How do I factorise (-2x^2 + 5x + 7)?

- 2x² + 5x + 7 = 0
x² - 5/4x = 7/2 + (- 5/4)²
x² - 5/4x = 56/16 + 25/16
(x - 5/4)² = 81/16
x - 5/4 = ± 9/4

= x - 5/4 - 9/4, = x - 14/4, = x - 7/2, = 2x - 7
= x - 5/4 + 9/4, = x + 4/4, = x + 1

Answer: - (2x - 7)(x + 1)

Proof:
= - (2x - 7)(x + 1)
= - (2x[x] + 2x[1] - 7[x] - 7[1])
= - (2x² + 2x - 7x - 7)
= - (2x² - 5x - 7)
= - 2x² + 5x + 7

(-2x + 7)(x + 1)

hi Em :) I responded your different question related to factorisation, and those are the comparable form of issues. i think of that in case you study which you would recognize a thank you to do those, so all i will do is say what form of an expression everyone seems to be (so which you recognize which area of my final answer to maintain on with) and inform you the respond which you will envision your person on. a million. Quadratic ( x + 3 ) ( x - 2 ) 2. distinction of two sqaures ( x + 2 ) ( x - 2) 3. Quadratic ( x - 5 ) ( x + 3 ) 4. Quadratic ( x + 7 ) ( x - 4 ) 5. distinction of two squares ( x + 4 ) ( x - 4 ) 6. Quadratic ( x + 6 ) ( x - 10 ) 7. Quadratic ( x + 6 ) ( x + a million ) 8. Quadratic ( x - 6 ) ( x + a million ) 9. distinction of two squares ( x + 5 ) ( x - 5 ) 10. distinction of two squares ( x + 3 ) ( x - 3 ) wish I helped :D

Assuming it is factorisable "nicely", using the rational root theorem, we can establish that the possible roots are ±(1 or 7)/(1 or 2) which can be tested (only eight possibilities). However, this technique is better for higher degree polynomials, while for this it may be better to use your head:
1. (7 + 5x + –2x^2) = (7 + ax)(1 + bx) where a*b = –2
(you can assume the sign of both the constants as long as they multiply to give 7, since it is decided in a and b)
2. 5 = a + 7b --- from here you can "observe" that a is –2 and b is 1
3. (7 + 5x – 2x^2) = (7 – 2x)(1 + x)

-2x^2 + 5x + 7
= -(2x^2 - 5x - 7)
= -(2x^2 + 2x - 7x - 7)
= -[(2x^2 + 2x) - (7x + 7)]
= -[2x(x + 1) - 7(x + 1)]
= -(x + 1)(2x - 7)

( - 2x + 7 ) ( x + 1 )

= -2x^2 - 2x + 7x + 7

= -2x ( x + 1 ) + 7 ( x+1)

= ( x + 1) ( -2x + 7)

Here,
(-2x^2 + 5x + 7)
= - (2x^2 - 5x - 7)
= - (2x^2 - 7x + 2x - 7)
= - { x(2x - 7) +1(2x -7)
= - (2x-7)(x+1)

-4x+5x+7
x+7

i'm sure