Question

Fill in the missing number to complete the factorization:

x^3+14x^2+59x+70=(x+2)(x+5)(x+__________)

Answer 1

@amistre64 @ganeshie8 @Directrix

Answer 2

@zepdrix

Answer 3

Hint : constant term

Answer 4

\[\large\rm x^3+14x^2+59x+\color{orangered}{70}=(x+\color{orangered}{2})(x+\color{orangered}{5})(x+\color{orangered}{?})\]

Answer 5

Guessing the rational root theorem?

Answer 6

I don't get what you mean by constant term

Answer 7

The Remainder Theorem

Answer 8

with Factorization

Answer 9

constant term is the one without any x's attached to it

Answer 10

10?

Answer 11

\[\large\rm x^3+14x^2+59x+\color{orangered}{70}=(x+\color{orangered}{2})(x+\color{orangered}{5})(x+\color{orangered}{?})\]

look at left hand side, whats the constant term ?

Answer 12

7?

Answer 13

do you mean 70 ?

Answer 14

yea

Answer 15

so 70 would be the constant term for the (x+____)

Answer 16

since above is an equation, left side and right side must have the same constant term

Answer 17

\[\large\rm x^3+14x^2+59x+\color{orangered}{70}=(x+\color{orangered}{2})(x+\color{orangered}{5})(x+\color{orangered}{?})\]

look at right hand side, what could be the constant term ?

Answer 18

okay

Answer 19

you get the constant term on right hand side by multiplying these : \(\color{red}{2,5,?}\)

Answer 20

\[\color{Red}{70 = 2*5*?} \implies \color{red}{\dfrac{70}{10} = ?}\]

Answer 21

I DID SAID 7

Answer 22

you're correct