x**2 - k*x = 0. What is x?
-2, 0
Let c(i) = -10*i**4 - 30*i**3 - 26*i**2 - 10*i. Let t(u) = u**4 + u**3 + u. Let n(v) = c(v) + 4*t(v). Suppose n(x) = 0. What is x?
-3, -1, -1/3, 0
Factor 1/2*c**2 - c + 0.
c*(c - 2)/2
Let g(x) be the third derivative of x**6/60 + 4*x**5/5 + 23*x**4/12 + 216*x**2. Suppose g(w) = 0. Calculate w.
-23, -1, 0
Let c be ((-8)/36)/((-51)/459). Factor -2*g - 2/3*g**c - 4/3.
-2*(g + 1)*(g + 2)/3
Let l(o) be the second derivative of 0 - 3/50*o**6 + 14*o + 0*o**3 - 3/50*o**5 - 1/70*o**7 + 0*o**2 + 0*o**4. Factor l(u).
-3*u**3*(u + 1)*(u + 2)/5
Suppose -2/7*m**3 + 0*m**2 + 54/7*m - 108/7 = 0. What is m?
-6, 3
Let x(o) be the second derivative of 0*o**2 + 14*o + 0 - 15*o**4 - 10/3*o**3 - 81/4*o**5. Let x(s) = 0. What is s?
-2/9, 0
Let i = 11599/2 + -5953. Let k = -152 - i. Find b, given that -1/2*b**2 - b + k = 0.
-3, 1
Factor -1/3*c**2 - 62/3*c - 961/3.
-(c + 31)**2/3
Let x(h) be the first derivative of h**4/10 - 8*h**3/15 + h**2/5 + 12*h/5 - 26. Factor x(p).
2*(p - 3)*(p - 2)*(p + 1)/5
Let k(g) be the second derivative of g**4/4 + 3*g**3 - 21*g**2/2 - 188*g. Factor k(a).
3*(a - 1)*(a + 7)
Let v(u) = -13*u**3 + 91*u**2 - 247*u + 139. Let d(m) = 20*m**3 - 136*m**2 + 372*m - 208. Let s(p) = -5*d(p) - 8*v(p). Factor s(r).
4*(r - 9)*(r - 2)*(r - 1)
Factor -117*d**2 - 3*d + 6 - 115*d**2 + 229*d**2.
-3*(d - 1)*(d + 2)
Let l(y) = -y**2 + 8*y + 66. Let j be l(13). Suppose c - 6 + j = 0. Determine z, given that 2/5*z + 2/5*z**4 - 4/5*z**2 + 2/5 - 4/5*z**3 + 2/5*z**c = 0.
-1, 1
Factor 4/3*s**2 + 1/3*s**5 - 5/3*s**4 + 0 - 8/3*s + 2*s**3.
s*(s - 2)**3*(s + 1)/3
Let g(t) = -6*t**3 + 3*t**2 + t + 2. Let m(p) = -2*p**2 - p**3 + 5*p**2 - 2*p**2. Let w(s) = 2*g(s) - 10*m(s). Find n such that w(n) = 0.
-2, -1, 1
Let m = 22 - 18. Let n(h) = -2*h - 5*h**4 - h**m + 2*h**2 + 4*h**3 - 2*h - 2*h. Let p(v) = v**5 + v**2 + 1. Let w(k) = -2*n(k) - 4*p(k). Factor w(g).
-4*(g - 1)**4*(g + 1)
Let g(n) be the third derivative of 27*n**8/1120 - 27*n**7/560 + 3*n**6/80 - n**5/80 - 5*n**3/6 - 4*n**2. Let s(j) be the first derivative of g(j). Factor s(a).
3*a*(3*a - 1)**3/2
Let z(d) be the second derivative of -5/2*d**3 + 5/12*d**4 - 38*d + 5*d**2 + 0. Factor z(m).
5*(m - 2)*(m - 1)
Factor 0*a**2 + 0 + 2/9*a**5 - 8/9*a**3 + 0*a**4 + 0*a.
2*a**3*(a - 2)*(a + 2)/9
Let g = -28 - -31. Factor 10*j**2 + 9 + 10 - 15*j**g - 19 - 60*j**4 - 35*j**5.
-5*j**2*(j + 1)**2*(7*j - 2)
Let w(x) be the third derivative of x**6/72 - x**5/12 + 5*x**4/24 + x**3 + 2*x**2. Let r(q) be the first derivative of w(q). Suppose r(k) = 0. What is k?
1
Let f be 5/4*(-4 - -8). Suppose -t - 3*t + 6*t = 0. Factor -1/2*c**3 + 1/2*c**f + t*c - 1/2*c**4 + 1/2*c**2 + 0.
c**2*(c - 1)**2*(c + 1)/2
Let v(g) be the second derivative of -g**7/42 + 11*g**6/30 - 43*g**5/20 + 73*g**4/12 - 28*g**3/3 + 8*g**2 - 76*g + 1. Factor v(c).
-(c - 4)**2*(c - 1)**3
Suppose 8 = q + 3. Let k(b) be the first derivative of 0*b - 7/2*b**4 - 6/5*b**q + 0*b**3 + 4*b**2 - 5. Factor k(a).
-2*a*(a + 1)*(a + 2)*(3*a - 2)
Let n(z) = z**3 - 8*z**2 - 10*z + 11. Let v = 46 - 37. Let m be n(v). Factor 0*p + 0 + 2/7*p**m - 2/7*p**3.
-2*p**2*(p - 1)/7
Factor -212/5*u**2 + 2/5*u**5 + 4*u**3 + 266/5*u - 98/5 + 22/5*u**4.
2*(u - 1)**3*(u + 7)**2/5
Factor 2/5*r + 2/25*r**2 + 12/25.
2*(r + 2)*(r + 3)/25
Let o be (-390)/(-60) - 6/4. Factor 2*y**5 + 12*y**4 + 6*y**2 + 0*y**4 - o*y**5 - 15*y**3.
-3*y**2*(y - 2)*(y - 1)**2
Let r = 2706 + -2701. Let k(c) be the first derivative of 0*c - 2/21*c**3 + 0*c**2 + 2/35*c**r - 9 + 0*c**4. Find v, given that k(v) = 0.
-1, 0, 1
Suppose -4*p = -24 - 8. Suppose -n = -5*n + p. Find z such that 1/2*z + 1/2*z**n + 0 - 1/2*z**4 - 1/2*z**3 = 0.
-1, 0, 1
Let o(p) = -p**3 - 24*p**2 + 28*p + 80. Let j be o(-25). Suppose -j*x = -0*x + 3*i - 10, -x - 5*i = -2. Factor 3*z**x - 12/5*z**3 + 0 - 3/5*z.
-3*z*(z - 1)*(4*z - 1)/5
Factor -3/2*r**4 + 0 + 3/2*r**2 - 6*r + 6*r**3.
-3*r*(r - 4)*(r - 1)*(r + 1)/2
Let h(w) = 5*w**2 - 4*w. Let f be ((-6)/7)/1*(-42)/6. Let n(i) = 4*i**2 - 4*i. Let v(k) = f*n(k) - 5*h(k). Factor v(r).
-r*(r + 4)
Let n(u) be the second derivative of -u**4/24 - 77*u**3/6 - 5929*u**2/4 - u - 16. Factor n(j).
-(j + 77)**2/2
Let k(f) be the third derivative of 0 + 1/45*f**5 - 12*f**2 + 0*f + 1/180*f**6 + 0*f**4 + 0*f**3 - 1/315*f**7. Determine g so that k(g) = 0.
-1, 0, 2
Let s = -8638 - -8640. What is v in 10/11 + 12/11*v + 2/11*v**s = 0?
-5, -1
Suppose 6*c = 3*c + 6. Factor -23*y**2 - 4*y**4 + 4*y**3 - 17*y**2 - 4*y**5 + 44*y**c.
-4*y**2*(y - 1)*(y + 1)**2
Let x = 807/2344 + 9/293. Solve 3/4*w**3 - 3/8 - 3/8*w - 3/8*w**5 + 3/4*w**2 - x*w**4 = 0.
-1, 1
Let m(u) = u**5 + u**2 + 2. Let g(v) = -10*v**5 - 50*v**4 - 90*v**3 + 135*v**2 + 215*v - 220. Let z(b) = g(b) + 5*m(b). Suppose z(s) = 0. Calculate s.
-7, -3, -2, 1
Let x be (-2)/3*(-7 - (-8 + 22)). Let y(q) = -q**3 + 14*q**2 + q. Let m(d) = -7*d**2 - d. Let v(c) = x*m(c) + 6*y(c). Solve v(o) = 0.
-4/3, -1, 0
Suppose -4*a = -9*a. Suppose -i + 3 = -a*i. Factor 3 - 2*g**2 - g + i - 6.
-g*(2*g + 1)
Let f(r) be the first derivative of 2/21*r**3 + 8/7*r + 5 - 5/7*r**2. Factor f(x).
2*(x - 4)*(x - 1)/7
Let w(q) be the third derivative of -q**7/84 - q**6/24 - q**5/24 - 47*q**2. Factor w(f).
-5*f**2*(f + 1)**2/2
Factor 10*c - 5*c**3 + 20 + 44 - 65*c - 45*c + 45*c**2 - 4.
-5*(c - 6)*(c - 2)*(c - 1)
Let z be 3/(-42)*((17 - 4) + 6 + -31). Factor 114/7*o**2 - 24/7*o**5 - 150/7*o**3 + 96/7*o**4 + z - 6*o.
-6*(o - 1)**3*(2*o - 1)**2/7
Let m(h) be the third derivative of -1/96*h**4 - 1/420*h**7 + 1/1344*h**8 + 1/120*h**5 + 0*h**3 + 0 + 8*h**2 + 0*h**6 + 0*h. Let m(c) = 0. Calculate c.
-1, 0, 1
Let h(y) be the first derivative of 0*y**2 - 2/3*y**3 - 13 + 1/3*y**6 - 1/2*y**4 + 2/5*y**5 + 0*y. Factor h(c).
2*c**2*(c - 1)*(c + 1)**2
Suppose -3 = 20*v - 21*v. Find j such that -12*j**2 - 65 + 4*j**4 - 8*j**v + 16*j + 81 + 0*j**2 = 0.
-1, 2
Let b(x) be the first derivative of x**8/336 + 13*x**7/210 + 2*x**6/5 + 3*x**5/5 - 31*x**2/2 - 16. Let q(n) be the second derivative of b(n). Factor q(j).
j**2*(j + 1)*(j + 6)**2
Let b be (5 + 14/(-4))/((-3)/4). Let a be (b/(-20))/(2/5). Factor 1/4*i**3 - 1/4*i**2 - a*i + 1/4.
(i - 1)**2*(i + 1)/4
Let l(v) be the second derivative of -v**5/40 - 169*v**4/24 - 7055*v**3/12 + 7225*v**2/4 + 190*v + 3. Factor l(f).
-(f - 1)*(f + 85)**2/2
Let 10648/7 + 1/7*h**3 + 1452/7*h + 66/7*h**2 = 0. What is h?
-22
Let m(c) = -c**3 + 18*c**2 - 18*c + 20. Let f be m(17). Factor 4*g - 73*g**2 + 169*g**2 + 32*g + 196*g**f + 72*g**2.
4*g*(7*g + 3)**2
Let t(l) be the first derivative of l**6/39 - 6*l**5/65 - 5*l**4/13 - 4*l**3/39 + 9*l**2/13 + 10*l/13 + 85. What is x in t(x) = 0?
-1, 1, 5
Let c(f) = f**3 + 17*f**2 + 28*f - 22. Let w be c(-15). Let m be 3/(-24)*-4*w. Factor 0 - 1/2*d**3 - 1/2*d**2 - 1/6*d**m - 1/6*d.
-d*(d + 1)**3/6
Let d(t) be the second derivative of -t**8/2240 - t**7/420 + t**6/240 + t**5/20 + 7*t**4/12 + 3*t. Let g(m) be the third derivative of d(m). Factor g(v).
-3*(v - 1)*(v + 1)*(v + 2)
Suppose -5*u = -u, 0 = -5*s - u + 25. Suppose 10*c - 3*y - 47 = s*c, -4*y = 5*c - 54. Factor c*k - k**3 + 15 + 6*k**3 + 13*k**2 + 12*k**2 + 25*k.
5*(k + 1)**2*(k + 3)
Let t(m) = 30*m**5 + 90*m**4 - 120*m**3 - 21*m + 21. Let b(y) = -3*y**5 - 9*y**4 + 12*y**3 + 2*y - 2. Let n(r) = 21*b(r) + 2*t(r). Find j, given that n(j) = 0.
-4, 0, 1
Let h(n) = -1 + 10*n - 11*n + 0*n. Let m be h(-3). Determine u, given that -u**2 + 8*u + 0 - 7*u**m - 2 = 0.
1/2
Let l(x) be the first derivative of 7 + 0*x - 2/25*x**5 - 3/20*x**4 + 8/15*x**3 - 2/5*x**2 + 1/30*x**6. Factor l(h).
h*(h - 2)*(h - 1)**2*(h + 2)/5
Determine y so that -7 - 33*y - 4 + 2 + 12*y**2 = 0.
-1/4, 3
Let t(u) be the third derivative of u**5/420 - 11*u**4/42 + 242*u**3/21 + 46*u**2. Determine z so that t(z) = 0.
22
Let a(v) be the first derivative of 1/6*v**2 + 0*v + 6 + 0*v**5 - 1/6*v**4 + 1/18*v**6 + 0*v**3. Factor a(d).
d*(d - 1)**2*(d + 1)**2/3
Let 52/9*y**2 - 40/3*y + 0 - 4/9*y**3 = 0. Calculate y.
0, 3, 10
Suppose -3*k = -9, 4*l - 14 - 9 = -5*k. Solve 0*m**2 + 31*m + l*m**2 + m**3 - 34*m = 0.
-3, 0, 1
Let o(f) be the first derivative of 1/3*f**3 + 0*f**2 + 0*f - 43. Factor o(u).
u**2
Let i be -4*(-1)/12 - -1. Let j = 620/3 + -206. Factor 2/3 - i*k + j*k**2.
2*(k - 1)**2/3
Factor -6*y**5 - 31*y + 3