Factor the expression \(-35x^2 - 41x - 12\).
Answer (2)
0\ then\ ax^2+bx+c=a(x-x_1)(x-x_2)\ where\ x_{1;2}=\frac{-b\pm\sqrt\Delta}{2a}\\\========================================"> a x 2 + b x + c Δ = b 2 − 4 a c i f Δ > 0 t h e n a x 2 + b x + c = a ( x − x 1 ) ( x − x 2 ) w h ere x 1 ; 2 = 2 a − b ± Δ = ˉ ======================================
0\\\\\sqrt\Delta=\sqrt1=1\\\\x_1=\frac{-(-41)-1}{2\cdot(-35)}=\frac{41-1}{-70}=\frac{40}{-70}=-\frac{4}{7}\\\\x_2=\frac{-(-41)+1}{2\cdot(-35)}=\frac{41+1}{-70}=\frac{42}{-70}=-\frac{21}{35}=-\frac{3}{5}\\\\therefore:\\\\\boxed{-35x^2-41-12=-35\left(x+\frac{4}{7}\right)\left(x+\frac{3}{5}\right)}"> − 35 x 2 − 41 x − 12 a = − 35 ; b = − 41 ; c = − 12 Δ = ( − 41 ) 2 − 4 ⋅ ( − 35 ) ⋅ ( − 12 ) = 1681 − 1680 = 1 > 0 Δ = 1 = 1 x 1 = 2 ⋅ ( − 35 ) − ( − 41 ) − 1 = − 70 41 − 1 = − 70 40 = − 7 4 x 2 = 2 ⋅ ( − 35 ) − ( − 41 ) + 1 = − 70 41 + 1 = − 70 42 = − 35 21 = − 5 3 t h ere f ore : − 35 x 2 − 41 − 12 = − 35 ( x + 7 4 ) ( x + 5 3 )
To factor the expression − 35 x 2 − 41 x − 12 , we calculate the discriminant and find the roots using the quadratic formula. The factored form of the expression is − 35 ( x + 7 4 ) ( x + 5 3 ) .
;
