Completely Factor: 18x²+11x+1?

Answer 1

First: multiply the 1st & 3rd coefficient to "18." Find two numbers that give you "18" when multiplied & "11" (2nd/middle coefficient) when added/subtracted. The numbers are: "9 & 2 "

Sec: rewrite the expression with the new middle coefficients...

18x² + 9x + 2x + 1

Third: factor - when you have 4 terms, group "like" terms...

(18x² + 9x) + (2x + 1)

*Find the least common factors for each parenthesis...

9x(2x + 1) + 1(2x + 1)

= (2x + 1)(9x + 1)

Answer 2

18x^2 + 11x + 1

Find factors of 18 (as 18 x 1) which equal 11, which in this case are 9 and 2 as 9 + 2 = 11
18x^2 + 9x + 2x +1

Now factor in pairs
9x(2x + 1) + 1(2x +1)

And collect like factors
(2x + 1)(9x + 1)

Answer 3

For quadratics, set them equal to zero, and use the quadratic formula to solve this equation. Your answers (from the quadratic formula) will go into your factorization like this:
If the quadratic formula gives you x=a, x=b, and your coefficient on x^2 is c,
your factorization becomes
c(x-a)(x-b).
For instance, if the quadratic formula gives you x= -3, x=5, and your coefficient on x^2 is 7, your factorization is 7(x+3)(x-5), or (7x + 21)(x-5).
If the quadratic formula gives you one real solution, then your factorization is a square. If it gives you no real solutions, then the quadratic is impossible to factor (it's already a primitive polynomial).
For your polynomial, the quadratic formula gives (-11 +- sqrt(121 - 72) ) / 36 = (-11+-7)/36. So x= -1/2 or x= -1/9. Your coefficient on x^2 is 18, so your factorization is:
18(x+ 1/2)(x + 1/9)=2(x+1/2)9(x+1/9)=(2x+1)(9x+1)

Answer 4

18X^2+11x+1
=18x^2+9x+2x+1(factors of first term multiplying last term )
=9x(2x+1)1(2x+1)
=(2x+1)(9x+1)

Answer 5

8x^2 -11x+3 Do a coarse artwork, multiply 3 and eight to get 24. discover 2 numbers such that their product is 24 and sum -11. The numbers are -3 and -8. next positioned them interior the equation with x in front and eliminate -11x So 8x^2 - 3x - 8x + 3 x(8x - 3) - a million(8x - 3) (x - a million)(8x - 3) attempt something.

Answer 6

18x²+11x+1?
=(9x+1)(2x+1)

Answer 7

(9x +1) (2x +1)

Answer 8

can be factored into:
(9x+2)(2x+1)

Answer 9

(2x+1)(9x+1)