 in 1/2*n**d + n + 3/2*n**2 + 0 = 0?
-2, -1, 0
Let v(g) be the second derivative of -g**7/210 + g**6/120 + g**5/60 - g**4/24 + 3*g**2/2 + 3*g. Let z(u) be the first derivative of v(u). What is b in z(b) = 0?
-1, 0, 1
Determine f, given that -2/7*f**2 - 2/7*f + 0 = 0.
-1, 0
Let s(y) = -y**3 - 12*y**2 + y - y**5 - 10*y**2 + 23*y**2. Let q(d) = -6*d**5 - 12*d**3 + 8*d**2 + 10*d. Let n(h) = q(h) - 8*s(h). Find z such that n(z) = 0.
-1, 0, 1
Let b be (32/10)/(165/275). What is j in b*j + 2/3 + 32/3*j**2 = 0?
-1/4
Let u(z) be the second derivative of 1/100*z**5 + 0 + 0*z**2 + 4*z - 1/30*z**3 + 0*z**4. Factor u(r).
r*(r - 1)*(r + 1)/5
Let w be 5/(-2)*(-12)/15. Let m(k) = -k**2 + k + 3. Let q(a) = 1. Let z(i) = w*m(i) - 2*q(i). Factor z(o).
-2*(o - 2)*(o + 1)
Let t(m) be the second derivative of 3/20*m**5 + 1/12*m**3 + 0 + 3*m - 1/6*m**4 + 0*m**2 - 1/15*m**6 + 1/84*m**7. Determine a so that t(a) = 0.
0, 1
Let m(t) be the third derivative of -t**6/160 + 7*t**5/240 - 5*t**4/96 + t**3/24 + 5*t**2. Factor m(g).
-(g - 1)**2*(3*g - 1)/4
Find k such that 1/10*k + 0 + 1/10*k**3 + 1/5*k**2 = 0.
-1, 0
Factor 25/4*a**4 - 21/4*a**3 - 9/4*a**5 + 1/2*a + 3/4*a**2 + 0.
-a*(a - 1)**3*(9*a + 2)/4
Let o(d) be the second derivative of -43/12*d**4 + 4*d**3 + 0 - 2*d**2 + 3/2*d**5 - 7/30*d**6 - 2*d. Solve o(v) = 0 for v.
2/7, 1, 2
Let l(b) be the third derivative of -5/36*b**6 + 5/36*b**4 + 1/18*b**5 - 3*b**2 + 0*b - 1/9*b**3 - 8/63*b**7 + 0 - 2/63*b**8. Factor l(x).
-2*(x + 1)**3*(4*x - 1)**2/3
Let w be (50/120)/((-1)/(-172)). Let y = -71 + w. Factor 0 + 0*b - y*b**2.
-2*b**2/3
Let d = 9 + -12. Let q be (-1 + d)*1/(-1). Let 4/7*c**3 - 2/7*c**q + 0*c**2 + 2/7 - 4/7*c = 0. Calculate c.
-1, 1
Let 10/3 - 5/3*g**2 - 5/3*g = 0. Calculate g.
-2, 1
Let o(u) = -6*u**2 - 43*u + 5. Let q(m) = 3*m**2 + 22*m - 2. Let t(r) = 2*o(r) + 5*q(r). Determine w, given that t(w) = 0.
-8, 0
Let l(n) = -2*n**3 - 4*n + 2*n**3 - 2*n**3 - 3*n**2 - n**3. Let f(g) = -7*g**3 - 6*g**2 - 9*g. Let q(x) = -2*f(x) + 5*l(x). Suppose q(u) = 0. What is u?
-2, -1, 0
Let i(a) be the third derivative of -a**7/1890 - 2*a**6/135 - 8*a**5/45 - 32*a**4/27 - 128*a**3/27 + 34*a**2. Factor i(q).
-(q + 4)**4/9
Let t(x) be the second derivative of x**7/14 - x**6/10 - 9*x**5/10 - x**4/2 + 5*x**3/2 + 9*x**2/2 + 6*x. Factor t(w).
3*(w - 3)*(w - 1)*(w + 1)**3
Let m(a) be the second derivative of a**6/180 + a**5/40 + a**4/36 + 7*a. Find f such that m(f) = 0.
-2, -1, 0
Let b be (1 + 3/4)*4. Determine z so that b*z**2 - 1 + z**2 - 4*z**4 + 0*z**4 - 3 = 0.
-1, 1
Suppose 3*r - 2*d - 6 = 0, 0*d - 6 = -5*r + 2*d. Suppose r*u = 3*k + 5*u - 1, k - 5*u - 7 = 0. Factor 2/5*x**k + 0*x - 2/5.
2*(x - 1)*(x + 1)/5
Let c(o) be the second derivative of 33*o**6/50 + 213*o**5/100 + 41*o**4/20 + o**3/10 - 3*o**2/5 - o + 2. What is n in c(n) = 0?
-1, -1/3, 2/11
Let h(d) be the first derivative of -d**6/6 + 9*d**5/20 - 3*d**4/8 + d**3/12 - 3. Solve h(k) = 0 for k.
0, 1/4, 1
Let j(z) be the first derivative of -z**4/2 - 2*z**3/3 + z**2 - 2*z - 3. Let o(t) be the first derivative of j(t). Suppose o(g) = 0. What is g?
-1, 1/3
Let x(g) = -7*g + 51. Let f be x(7). Determine u, given that 4/3*u**3 - 2/3*u**5 - 2/3 + 4/3*u**f - 2/3*u - 2/3*u**4 = 0.
-1, 1
Let o(f) be the third derivative of f**8/672 - f**7/420 - f**6/240 + f**5/120 - 36*f**2. Factor o(w).
w**2*(w - 1)**2*(w + 1)/2
Let m = 2 + 3. Suppose -m + 1 = -w. Factor j + j**2 - 4*j**4 + 3*j**3 + 3*j**4 - w*j**3.
-j*(j - 1)*(j + 1)**2
Let o(t) be the second derivative of t**4/90 - t**3/9 + 2*t**2/5 + t + 17. Solve o(x) = 0 for x.
2, 3
Let s = -5 + 6. Let y(r) = -r**2 + 2*r - 1. Let q be y(s). Factor 2/5*z + q - 2/5*z**2.
-2*z*(z - 1)/5
Let f(d) be the first derivative of -27*d**5/20 - 27*d**4/16 - d**3/2 - 5. Suppose f(g) = 0. Calculate g.
-2/3, -1/3, 0
Factor -4*x**2 + x + 4*x**2 + x - 2*x**2 + 4.
-2*(x - 2)*(x + 1)
Let i(s) be the first derivative of s**6/14 - 3*s**5/35 - 3*s**4/28 + s**3/7 - 4. Factor i(r).
3*r**2*(r - 1)**2*(r + 1)/7
Let p(w) = -w**2 - w. Let q(j) = j**5 - 4*j**4 + 6*j**3 + 5*j. Let z(u) = -4*p(u) - q(u). Solve z(i) = 0.
0, 1
Let d = -7 + 15. Let -5*k + 3*k**4 + d*k - 8*k**2 + 7*k**3 + 17*k**2 + 2*k**3 = 0. Calculate k.
-1, 0
Let s be -5 + (0 + 4 - 0). Let r be 2 + 15/(-6) - s. Factor 0*g - r*g**3 + 1/2*g**2 + 0.
-g**2*(g - 1)/2
Let p(k) be the second derivative of -1/4*k**4 - 3/20*k**5 + 0*k**2 + 4*k + 0*k**3 + 0. Find t, given that p(t) = 0.
-1, 0
Suppose -5*y + 5 = -5. Let h(l) be the first derivative of -3 + 0*l + 2/3*l**3 - l**y. Suppose h(d) = 0. What is d?
0, 1
Suppose 2*x - 5*x + 42 = 0. Suppose -4*m = 3*m - x. Factor 1/3 + 0*s**m + 5/3*s**3 + 1/2*s**5 - 5/6*s - 5/3*s**4.
(s - 1)**4*(3*s + 2)/6
Suppose 5*t = u + 146, 4*t + 5*u - 29 - 82 = 0. Let w = t + -25. Solve 6/5 - 6/5*g**2 - 12/5*g**3 + 3/5*g**5 + 9/5*g + 0*g**w = 0 for g.
-1, 1, 2
Let l(x) be the second derivative of x**5/4 - 15*x**4/4 + 20*x**3 - 40*x**2 - 15*x. Solve l(w) = 0.
1, 4
Let c(b) be the third derivative of 3*b**2 + 0 + 1/360*b**6 + 0*b - 1/24*b**4 - 1/9*b**3 + 0*b**5. Factor c(f).
(f - 2)*(f + 1)**2/3
Determine t, given that t**3 - 1/4*t**4 + 0*t - 3/4*t**2 + 0 = 0.
0, 1, 3
Suppose 0 = c + 5 + 5. Let v be c/(-104) - 2/(-13). Factor 0 - 3/4*s**3 - 1/4*s**4 - 3/4*s**2 - v*s.
-s*(s + 1)**3/4
Let d = 16 - 95/6. Let t(z) be the second derivative of 0 - 2*z - 1/6*z**4 + 1/2*z**2 - d*z**3. Let t(k) = 0. Calculate k.
-1, 1/2
Let v(p) be the third derivative of -p**7/2520 - p**6/2880 + p**4/8 - 2*p**2. Let g(d) be the second derivative of v(d). Determine a, given that g(a) = 0.
-1/4, 0
Let c(n) = -29*n**4 + 17*n**3 + 24*n**2 + 17*n + 5. Let m(u) = -5*u**4 + 3*u**3 + 4*u**2 + 3*u + 1. Let k(o) = 6*c(o) - 34*m(o). Factor k(r).
-4*(r - 1)**2*(r + 1)**2
Suppose 3*x - 5 - 21 = -4*m, -2*x - 5*m = -29. Factor -18/7 - 2/7*l**x + 12/7*l.
-2*(l - 3)**2/7
Let a(c) = c**2 - 10*c + 14. Let g be a(10). Suppose -5*u + g + 1 = 0. Factor -10*r**2 + 15/4*r - 15/2*r**4 + 7/4*r**5 - 1/2 + 25/2*r**u.
(r - 1)**4*(7*r - 2)/4
Factor 5 - 89*a**2 - 1 - 6*a + 91*a**2.
2*(a - 2)*(a - 1)
Let f(x) = 2*x + 4. Let l be f(7). Let g be 0 - (14/l - 1). Factor g + 2/9*q**2 + 4/9*q.
2*(q + 1)**2/9
Let t(c) = -242*c**4 - 1820*c**3 - 2820*c**2 + 2080*c - 317. Let z(j) = j**4 + 1. Let v(h) = -t(h) + 3*z(h). Factor v(i).
5*(i + 4)**2*(7*i - 2)**2
Let m = -4/3 - -3/2. Let z(r) be the first derivative of -1/2*r + 1 - m*r**3 - 1/2*r**2. Determine f, given that z(f) = 0.
-1
Let k(y) be the first derivative of -y**6/90 + y**5/180 + y**4/36 + y**3 + 3. Let b(r) be the third derivative of k(r). Find p such that b(p) = 0.
-1/3, 1/2
Let a(h) = -4*h**4 + 12*h**3 + 16*h**2 + 8*h. Let o(f) = -f**2 - 5*f + 5. Let r be o(-6). Let i(u) = u**5 - u**2. Let p(n) = r*a(n) + 4*i(n). Factor p(z).
4*z*(z - 2)*(z + 1)**3
Let p = 3186 - 35014/11. Determine a, given that -16/11*a - p - 2/11*a**2 = 0.
-4
Let t(c) be the second derivative of -c**5/30 + 2*c**4/9 - 5*c**3/9 + 2*c**2/3 + 6*c. Factor t(f).
-2*(f - 2)*(f - 1)**2/3
Let o**2 + 3*o**2 - 8*o**2 + 4*o**4 = 0. What is o?
-1, 0, 1
Let p be (3/(-9) - 68/(-180))*12. Factor -2/15*d + 8/15*d**2 + 0 - 2/15*d**5 - 4/5*d**3 + p*d**4.
-2*d*(d - 1)**4/15
Suppose -6*a + 1 = -5*a. Let j be (-1)/a - (-6)/1. Find o, given that o**4 - 8*o**5 + o - o**2 + o**4 + 7*o**j - o**2 = 0.
-1, 0, 1
Let 2/5*y**2 - 2/5*y + 0 = 0. What is y?
0, 1
Let o(s) be the second derivative of 4*s**7/189 + s**6/45 - s**5/90 + 33*s. Factor o(c).
2*c**3*(c + 1)*(4*c - 1)/9
What is r in 2/3 - 11/9*r + 4/9*r**2 + 1/9*r**3 = 0?
-6, 1
Let m(p) be the third derivative of p**7/1680 + p**6/360 - p**3/3 - 3*p**2. Let w(y) be the first derivative of m(y). Factor w(s).
s**2*(s + 2)/2
Let d(n) = -n**4 + n**2 + 1. Suppose -3 = -3*u + 3. Let k(m) = 4*m**4 - 7*m**3 + 7*m**2 - 5*m - 1. Let r(y) = u*d(y) + k(y). Factor r(l).
(l - 1)**3*(2*l - 1)
Let v(g) = g**2 - g - 8. Let o be v(-3). What is t in -1 + 1/2*t**o - 3/2*t**3 + 1/2*t**2 + 3/2*t = 0?
-1, 1, 2
Let j(n) be the first derivative of 8/9*n**3 + 1/18*n**4 + 8 + 0*n + 4/9*n**2 + 4/27*n**6 - 8/15*n**5. Factor j(f).
2*f*(f - 2)**2*(2*f + 1)**2/9
Suppose -2*b = 3*x - 5, -4*x = b + b - 8. Solve 0 + 0*n + 12/5*n**5 + 3/5*n**x + 0*n**2 - 3*n**4 = 0.
0, 1/4, 1
Let a(j) = 7*j**5 + 2*j**4 + 4*j**3 + 2*j**2 - 11*j - 4. Let o(