 r(t) = 0?
1
Let m(v) be the first derivative of -v**2 - 1/24*v**4 + 0*v + 1/120*v**6 + 0*v**3 + 0*v**5 - 1. Let f(k) be the second derivative of m(k). Solve f(n) = 0 for n.
-1, 0, 1
Determine r so that r**2 + 1/4*r**5 + 1/4*r + 3/2*r**3 + r**4 + 0 = 0.
-1, 0
Let v(t) = 2*t**2 - 5*t + 1. Let h be v(3). Determine u so that -2*u**4 + 0*u**h - u**4 + u**4 = 0.
0
Let o(y) be the third derivative of -y**6/1260 + y**5/420 + y**3/6 - y**2. Let a(t) be the first derivative of o(t). Determine f, given that a(f) = 0.
0, 1
Let l(c) be the third derivative of -c**10/60480 + c**8/13440 + c**4/8 + 3*c**2. Let h(z) be the second derivative of l(z). What is w in h(w) = 0?
-1, 0, 1
Let q(r) be the first derivative of -5/4*r**4 + 1 - r**2 + 9/5*r**5 - 3*r**3 + 7/6*r**6 + 0*r. Factor q(m).
m*(m - 1)*(m + 1)**2*(7*m + 2)
Let d(s) = -s**2 - 10*s - 21. Let j be d(-6). Factor 0*w + 0 + 2/5*w**j + 4/5*w**2.
2*w**2*(w + 2)/5
Factor -8*h**3 - 20*h + 13*h**3 + 8 - 8*h**3 + 14*h**2.
-(h - 2)**2*(3*h - 2)
Let o(r) be the first derivative of -r**3/3 - 3*r**2/4 + r - 12. Let o(l) = 0. Calculate l.
-2, 1/2
Factor -1/2*x**3 + 7/4*x**4 + 1/2*x - 7/4*x**2 + 0.
x*(x - 1)*(x + 1)*(7*x - 2)/4
Let y(f) be the first derivative of -f**3/3 + 4*f - 16. Factor y(l).
-(l - 2)*(l + 2)
Let i = 1 - 1. Let v(x) be the first derivative of -1/4*x**3 + i*x - 1/8*x**2 - 2. Determine m, given that v(m) = 0.
-1/3, 0
Let x(b) = 2*b**2 + 2. Let m be x(2). Let c be ((-1)/2)/((-15)/m). Determine t so that -c + 1/3*t**2 + 0*t = 0.
-1, 1
Suppose 1/4*w**2 + 0 + 0*w = 0. Calculate w.
0
Let j(t) be the first derivative of t**5/30 - 4*t**4/21 + 4*t**3/21 - 3*t**2 - 3. Let w(g) be the second derivative of j(g). Determine k so that w(k) = 0.
2/7, 2
Let i(c) = c**2 - 7*c + 1. Let d be i(4). Let h = 13 + d. Solve -4*v**4 - 3*v**3 + 3*v - 4*v**2 + v**4 + 0*v**2 + 7*v**h = 0.
-1, 0, 1
Let n(w) = 24*w**3 + 40*w**2 - 24*w - 28. Let s(z) = -z**3 + z + 1. Let f(q) = -n(q) + 12*s(q). Suppose f(h) = 0. Calculate h.
-10/9, -1, 1
Let n(f) be the third derivative of f**7/280 - 3*f**6/160 + f**5/80 + 3*f**4/32 - f**3/4 + 6*f**2. Factor n(p).
3*(p - 2)*(p - 1)**2*(p + 1)/4
Let m(u) be the second derivative of -7*u**6/40 - 4*u**5/5 - u**4/2 - u**2 - u. Let r(n) be the first derivative of m(n). Factor r(d).
-3*d*(d + 2)*(7*d + 2)
Let g = 305/23 + 11/46. Let c = g - 13. Factor -1/2*y**2 + 1 - c*y.
-(y - 1)*(y + 2)/2
Let x(s) be the third derivative of s**6/105 - s**5/210 - s**4/21 + s**3/21 + 10*s**2. Factor x(z).
2*(z - 1)*(z + 1)*(4*z - 1)/7
Let y(k) be the first derivative of k**6/120 - k**5/30 + k**4/24 + 2*k**2 - 4. Let i(f) be the second derivative of y(f). Factor i(h).
h*(h - 1)**2
Let r(a) be the second derivative of 0*a**2 - 1/25*a**5 + 0 - 1/75*a**6 + 0*a**3 + a - 1/30*a**4. What is l in r(l) = 0?
-1, 0
Let g(s) be the first derivative of 3/4*s**6 + 2 + 3/4*s**2 - 3/2*s**4 + 6/5*s**5 + 3*s - 3*s**3. Determine f so that g(f) = 0.
-1, 2/3, 1
Let y be 5/(-15)*(-2 - (-2)/1). Factor y*w**2 + 1/4 + 1/2*w - 1/4*w**4 - 1/2*w**3.
-(w - 1)*(w + 1)**3/4
Let f(g) = -g**3 + g**2 - g + 1. Let m be f(1). Suppose m*t = t - 2. Factor -1/2*o**4 + 0*o**t - 1/2*o**5 + 0*o + 0 + 0*o**3.
-o**4*(o + 1)/2
Let k(m) be the first derivative of -2*m**3/15 + 2*m**2/5 + 6*m/5 - 17. Factor k(v).
-2*(v - 3)*(v + 1)/5
Let p(k) be the first derivative of 1/10*k**4 + 9 - 1/10*k**2 - 1/30*k**6 + 0*k**3 + 0*k + 0*k**5. Solve p(i) = 0 for i.
-1, 0, 1
Let q(y) = -6*y**4 + 3*y**3 + 3*y - 3. Let a(x) = 5*x**4 - 2*x**3 - x**2 - 2*x + 2. Let p(c) = 3*a(c) + 2*q(c). Factor p(k).
3*k**2*(k - 1)*(k + 1)
Let r = 2 - 2. Let k be 18/42 + 9/(-21). Factor 2/3*n**4 + 0*n**2 + 2/3*n**3 + r*n + k.
2*n**3*(n + 1)/3
Suppose -2/9*z + 2/9*z**4 + 2/9 + 4/9*z**3 - 2/9*z**5 - 4/9*z**2 = 0. Calculate z.
-1, 1
Let w(o) be the second derivative of o**4/24 + 3*o**3/4 - 5*o**2/2 + 30*o. Factor w(u).
(u - 1)*(u + 10)/2
Let j(a) be the third derivative of a**5/20 - a**4/8 - 3*a**2. Factor j(c).
3*c*(c - 1)
Let y(i) be the third derivative of 3*i**8/112 + i**7/14 + i**6/40 - i**5/20 + 25*i**2. Factor y(q).
3*q**2*(q + 1)**2*(3*q - 1)
Suppose i = f, -6 = -3*i - 0*i. Let v(j) be the second derivative of 0*j**6 + 0*j**4 - 1/10*j**5 + 1/42*j**7 + 3*j + 0*j**f + 0 + 1/6*j**3. Factor v(k).
k*(k - 1)**2*(k + 1)**2
Let x(c) be the first derivative of -c**4/10 - 8*c**3/15 - 3*c**2/5 + 13. Factor x(i).
-2*i*(i + 1)*(i + 3)/5
Let v = -207 + 1865/9. Factor -v*o**4 + 4/9*o**3 - 4/9*o + 0*o**2 + 2/9.
-2*(o - 1)**3*(o + 1)/9
Let x(j) = j - 2 + j + 2*j**2 + j + j**2. Let i(k) = 8*k**2 + 9*k - 6. Let p(z) = -4*i(z) + 11*x(z). Factor p(l).
(l - 2)*(l - 1)
Let z(x) = -3*x - 4. Let w be z(-3). Suppose -4*o**2 + 18*o**2 - 3*o**3 - w*o**2 - 9*o + 3 = 0. What is o?
1
Let b(y) be the third derivative of y**8/9240 + y**7/2310 + y**6/1980 - y**3/6 + 3*y**2. Let f(l) be the first derivative of b(l). Factor f(n).
2*n**2*(n + 1)**2/11
Let y(p) be the second derivative of 4*p**6/45 + p**5/15 - 13*p. Factor y(d).
4*d**3*(2*d + 1)/3
Let k(w) be the first derivative of 0*w**5 + 0*w**2 + 0*w + 1/10*w**4 - 1/15*w**6 + 0*w**3 - 3. Solve k(f) = 0.
-1, 0, 1
Factor -4/5 + 2/5*p**3 - 2/5*p + 4/5*p**2.
2*(p - 1)*(p + 1)*(p + 2)/5
Let y be ((-2)/(-1))/(16/((-24)/(-6))). Let -1/4*u**2 - 1/4 + y*u = 0. What is u?
1
Let n = 3 + -1. Let l - l**2 - 2*l**n + 0*l + 4*l**2 = 0. What is l?
-1, 0
Let d(k) be the third derivative of k**8/252 - 2*k**7/315 - k**6/30 + k**5/45 + k**4/9 - 2*k**2. Find q, given that d(q) = 0.
-1, 0, 1, 2
Let m = -243 + 245. Solve -1/2*p + 1/4*p**m + 1/4 = 0 for p.
1
Let p(h) be the first derivative of 2*h**5/25 + h**4/5 - 2*h**3/5 - 8*h**2/5 - 8*h/5 + 6. Factor p(b).
2*(b - 2)*(b + 1)**2*(b + 2)/5
Factor -14/17*n**4 + 0*n + 0 + 4/17*n**3 + 0*n**2 + 10/17*n**5.
2*n**3*(n - 1)*(5*n - 2)/17
Let t(b) be the first derivative of -1/5*b**4 + 0*b - 1/25*b**5 + 0*b**2 - 1 - 4/15*b**3. Factor t(v).
-v**2*(v + 2)**2/5
Let z = -1/630 - -4321/630. Let k be 32/28 - (-2 + -2 + 4). Solve z*o**3 + 0*o + 0 - 10*o**4 - k*o**2 = 0.
0, 2/7, 2/5
Let i(v) be the first derivative of 1/10*v**5 - 2*v - 2/3*v**3 + 0*v**2 + 1 - 1/6*v**4. Let a(k) be the first derivative of i(k). Factor a(x).
2*x*(x - 2)*(x + 1)
Let b(w) be the second derivative of -w**6/540 - w**3/3 + 5*w. Let c(x) be the second derivative of b(x). Factor c(l).
-2*l**2/3
Let q be ((-8)/(-6))/((-14)/(-21)). Let u(z) be the third derivative of q*z**2 + 0*z**3 + 1/75*z**5 + 0*z - 1/300*z**6 + 0 - 1/60*z**4. Factor u(w).
-2*w*(w - 1)**2/5
Let b(p) be the third derivative of p**5/360 - p**4/72 - 51*p**2. Factor b(v).
v*(v - 2)/6
Let i be ((-6)/8)/(-2 + 87/48). Factor -32/7*a**i + 4/7*a - 24/7*a**3 + 0 - 12/7*a**5 + 0*a**2.
-4*a*(a + 1)**3*(3*a - 1)/7
Suppose 4*c = -j + 9, 3 = 5*c - c + 3*j. Suppose r + 4*p = 3*r + 8, 2*r + 5 = c*p. Factor 2/9*k + 0 - 2/3*k**r - 8/9*k**3.
-2*k*(k + 1)*(4*k - 1)/9
Let a be 252/88 + (3 - 6). Let h = a - -17/44. Factor -h*f**2 - 1/4 - 1/2*f.
-(f + 1)**2/4
Let c(u) be the second derivative of -5/12*u**4 + 0 + 1/21*u**7 + u**2 + 4*u - 1/4*u**5 + 1/2*u**3 + 1/10*u**6. Suppose c(f) = 0. What is f?
-2, -1, -1/2, 1
Suppose 5*g = -2*t - 13 + 3, 3*t - 8 = 4*g. Suppose t = -l + 2*l - 2. Factor -l*x**2 + 8*x**4 + 2*x**3 - x**4 - 2*x - 5*x**4.
2*x*(x - 1)*(x + 1)**2
Let x(p) be the third derivative of 3*p**8/56 + p**7/15 - p**6/3 + 2*p**5/15 + 15*p**2 + 3*p. Determine y, given that x(y) = 0.
-2, 0, 2/9, 1
Let f = -307 - -1541/5. Let w(u) be the second derivative of 0*u**2 + 3*u + 7/15*u**6 + f*u**5 + 0 - 2/3*u**3 + 1/2*u**4. Find j such that w(j) = 0.
-1, 0, 2/7
Let d(z) = -z**5 - 18*z**4 - 34*z**3 - 24*z**2 - 2. Let b(g) = -15*g**5 - 288*g**4 - 543*g**3 - 384*g**2 - 33. Let p(i) = -2*b(i) + 33*d(i). Factor p(f).
-3*f**2*(f + 2)**3
Let i(v) be the first derivative of -2*v**3/21 - 4*v**2/7 - 6*v/7 + 13. Let i(k) = 0. Calculate k.
-3, -1
Let g be (-135)/(-162) - 1/2. Factor 4/3 + g*d**2 - 4/3*d.
(d - 2)**2/3
Let u(d) be the first derivative of d**5/80 - 5*d**4/48 + d**3/3 - d**2/2 - 4*d - 2. Let f(g) be the first derivative of u(g). Factor f(q).
(q - 2)**2*(q - 1)/4
Let g = -21 + 25. Factor 1/4*k**3 + 1/4*k**5 + 0*k**2 - 1/2*k**g + 0 + 0*k.
k**3*(k - 1)**2/4
Factor -3*f**3 + 0 - 11/3*f**2 - 2/3*f.
-f*(f + 1)*(9*f + 2)/3
Let n = 4 - 0. Suppose -z - 4 = 