Question

Factorize the following ⤵⤵

${4x}^{3} - {4x}^{2} - 21x 9$
Solve the following sums with proper steps.​

Answer 1

Answer:

$\underline{\huge{\texttt{(2x + 1) (2x + 3) (x - 3)}}}$

Step-by-step explanation:

where p = factor of constant (9) and q = factor of leading coefficient (4)

p = ±1, ±3, ±9

q = 1, 2, 4

Using trial and error, we find that 3 is a root

Now we use synthetic division to find quadratic factor:

3 | 4 -4 -21 -9

.. | .. 12 24. 9

.. ----------------

... 4 . 8 . 3 . 0

So dividing $(4x^3 - 4x^2 - 21x - 9)$ by (x - 3), we get $(4x^2 + 8x + 3)$

$(4x^3 - 4x^2 - 21x - 9) = 0 \\(x - 3) (4x^2 + 8x + 3) = 0 \\(x - 3) (4x^2 + 2x + 6x + 3) = 0 \\(x - 3) (2x (2x + 1) + 3 (2x + 1)) = 0\\ (x - 3) (2x + 1) (2x + 3) = 0$

x = 3, -1/2, -3/2

Answer 2

Answer:

4x³-4x²-21x-9=0

x(4x²-4x-21)-9=0

4x²-4x-21-9=0

4x²-4x-12=0

4(x²-x-3)=0

x²-x-3=0

then we use discriminant

I hope it help u☺️