 - 2*i**2 + 4*i**k = 0. Calculate i.
0, 2
Let t(o) = -o**3 + 7*o**2 - 6*o + 4. Let s be t(6). Factor -237 - s*a**2 + 237 + 4*a.
-4*a*(a - 1)
Let q(c) be the third derivative of 1/18*c**4 + 0*c - 1/270*c**5 - 1/3*c**3 - 2*c**2 + 0. Factor q(k).
-2*(k - 3)**2/9
Let a(o) = 6*o - 202. Let m be a(34). Factor 0*d - 4/7 + 1/7*d**m.
(d - 2)*(d + 2)/7
Let d = 146/201 + -4/67. Solve -1/3*k**3 + 0*k + d*k**2 - 1/3*k**4 + 0 = 0 for k.
-2, 0, 1
Suppose -16 = -5*v + 4*j, 10 = 5*v - j - 9. Factor v*n - 2 - 2*n**2 - 8*n**3 + 6*n**3 + 6*n - 4.
-2*(n - 1)**2*(n + 3)
Let g be 2/23 - (2568/966 - 3). Factor 0 + 0*z + 3/7*z**2 - g*z**3.
-3*z**2*(z - 1)/7
Factor 1/4*p**4 + 1/4*p**2 - 3/4*p + 3/4*p**3 - 1/2.
(p - 1)*(p + 1)**2*(p + 2)/4
Let a = -50 + 50. Let g(h) be the third derivative of 0 + 1/330*h**5 + 1/1848*h**8 + 1/220*h**6 + 0*h + 0*h**4 + a*h**3 + 3*h**2 + 1/385*h**7. Factor g(q).
2*q**2*(q + 1)**3/11
Let f(w) = 2*w**2 - w - 1. Let i be f(-1). Find k, given that 4*k - k + 2*k**3 + 0*k + 2 + 6*k**i + 3*k = 0.
-1
Let u(p) = -6*p**3 - 28*p**2 + 14*p. Let f(q) = -2*q**3 - 9*q**2 + 5*q. Let r(l) = -14*f(l) + 5*u(l). Factor r(j).
-2*j**2*(j + 7)
Let n be 4 - 2 - 2*1. Suppose -5*t - 4*f + 35 = n, t + t + 4*f - 26 = 0. Factor -7/5*p**t + 7/5*p + 2/5 - 2/5*p**2.
-(p - 1)*(p + 1)*(7*p + 2)/5
Let p(j) = 8*j + 3 + 7*j**2 + 0*j**2 - j**3 - 1. Let t be p(8). Factor n**3 - t*n + 0*n + n.
n*(n - 1)*(n + 1)
Let m(g) be the second derivative of -g**4/30 + 2*g**3/15 - g**2/5 - 22*g. What is n in m(n) = 0?
1
Let c = -156 + 627/4. Factor -1/4*w**3 + 3/4*w**2 - c*w + 1/4.
-(w - 1)**3/4
Let k(q) be the second derivative of 1/72*q**4 + 0 + 0*q**3 + 2*q + 1/180*q**6 + 0*q**2 + 1/60*q**5. Factor k(u).
u**2*(u + 1)**2/6
Suppose 12*k**2 + 4*k**3 - 2 + 4*k**2 + 18*k + 10 + 2*k = 0. What is k?
-2, -1
Let g(h) be the third derivative of h**6/60 - 3*h**5/40 + h**4/8 - h**3/12 + 10*h**2. Factor g(n).
(n - 1)**2*(4*n - 1)/2
Let j(f) be the third derivative of f**5/45 + f**4/18 - 14*f**2. Solve j(w) = 0 for w.
-1, 0
Let g = -52 - -469/9. Let x = 2/9 + g. Factor -1/3*c + x*c**2 + 0.
c*(c - 1)/3
Let z(m) be the second derivative of -m**4/12 + m**3 - m**2/2 + 2*m. Let g be z(5). Let -3*f**2 + 1 + g*f**2 - f**3 + 2*f**2 - 3*f = 0. Calculate f.
1
Find w such that 3/2*w**4 + 9/2*w**2 + 3/2*w + 0 + 9/2*w**3 = 0.
-1, 0
Let m(n) be the second derivative of -n**4/10 + 5*n**3/6 - 2*n**2/5 + n + 5. Factor m(j).
-(j - 4)*(6*j - 1)/5
Factor 4/5*n**3 - n - 4/5*n**4 + 2/5*n**2 + 2/5 + 1/5*n**5.
(n - 2)*(n - 1)**3*(n + 1)/5
Suppose 13 = 2*m + 9. Let 0*k**5 + 3*k**5 + 2*k**3 - 4*k**5 - k**4 - 2*k + m*k**2 + k - 1 = 0. What is k?
-1, 1
Let k be 10/3 - 3/9. Let m be (0 - 0)/k*-1. Factor m - 3*u**2 + 3/2*u + 3/2*u**3.
3*u*(u - 1)**2/2
Let d(t) be the first derivative of 1/84*t**4 + 0*t + 0*t**5 + 1 - 1/1260*t**6 + 0*t**2 - 1/3*t**3. Let f(l) be the third derivative of d(l). Factor f(n).
-2*(n - 1)*(n + 1)/7
Let r = 462 + -1385/3. Let -1/3*a**2 + 0 + 0*a**3 + r*a**4 + 0*a = 0. What is a?
-1, 0, 1
Suppose 3 = -16*q + 35. Let y(w) = w + 2. Let o be y(3). Determine n, given that 0*n**q + 2/9*n**3 - 2/9*n**o + 0*n**4 + 0 + 0*n = 0.
-1, 0, 1
Let d be -10 + (-225)/(-10) + -12. Let v be 14/(-4)*3/(-7). Factor -7/4*j + 2*j**4 - v*j**2 + j**3 - d + 3/4*j**5.
(j - 1)*(j + 1)**3*(3*j + 2)/4
Let k be 7 - 5 - (0 + -1). Factor -k*i**4 + 0*i**2 + 15*i**5 + 3*i**3 - 14*i**5 - i**2.
i**2*(i - 1)**3
Suppose 4*i - 7 = 5. Let l(c) be the first derivative of 4*c + 3*c**2 + 2 + 2/3*c**i. Solve l(g) = 0 for g.
-2, -1
Let l(m) = -m**2 - m + 1. Let w(i) = -4*i**2 + 8 - 2*i - 5*i + 3*i - 5. Let p(q) = -10*l(q) + 2*w(q). Factor p(o).
2*(o - 1)*(o + 2)
Let c(y) be the first derivative of y**5/140 + y**4/56 + y**2 + 7. Let o(n) be the second derivative of c(n). Solve o(h) = 0 for h.
-1, 0
Let p(n) = n**3 - 6*n**2 + 3. Let v be p(6). Suppose 5*j - v*s = 29, j - 4*s = 5*j - 4. Find c such that -3*c**j + 0*c - c**4 - 4*c**2 + c**5 + 6*c**3 + c = 0.
0, 1
Let a be (-1)/(2/(-8 - -4)). Let -2*u**4 - 9*u + 9*u + a*u**2 = 0. What is u?
-1, 0, 1
Suppose -3 = -2*q - 19. Let u be ((-10)/q - 2)*-3. Factor 5/4*k**2 + 1/4*k + 0 + u*k**3 + 7/4*k**4 + 1/2*k**5.
k*(k + 1)**3*(2*k + 1)/4
Let l = 12 + -8. Suppose -m - 4*m + 21 = -3*o, m - l*o = 11. Factor -x**m + 0 + 5/2*x**4 + x - 5/2*x**2.
x*(x - 1)*(x + 1)*(5*x - 2)/2
Let y = -1618/3 - -542. Factor y*q**2 + 4*q + 3/2.
(4*q + 3)**2/6
Let o(r) = 2*r + 36. Let c be o(-16). Let x(p) be the first derivative of -p**2 - p**3 + 0*p - 1/4*p**c + 1. Suppose x(u) = 0. Calculate u.
-2, -1, 0
Let c = 652 - 640. Factor 56/3*k**3 + 4/3*k**5 + 64/3*k**2 + 8/3 + 8*k**4 + c*k.
4*(k + 1)**4*(k + 2)/3
Let d(l) be the first derivative of -4 + 0*l - 1/6*l**2 - 1/9*l**3 + 1/12*l**4 + 1/15*l**5. Find q such that d(q) = 0.
-1, 0, 1
Let h be (1/2)/((-3)/(-54)). Let x(g) = -g**2 + 10*g - 7. Let c be x(h). Factor -y**2 - 2*y**3 + 2*y + y**c.
-2*y*(y - 1)*(y + 1)
What is p in 34*p**2 + p**2 + 25*p**4 - 45*p**3 - 5*p**5 - 4*p - p - 5*p = 0?
0, 1, 2
Let q(k) = 2*k + 14. Let y be q(-6). Let p(n) be the second derivative of 1/5*n**y + 1/30*n**4 + 2/15*n**3 - 2*n + 0. Factor p(x).
2*(x + 1)**2/5
Let f(m) be the second derivative of -m**5/20 - m**4/12 + 5*m**3/6 - 3*m**2/2 - 6*m. Factor f(s).
-(s - 1)**2*(s + 3)
Let b be -7 + (-2 + 0)/1. Let r = b - -9. Factor 0*o**2 + r + 0*o - 1/4*o**3 - 1/4*o**4.
-o**3*(o + 1)/4
Let w(o) = -o**2 + o - 1. Let m(y) = -6*y**2 + 5*y - 4. Let s = -8 - -11. Let z(k) = s*m(k) - 15*w(k). Factor z(f).
-3*(f - 1)*(f + 1)
Let k be -1 + 65/15 + -3. Factor k*x - 2/3 + 1/3*x**2.
(x - 1)*(x + 2)/3
Suppose 4*l = l. Let b(y) be the first derivative of l*y + 0*y**2 + 2 - 2/21*y**3 + 1/14*y**4. Factor b(h).
2*h**2*(h - 1)/7
Find q such that 24*q + 10*q**2 + 14*q**2 + 8 - 38*q**2 = 0.
-2/7, 2
Factor 48/5*h**2 + 72/5*h**3 + 0*h + 0 + 27/5*h**4.
3*h**2*(3*h + 4)**2/5
Let q = -21 + 23. Let l(k) be the second derivative of -2*k - 1/6*k**3 + 0 - 1/2*k**q - 1/48*k**4. Factor l(i).
-(i + 2)**2/4
Suppose 4*t = -2*z + 8, 6*z = -2*t + 3*z + 4. What is a in 2*a + 2*a**t - 2*a**2 + a**2 + 0*a**2 = 0?
-2, 0
Suppose 5*x - 27 = 3*c, -7 = 3*x + 2*c - 8. Factor 9/5*o**2 - o**x + 1/5*o**4 - 7/5*o + 2/5.
(o - 2)*(o - 1)**3/5
Find c such that 6*c**3 - c + 7*c - 33*c**2 + 51*c**3 - 21*c**4 - 9*c**3 = 0.
0, 2/7, 1
Let j(n) be the second derivative of n**5/210 - 3*n**2 - 4*n. Let k(q) be the first derivative of j(q). Let k(u) = 0. Calculate u.
0
Let k(a) be the first derivative of -a**4 + 13*a**3/3 - 6*a**2 + 9*a/4 - 5. Find u, given that k(u) = 0.
1/4, 3/2
Let t(j) = j**4 + j. Let k(p) = -p**3 - p. Let b(o) = 24*o**4 + o**3 - 6*o**2 + 13*o. Let d(y) = b(y) - 2*k(y). Let i(u) = d(u) - 18*t(u). Factor i(f).
3*f*(f - 1)*(f + 1)*(2*f + 1)
Find o such that 4*o**3 - 9 + 3*o - 18*o**2 + 1 + 3*o + 18*o = 0.
1/2, 2
Let p(f) be the second derivative of 0 - f + 0*f**2 - 1/6*f**4 - 1/3*f**3. Let p(w) = 0. What is w?
-1, 0
Let p be ((-94)/480)/(-1) + 46/(-345). Let b(d) be the third derivative of 0*d**3 - p*d**4 - 1/40*d**5 + 0 + 0*d + d**2. Factor b(s).
-3*s*(s + 1)/2
Let w be -9 - (2 - (0 - 0)). Let j be (-84)/(-22) + (-2)/w. Factor z**j - 3*z**3 + 5*z**3 + z**2 + 0*z**4.
z**2*(z + 1)**2
Let d be (1 - 1) + 4 + 2. Let c(w) = w**2 - 4*w - 6. Let z be c(d). Let z*q**2 + 4*q + 6*q**3 - 2*q + 2*q**4 + 0*q**2 = 0. What is q?
-1, 0
Let a(i) be the third derivative of -i**6/780 + i**5/130 - 4*i**3/39 + 38*i**2. Determine q so that a(q) = 0.
-1, 2
Let u(f) = f**3 + 7*f**2 - 7*f + 8. Let b be u(-8). Suppose b*j = -j + 5. Solve -3*g + g**3 - 5 - 2 + j = 0 for g.
-1, 2
Factor 1/7*a**3 + 1/7*a**2 + 0 + 0*a.
a**2*(a + 1)/7
Let u(m) be the second derivative of -m**5/30 + m**4/6 - m**2 - 2*m. Let f(d) be the first derivative of u(d). Factor f(c).
-2*c*(c - 2)
Let j(m) be the first derivative of -4*m**3/3 + 2*m**2 + 8*m + 4. Find v such that j(v) = 0.
-1, 2
Let i(c) = -c**2 + 11*c + 1. Let x be i(11). Factor 2 + 2*w**3 + 4*w**2 + x - 3.
2*w**2*(w + 2)
Factor 3*w**4 - 16*w**3 + 28*w**3 + 6*w**2 - 9*w - 3*w - 9 + 0.
3*(w - 1)*(w + 1)**2*(w + 3)
Let 2/11 + 2/11*f**2 + 4/11*f = 0. What is f?
-1
Suppose -2*j - 10 = 0, 2*o - 14 = 3*j + 25. Let g be 2/o*(-24)/(-9). Determine u, given that 0*u + 2/3*u**4 + 0 + g*u**2 - 10/9*u**3 = 0.
0, 2/3, 1
Suppose n = -81 + 84. Let q(j) be t