 0*f**3 - 5*f + 1/18*f**4 + 0*f**2 - 1/15*f**5 + 1/45*f**6. What is w in k(w) = 0?
0, 1
Let z be (-4*1/6)/(3/(-9)). Let r(w) be the first derivative of -1/9*w**3 + 0*w - z + 1/6*w**2. Suppose r(n) = 0. What is n?
0, 1
Let s(j) be the third derivative of j**7/280 - 9*j**6/320 + 7*j**5/80 - 9*j**4/64 + j**3/8 + 8*j**2. Determine n, given that s(n) = 0.
1/2, 1, 2
Let y(u) = -6*u**3 - 2*u**2. Suppose -d - 4*k + 3 = 0, k = -k + 2. Let r(h) = -h**3. Let p(z) = d*y(z) + 4*r(z). Solve p(x) = 0.
-1, 0
Let c = 1 - 7. Let n be 2 - -1*(c - -4). Factor 1/6*d + 1/6*d**2 + n.
d*(d + 1)/6
Suppose 0 = q - 3*q - 8. Let y = 0 - q. Suppose 1/4*v + 0 - 1/2*v**3 + 0*v**y + 0*v**2 + 1/4*v**5 = 0. Calculate v.
-1, 0, 1
Let y(m) be the third derivative of m**5/60 - m**4/2 + 8*m**2. Let n be y(12). Let 7/3*f**5 - 3*f**3 + 2/3*f + n - 5/3*f**4 + 5/3*f**2 = 0. What is f?
-1, -2/7, 0, 1
Suppose 4*j + 3*v + 6 = 3, 0 = -5*j - 3*v. Let n(u) be the third derivative of 1/420*u**6 + 0 + 1/42*u**4 + 0*u + 0*u**j - 1/70*u**5 + 2*u**2. Factor n(r).
2*r*(r - 2)*(r - 1)/7
Let a be (5/2)/(1/6). Suppose 0*i + 3*i = a. Suppose -2*n + 4*n - 1 + 2*n**i - 1 - 4*n**3 - 2*n**4 + 4*n**2 = 0. What is n?
-1, 1
Let k(i) be the first derivative of -2*i**3/9 + i**2/3 - 36. What is p in k(p) = 0?
0, 1
Let d(n) be the third derivative of 1/16*n**8 + 0 + 23/70*n**7 + 27/40*n**6 + 13/20*n**5 + 0*n - 6*n**2 + 1/4*n**4 + 0*n**3. Solve d(j) = 0 for j.
-1, -2/7, 0
Let z = -175/4 + 44. Factor 0 + z*j - 1/4*j**2.
-j*(j - 1)/4
Let m = -86/3 + 29. Let x(t) be the first derivative of 2*t + 4/3*t**3 - m*t**6 - 6/5*t**5 - 1 - t**4 + 3*t**2. Determine s, given that x(s) = 0.
-1, 1
Let a(r) be the first derivative of -2*r**3/21 + 2*r**2/7 - 5. Factor a(d).
-2*d*(d - 2)/7
Let g(d) be the first derivative of -d**6/8 + 9*d**5/10 - 39*d**4/16 + 3*d**3 - 3*d**2/2 - 21. Let g(a) = 0. Calculate a.
0, 1, 2
Factor -2 + 1/2*z**2 + 3/2*z.
(z - 1)*(z + 4)/2
Determine z, given that 23*z**3 + 1 + z - 24*z**3 - 5*z**2 + 4*z**2 = 0.
-1, 1
Let b(v) be the first derivative of -2*v**3/21 - 30. Determine m so that b(m) = 0.
0
Suppose a**3 + 3*a**3 - a**3 - 3*a**2 = 0. Calculate a.
0, 1
Let c = -14 - -16. Factor 2/7*o**c + 0 - 4/7*o.
2*o*(o - 2)/7
Let k(q) be the first derivative of q**6/900 - q**5/300 - q**3 + 6. Let u(b) be the third derivative of k(b). Find h such that u(h) = 0.
0, 1
Suppose -2*x = -6*x + 8. Let q(l) be the first derivative of 0*l**3 + 0*l**5 + 1/4*l**4 - 1/12*l**6 + 0*l - 1/4*l**x + 3. Factor q(g).
-g*(g - 1)**2*(g + 1)**2/2
Let o(t) be the first derivative of -2*t**5/5 + 4*t**3/3 - 2*t + 8. Let o(a) = 0. What is a?
-1, 1
What is d in -196/5 - 4/5*d**2 - 56/5*d = 0?
-7
Suppose 15 = 5*v, -2*v = -3*j + v - 3. Let w(q) be the first derivative of 2*q - j + 2/3*q**3 + 2*q**2. Factor w(t).
2*(t + 1)**2
Determine c so that -4/9*c**2 + 2/9*c**5 + 0*c + 4/9*c**4 - 2/9*c**3 + 0 = 0.
-2, -1, 0, 1
Factor 3*t**3 - t**3 + 28*t**4 - 2*t + 4*t**2 - 1 - 31*t**4.
-(t - 1)**2*(t + 1)*(3*t + 1)
Let t = 520 + -4151/8. Let k(y) be the first derivative of 9/20*y**5 - 1/2*y**3 - 3/4*y - t*y**2 + 1/8*y**6 + 3/8*y**4 + 1. What is p in k(p) = 0?
-1, 1
Suppose -2*i**2 - 6*i + 4*i**2 - 4 + 4 = 0. Calculate i.
0, 3
Let c(l) be the first derivative of 0*l - 7 - 2/9*l**3 + 0*l**2 - 1/12*l**4. Factor c(y).
-y**2*(y + 2)/3
Let j(k) be the second derivative of k + 1/30*k**4 + 0*k**2 + 0 - 1/75*k**6 + 1/105*k**7 - 1/50*k**5 + 0*k**3. Factor j(m).
2*m**2*(m - 1)**2*(m + 1)/5
Factor 0 - 1/2*b - 2*b**3 - 5/2*b**2.
-b*(b + 1)*(4*b + 1)/2
Let j(g) be the third derivative of -g**6/660 + 2*g**5/165 - g**4/44 - 5*g**2. Determine x so that j(x) = 0.
0, 1, 3
Let t(l) be the third derivative of -l**6/600 + l**5/150 - l**4/120 - 24*l**2. Determine s so that t(s) = 0.
0, 1
Let d(q) be the third derivative of -q**7/6 - q**6/12 + 7*q**5/12 + 5*q**4/12 + 13*q**2. Let d(c) = 0. What is c?
-1, -2/7, 0, 1
Suppose -2*k = 4*a - 14, 3*a + 4*k + 2 = 20. Factor 0 - 1/2*m**a + 0*m - 1/2*m**3.
-m**2*(m + 1)/2
Let z(d) be the second derivative of -1/4*d**4 + 0 + 0*d**2 - 1/2*d**3 - 2*d. Factor z(r).
-3*r*(r + 1)
Let m(f) = f**3 - f**2 - f. Let o(w) = -6*w**3 - w**2 - 6*w - 6. Let c(i) = -10*m(i) - 2*o(i). Find y such that c(y) = 0.
-3, -2, -1
Let l(a) be the third derivative of a**6/360 - a**5/90 + a**4/72 + 20*a**2. Solve l(c) = 0.
0, 1
Let u(v) be the third derivative of v**6/360 - v**4/72 - 15*v**2. Solve u(a) = 0 for a.
-1, 0, 1
Let z(s) = s**3 - 7*s - 8. Let i be 4*(-1 - (-6)/3). Let c(l) = -1 + 4*l - l**3 + l - i*l. Let p(n) = 2*c(n) - z(n). What is a in p(a) = 0?
-1, 2
Let i(k) = k**2 - k + 1. Let b(w) = -w**2 + w - 1. Let o(y) = -3*y + 2 - 5*y + 2*y + 5*y. Let t(n) = 2*b(n) - o(n). Let x(m) = 6*i(m) + 2*t(m). Factor x(d).
2*(d - 1)*(d + 1)
Let s = 23 - 20. Let n(h) = h**2 - 2*h - 3. Let v be n(s). Suppose -6/5*i**3 + 4/5*i + v + 2/5*i**2 = 0. Calculate i.
-2/3, 0, 1
Let c be (-3)/2*2/(-3). Factor c - 2*f - 2 - 2*f**2 + f**2.
-(f + 1)**2
Let l(g) = g**2 - 4*g - g**3 + 3*g + g + g. Let f(o) = 10*o**3 + 7*o**2 + 4*o + 2. Let p(q) = f(q) + 5*l(q). Factor p(s).
(s + 1)**2*(5*s + 2)
Factor -1/3*f**2 + 2/3 - f + f**3 - 1/3*f**4.
-(f - 2)*(f - 1)**2*(f + 1)/3
Let s(z) be the first derivative of -3*z**5/20 - z**4/2 - z**3/2 + 3*z + 1. Let c(k) be the first derivative of s(k). Factor c(i).
-3*i*(i + 1)**2
Suppose -3*a + 33 = 3. Let g be 5/a + 0 + 1. Solve 0*z + 0 - 1/2*z**5 - 3/2*z**3 - g*z**4 - 1/2*z**2 = 0 for z.
-1, 0
Let m(f) = -4*f**3 + 2*f**2 - 4*f - 3. Let c(u) = -u**3 - u - 1. Let r(t) = 3*c(t) - m(t). Factor r(y).
y*(y - 1)**2
Suppose 2*z = -3*z. Suppose z - 2/5*m - 2/5*m**2 = 0. What is m?
-1, 0
Suppose 2*p + p - 7*p = 0. Factor 0*t**4 + 2/7*t + p*t**2 + 2/7*t**5 + 0 - 4/7*t**3.
2*t*(t - 1)**2*(t + 1)**2/7
Suppose -4*f + s = 3, 4*f + s = -0 + 3. Let t = 5 - f. Factor -1 + 4*y**2 - t*y**3 - 14*y**2 - 5*y**3 - y**5 - 5*y - 5*y**4.
-(y + 1)**5
Let t(y) be the third derivative of y**7/1365 + y**6/260 - y**5/78 - y**4/52 + 4*y**3/39 + 23*y**2. Suppose t(z) = 0. What is z?
-4, -1, 1
Let s = -10 - -18. Suppose -5*m**4 + 8*m**3 - s*m**5 + 0*m**3 + 3*m**4 + 2*m**2 = 0. Calculate m.
-1, -1/4, 0, 1
Let i(w) be the second derivative of -3*w + 0 + 1/21*w**4 + 1/21*w**3 - 1/147*w**7 + 0*w**2 - 2/105*w**6 + 0*w**5. Determine l so that i(l) = 0.
-1, 0, 1
Let v(k) be the third derivative of -k**5/510 + k**4/204 + 2*k**3/17 - 5*k**2. Determine h so that v(h) = 0.
-2, 3
Let i = 268 + -268. Let 1/6*d + 1/3*d**2 + i = 0. What is d?
-1/2, 0
Let h(y) = 3*y - 30. Let i be h(10). Let u(d) be the second derivative of -2*d - 1/9*d**4 - 1/6*d**3 + 1/6*d**2 + i. Determine v so that u(v) = 0.
-1, 1/4
Suppose -7*q + 18 = 2*q. Factor 1/3*i**4 + 0*i**3 - 1/3*i**q + 0*i + 0.
i**2*(i - 1)*(i + 1)/3
Suppose 5 = -2*h - 3, -3*u = h + 4. Suppose 1/5*p**4 + 0*p - 1/5*p**2 + 0*p**3 + u = 0. Calculate p.
-1, 0, 1
Factor -1/2 + 4*q - 8*q**2.
-(4*q - 1)**2/2
Let v(g) be the second derivative of g**6/120 - g**5/40 - 5*g**3/6 + g. Let k(h) be the second derivative of v(h). Solve k(b) = 0.
0, 1
Let h(i) = -i - 1. Let y(v) be the first derivative of -2*v**3/3 + 7*v**2 + 8*v + 1. Let b(w) = 10*h(w) + y(w). Find f, given that b(f) = 0.
1
Let n(m) = -m**2 - 11*m + 12. Let i be n(-12). Let a be i + (-2 - -5 - 0). Factor 0*x**a + 0 + 2/7*x**4 + 2/7*x**5 + 0*x + 0*x**2.
2*x**4*(x + 1)/7
Suppose -4*r = -2*r - 2*t - 4, 4*t + 2 = 2*r. Factor -2 - 3*u**3 - u**5 + u**2 + 2 + r*u**4.
-u**2*(u - 1)**3
Let h(b) be the second derivative of -b**8/168 + b**6/30 - b**4/12 + b**2/2 - b. Let d(n) be the first derivative of h(n). Find w, given that d(w) = 0.
-1, 0, 1
Find y, given that 6/11*y**3 + 0 - 10/11*y**4 + 2/11*y + 10/11*y**2 - 8/11*y**5 = 0.
-1, -1/4, 0, 1
Suppose 4*d = -2*n + 8, 5*d - 16 = d - 4*n. Suppose 0*y + 2/9*y**2 + d - 2/9*y**3 = 0. Calculate y.
0, 1
Let r(q) be the second derivative of q**7/2520 - q**6/360 + q**5/120 - q**4/72 - q**3/6 + 3*q. Let u(j) be the second derivative of r(j). Solve u(l) = 0 for l.
1
Let a(s) be the second derivative of -s**6/120 - s**5/8 - s**4/2 + 5*s**3/12 + 25*s**2/8 + 34*s. Suppose a(y) = 0. What is y?
-5, -1, 1
Let d(j) be the first derivative of -49*j**5 - 175*j**4/2 + 5*j**3 + 50*j**2 - 20*j + 7. Suppose d(b) = 0. Calculate b.
-1, 2/7
Suppose 0*z - 3*z = -9. Let g(f) = 5*f**3 - 