomial is divided by (x - 3) the Remainder is 8 ? .

Sᴏʟᴜᴛɪᴏɴ :-

Let us Assume That, The added Number is a .

Than,

→ f(x) = 3x³ - 5x² + 6x

→ x - 3 = 0 => x = 3

→ Remainder = 8

So, By Remainder Theoram , we get,

→ f(3) = 3x³ - 5x² + 6x + a = 8

→ 3(3)³ - 5(3)² + 6*3 + a = 8

→ 3*27 - 5*9 + 18 + a = 8

→ 81 - 45 + 18 + a = 8

→ 54 + a = 8

→ a = 8 - 54

→ a = (-46)

Hence, we can Conclude That, if we add (-46) in The Given Polynomial we will get Remainder as 8 when divided by (x - 3).