0*n + i - 4/5*n**3 = 0. Calculate n.
-1/4, 0
Suppose 0 = -3*l + 5*w + 1, 2*l - 4*l + 9 = 5*w. Let y be (-13)/(-2) - (l + 1) - 3. Factor -y*x**2 + 0 + 1/2*x.
-x*(x - 1)/2
Let l(u) be the third derivative of -u**6/24 - u**5/6 - 5*u**4/24 + 60*u**2. Find j such that l(j) = 0.
-1, 0
Let b(l) be the second derivative of 3*l**5/40 + 3*l**4/8 - 6*l**3 - 60*l**2 + 143*l. Find o, given that b(o) = 0.
-4, 5
Let z(v) be the first derivative of -4*v**5 - 47*v**4 - 204*v**3 - 378*v**2 - 216*v - 70. What is c in z(c) = 0?
-3, -2/5
Let n(q) = -q**3 - q**2 + 2*q + 1. Let v(p) = -3*p**4 + 3*p**3 + 69*p**2 + 75*p + 6. Let j(b) = 6*n(b) - v(b). Let j(g) = 0. What is g?
-3, -1, 0, 7
Let o(t) be the second derivative of -13*t**5/25 + 28*t**4/15 - 8*t**3/15 - 2*t - 13. Find g such that o(g) = 0.
0, 2/13, 2
Suppose -2222 = -21*h + 1495. Let m = h - 1585/9. Factor -m*a**3 - 2*a**2 - 2/9 - 4/3*a.
-2*(a + 1)**2*(4*a + 1)/9
Suppose 0*d = d - 3. Factor -6*c + 16*c**2 - 6*c**d - 2 - 3 + 1.
-2*(c - 2)*(c - 1)*(3*c + 1)
Factor 36 - 3*j**3 - j**3 + 8*j**3 - 36*j**2 - 4*j + 0.
4*(j - 9)*(j - 1)*(j + 1)
Let t(r) be the third derivative of -1/42*r**7 + 0*r + 0 - 7/240*r**6 + 5*r**2 + 1/24*r**3 + 1/240*r**5 - 1/168*r**8 + 1/24*r**4. Suppose t(b) = 0. What is b?
-1, -1/2, 1/2
Let p(m) = -m**3 - 2*m**2 + 4*m - 3. Let z be p(3). Let u = 38 + z. Solve 4/9*h**u + 2/9*h + 2/9*h**3 + 0 = 0 for h.
-1, 0
Let l be (-2)/(-1) - 34/(-17). Let x(y) be the first derivative of 0*y - 2/3*y**3 - 3/2*y**2 + 1/4*y**l - 2. Find i, given that x(i) = 0.
-1, 0, 3
Let d be (-46)/14 + (-18)/(-63). Let g be (-20)/(-8) + d/6. Solve -4*p + 2*p - p**3 + p + g*p**2 = 0.
0, 1
Let m(o) = 2*o**2 - o. Let g(q) = -26*q**2 + 94*q + 36. Let b(h) = -g(h) - 8*m(h). Factor b(i).
2*(i - 9)*(5*i + 2)
Factor -32*u**2 - 5*u + 22*u**2 + 2 - u**3 + 6*u**3 + 8.
5*(u - 2)*(u - 1)*(u + 1)
Suppose -2*c = -7*c + 15. Suppose -c = -4*u + u - 3*q, -u = -5*q - 7. Find k, given that 3*k**3 - 2*k**4 + 0*k**2 - k**3 - 2*k + u*k**2 = 0.
-1, 0, 1
Let y(l) = 205*l**2 - 160*l - 20. Let j(b) = -198*b**2 + 159*b + 19. Let x(f) = -5*j(f) - 4*y(f). Factor x(z).
5*(z - 1)*(34*z + 3)
Let g(v) = 48*v**2 - 63*v + 69. Let q(a) = -7*a**2 + 9*a - 10. Let n(o) = -4*g(o) - 27*q(o). Determine w so that n(w) = 0.
1, 2
Let a(v) = 9*v**5 + 42*v**4 - 147*v**3 + 324*v**2 - 324*v + 126. Let t(y) = 2*y**5 + y**4 + 2*y**3 - y**2 + 1. Let o(k) = -a(k) + 6*t(k). Factor o(b).
3*(b - 5)*(b - 2)**3*(b - 1)
Let f(k) = 2*k**5 + k**4 + k**2 - k. Let t(s) = -21*s**5 + 9*s**3 - 22*s**2 + s. Let r(u) = -22*f(u) - 2*t(u). Suppose r(n) = 0. Calculate n.
-10, -1, 0, 1
Suppose 4*m + 2*m = 0. Let n(c) = m - 1 - 6 - 4*c**2 + 6*c + 3. Let w(v) = v**2. Let y(q) = -2*n(q) - 4*w(q). Let y(l) = 0. Calculate l.
1, 2
Let p(m) = 18*m**2 - 42*m - 12. Let k(u) = -9*u**2 + 22*u + 7. Let a(d) = -9*k(d) - 5*p(d). Let a(l) = 0. What is l?
1/3, 1
Suppose -145 = -18*d - 109. Factor 2/7 - 9/7*v**3 + 9/7*v - 2/7*v**d.
-(v - 1)*(v + 1)*(9*v + 2)/7
Let k = -4163 + 12490/3. Find d such that -k*d + 1/6*d**2 + 0 = 0.
0, 2
Let w(r) be the first derivative of -1/54*r**6 + 1/6*r**2 - 1/15*r**5 + 2/27*r**3 - 21 + 1/9*r - 1/18*r**4. Let w(t) = 0. What is t?
-1, 1
Find w, given that 0*w**3 - w**4 + w**2 + 0 + 1/2*w - 1/2*w**5 = 0.
-1, 0, 1
Let r be (0 - 24)/(-6) + 1. Let o(t) be the second derivative of 0*t**4 + 1/20*t**r + 0*t**3 + 0 + 1/21*t**7 + 2*t - 1/10*t**6 + 0*t**2. Solve o(s) = 0 for s.
0, 1/2, 1
Factor 2/3*d**3 + 0 + 34/3*d**2 - 12*d.
2*d*(d - 1)*(d + 18)/3
Suppose -21 = -p - 2*p. Let i(j) = -j + 9. Let c be i(p). Factor -5*o**4 + 9*o**3 - o**3 + 9*o**4 + 7*o**c - 3*o**2.
4*o**2*(o + 1)**2
Let p = 127 - 124. Let r(i) be the third derivative of 3*i**2 + 1/14*i**4 + 0*i - 1/105*i**5 - 4/21*i**p + 0. Factor r(z).
-4*(z - 2)*(z - 1)/7
Suppose -27*r - 12 - 11 = -23. Let r*i + 28/3*i**3 + 0 - 49/3*i**4 - 4/3*i**2 = 0. Calculate i.
0, 2/7
Let l(g) be the third derivative of g**8/1344 + g**7/120 - g**6/96 - 7*g**5/48 + g**4/24 + 7*g**3/6 + 10*g**2 + 8*g. Suppose l(x) = 0. Calculate x.
-7, -2, -1, 1, 2
Let z = 31 + -55/2. Let k(c) be the first derivative of -4 + 0*c**2 + 4/3*c**3 + 0*c - z*c**4. Factor k(d).
-2*d**2*(7*d - 2)
Let z = 150 + -168. Let q(o) = o**2 + 16*o - 36. Let u be q(z). Solve 1/2*t**2 + u*t + 0 + 1/2*t**3 = 0.
-1, 0
Let r = 16478 - 16476. Determine t so that -8/11 + 0*t - 2/11*t**3 + 6/11*t**r = 0.
-1, 2
Let o(n) be the third derivative of -n**9/22680 - n**8/5040 + 5*n**4/4 - 13*n**2. Let q(h) be the second derivative of o(h). Factor q(i).
-2*i**3*(i + 2)/3
Let i(u) be the third derivative of -u**7/840 + u**6/180 + 8*u**3/3 + 2*u**2. Let q(o) be the first derivative of i(o). Factor q(t).
-t**2*(t - 2)
Let m(d) = -9 + 7*d - 7*d + 2*d. Let r be m(9). Factor k**2 - r + 9 - k.
k*(k - 1)
Let a = -248 + 282. Suppose -2*f + a = 15*f. Factor 6*j**f + 6*j + 0 + 3/2*j**3.
3*j*(j + 2)**2/2
Let q(i) be the first derivative of 4*i**6/3 - 36*i**5/5 + 12*i**4 - 16*i**3/3 + 39. Factor q(w).
4*w**2*(w - 2)**2*(2*w - 1)
Let h = -277/9 + 1117/36. Determine m, given that 1/2 + 1/4*m - h*m**2 = 0.
-1, 2
Suppose 0*k - 77 = -11*k. Factor k*z**2 + 20*z - 2*z**2 + 9 - 23 - 11.
5*(z - 1)*(z + 5)
Let i(l) be the second derivative of l**7/17640 + l**6/210 + 6*l**5/35 - 17*l**4/12 + 14*l. Let c(u) be the third derivative of i(u). Let c(v) = 0. What is v?
-12
Let v(u) be the second derivative of u**5/20 + 107*u**4/6 + 11449*u**3/6 - 360*u. Factor v(z).
z*(z + 107)**2
Let k(b) be the first derivative of 64*b**4 - 320*b**3/3 + 34*b**2 - 4*b + 278. Suppose k(u) = 0. What is u?
1/8, 1
Solve -3/2*h - 9/2*h**3 - 5*h**2 + 0 - h**4 = 0.
-3, -1, -1/2, 0
Let c(l) = 3*l**2 + 15*l. Let s be c(-5). Suppose 0*m + s*m = -4*m. Factor 7/2*x**2 - 7/2*x**4 + x - x**3 + m.
-x*(x - 1)*(x + 1)*(7*x + 2)/2
Let h(x) be the third derivative of x**8/1512 - 17*x**6/540 - 2*x**5/15 - 5*x**4/27 + 41*x**2. Let h(i) = 0. Calculate i.
-2, -1, 0, 5
Let t(r) be the third derivative of -r**6/780 + 2*r**5/195 - 5*r**4/156 + 2*r**3/39 + 79*r**2. Factor t(s).
-2*(s - 2)*(s - 1)**2/13
Let p be (3 - 0)*(4 - 5). Let w = 0 - p. Determine b, given that -w*b**2 + b**2 + 5*b**2 + b**2 = 0.
0
Let s(m) be the second derivative of -m**5/4 + 655*m**4/12 + 1325*m**3/6 + 665*m**2/2 + 75*m - 4. Find j such that s(j) = 0.
-1, 133
Suppose 4*a = -2*m, -4*a = -5*m - 16 - 12. Solve 14 - 4 + 3*z**2 - 11*z - 4*z + a*z**2 = 0.
1, 2
Let o(r) be the first derivative of 0*r - 6 - 2*r**3 + 3/4*r**4 - 9/2*r**2. Factor o(s).
3*s*(s - 3)*(s + 1)
Let m = -64 + -25. Let u = -87 - m. Solve 2/9*x**3 + 0*x + 0 - 2/9*x**u = 0.
0, 1
Let a = 43/2 + -385/18. Let t(u) be the third derivative of 0*u - a*u**3 + 1/180*u**6 + 1/12*u**4 - 1/30*u**5 + 0 - 4*u**2. Find y, given that t(y) = 0.
1
Suppose -11*m + 28 = -9*m. Let c be ((-6)/3 + 6)/(-4 + m). Factor 0*o**2 - c - 3/5*o + 1/5*o**3.
(o - 2)*(o + 1)**2/5
Let x be (-12)/(-80)*-4*1/(-30). Let m(f) be the second derivative of -4*f - 1/30*f**4 + 1/5*f**2 - 1/15*f**3 + x*f**5 + 0. Factor m(o).
2*(o - 1)**2*(o + 1)/5
Let p be (38 - 31) + (-4 - -1). Let v(l) be the third derivative of 0*l + 0 + 1/150*l**6 - 1/525*l**7 - l**2 + 0*l**3 + 0*l**p - 1/150*l**5. Factor v(m).
-2*m**2*(m - 1)**2/5
Let a(r) = r**3 - 23*r**2 - 2*r + 50. Let b be a(23). Let k(m) be the second derivative of 6*m + 0*m**3 + 1/20*m**5 + 1/12*m**b + 0 + 0*m**2. Solve k(p) = 0.
-1, 0
Let w be (1/10)/(116 + -115). Let a(n) be the first derivative of 0*n + 0*n**3 - 9 + w*n**2 - 1/20*n**4. Factor a(b).
-b*(b - 1)*(b + 1)/5
Let h(l) be the third derivative of l**9/16632 - l**8/4620 + l**6/990 - l**5/660 - 2*l**3/3 + 16*l**2. Let k(p) be the first derivative of h(p). Factor k(y).
2*y*(y - 1)**3*(y + 1)/11
Let t be (0 - -2 - 3)*1. Let j = t - -1. Factor -3/4 + j*f + 3/4*f**2.
3*(f - 1)*(f + 1)/4
Let i(b) be the second derivative of 0 + 1/18*b**4 - 12*b + b**2 + 4/9*b**3. Factor i(l).
2*(l + 1)*(l + 3)/3
Let x(w) be the first derivative of -w**6/2 + 118*w**5/5 - 9*w**4 - 118*w**3/3 + 39*w**2/2 + 76. Let x(o) = 0. Calculate o.
-1, 0, 1/3, 1, 39
Let o(d) be the first derivative of -37 - d**3 + 757*d + 12*d**2 - 757*d. What is b in o(b) = 0?
0, 8
Let m(x) = 4*x**2 - 212*x - 192. Let s(k) = -k**2 + k - 1. Let z(o) = -m(o) - 8*s(o). Factor z(y).
4*(y + 1)*(y + 50)
Factor -1/5*n**2 + 4/5*n +