*m**2 - 3/4.
-3*(m - 1)**4/4
Let d be (1/(-3))/((-5)/45). Let i = d - -2. Determine z so that 6*z + z**3 + 0 - i*z**2 - 2 + z**3 - z**2 = 0.
1
Let f(l) be the first derivative of 0*l**4 + 0*l + 1/300*l**5 + 1/900*l**6 - 4/3*l**3 + 0*l**2 - 2. Let z(k) be the third derivative of f(k). Factor z(i).
2*i*(i + 1)/5
Let o(i) be the second derivative of -i**7/735 - i**6/140 - i**5/70 - i**4/84 - 5*i**2 - 4*i. Let l(x) be the first derivative of o(x). Factor l(r).
-2*r*(r + 1)**3/7
Let z be (-225)/(-90) + (-1)/2. Let y(b) be the second derivative of b + 8/51*b**3 + 1/102*b**4 + 0 + 16/17*b**z. Factor y(a).
2*(a + 4)**2/17
Let q(y) be the first derivative of y**6/33 + 38*y**5/55 + 17*y**4/11 - 4*y**3/33 - 35*y**2/11 - 34*y/11 - 752. Let q(g) = 0. What is g?
-17, -1, 1
Let k be 85/(-680) - 102/(-48). Let -6/5*h + 24/5 - 3/5*h**k = 0. What is h?
-4, 2
Let m(s) be the third derivative of s**7/2100 + s**6/120 + s**5/24 + 48*s**2 + 4. Factor m(i).
i**2*(i + 5)**2/10
Let u(v) be the second derivative of 1/6*v**3 - 1/24*v**4 + 16*v - 1/4*v**2 + 0. Factor u(k).
-(k - 1)**2/2
Let j(p) be the first derivative of p**5 - 10*p**4 + 35*p**3/3 + 194. Let j(s) = 0. Calculate s.
0, 1, 7
Let c(s) be the second derivative of -3*s + 5/6*s**4 + 5/42*s**7 - 1/6*s**6 + 5/6*s**3 + 0 - 5/2*s**2 - 1/2*s**5. Solve c(i) = 0 for i.
-1, 1
Let w(o) be the second derivative of -o**7/14 + 2*o**6/5 - 3*o**5/20 - 5*o**4/2 + 2*o**3 + 12*o**2 + 9*o + 5. Suppose w(y) = 0. Calculate y.
-1, 2
Let m(j) be the first derivative of -j**7/147 - 3*j**6/35 - 3*j**5/14 + 25*j**4/42 + 10*j - 55. Let d(b) be the first derivative of m(b). Factor d(y).
-2*y**2*(y - 1)*(y + 5)**2/7
Let b(a) be the third derivative of 1/156*a**4 + 0*a + 0 - 1/195*a**5 - 4*a**2 + 0*a**3 + 1/780*a**6. Solve b(f) = 0 for f.
0, 1
Let y(i) be the first derivative of -2/15*i**5 + 1/2*i**4 - 4/3*i**2 + 0*i + 7 + 0*i**3. Suppose y(g) = 0. What is g?
-1, 0, 2
Let s = -1 - -5. Suppose s*l = -3*w - 10, -4*w - 5*l = -0*l + 12. Solve -4*n**2 - 1 + 5*n**w + 0 = 0 for n.
-1, 1
Let 20*i**3 - 16/3*i + 8/3*i**4 + 0 - 20/3*i**5 + 16/3*i**2 = 0. What is i?
-1, 0, 2/5, 2
Suppose 0 = -252*c - 404*c + 176*c + 960. Let x be 1/(-1 - -3*1). Factor x*i**c + 0*i + 0 - 2*i**3.
-i**2*(4*i - 1)/2
Let m(k) be the third derivative of k**6/360 - 2*k**5/5 - 49*k**4/24 - 37*k**3/9 + 303*k**2. Solve m(z) = 0 for z.
-1, 74
Find m, given that -2/7*m**2 - 450/7 - 60/7*m = 0.
-15
Let h(q) = 52*q**3 - 12*q**2 + 4. Let z(f) = 52*f**3 - 13*f**2 + 5. Suppose 3*g - 22 = -5*i, 4*i = -3*g + 2*g + 12. Let b(p) = g*z(p) - 5*h(p). Factor b(r).
-4*r**2*(13*r - 2)
Let r = -5482 - -5482. Factor -2/5*q**2 + 0*q - 2/5*q**3 + r.
-2*q**2*(q + 1)/5
Let t be (20 - -4) + -1 - 5. Let y be (-22)/(-55) + t/(-70). Determine r, given that -y*r**2 + 1/7*r + 0 = 0.
0, 1
Factor -248*z**3 - 9*z**2 + 3*z**4 - 12*z + 260*z**3 + 6*z**2.
3*z*(z - 1)*(z + 1)*(z + 4)
Let r(m) = -m**3 + 3*m**2 + 11*m. Let a be r(-3). Let n be (28/a)/((-22)/6)*-1. Factor 0*k + 6/11*k**3 + n*k**2 + 2/11*k**4 + 0.
2*k**2*(k + 1)*(k + 2)/11
Factor 80/3*x + 4/9*x**3 - 8*x**2 + 800/9.
4*(x - 10)**2*(x + 2)/9
Let u(p) = -4*p**4 - 100*p**3 - 72*p**2 + 8*p + 8. Let t(y) = 3*y**4 + 66*y**3 + 48*y**2 - 5*y - 5. Let l(w) = 8*t(w) + 5*u(w). Solve l(c) = 0.
-6, -1, 0
Let y be (-12)/7*(-92)/552. Factor 6/7*h - 6/7*h**2 - 2/7 + y*h**3.
2*(h - 1)**3/7
Let r(b) be the third derivative of b**7/1680 - 29*b**6/960 + 9*b**5/160 + 29*b**4/192 - 7*b**3/12 - 1003*b**2. Factor r(q).
(q - 28)*(q - 1)**2*(q + 1)/8
Suppose -61 = -4*o + 15. Let s = -14 + o. Factor 3 - 60*r**2 - s - 18*r**5 - 51*r**3 - 18*r + 8*r**3 - 49*r**3 - 66*r**4.
-2*(r + 1)**3*(3*r + 1)**2
Let x(p) be the third derivative of 5/32*p**4 - 3/80*p**5 + 0*p + 1/480*p**6 + 0 + 25/24*p**3 + 38*p**2. What is b in x(b) = 0?
-1, 5
Let g(k) = 5*k**5 - 30*k**4 - 65*k**3 - 40*k**2 + 10*k - 10. Let t(w) = -w**5 - w**4 - w**2 + w - 1. Let n(o) = -g(o) + 10*t(o). Let n(p) = 0. What is p?
-1, -2/3, 0, 3
Let r(v) be the second derivative of v**6/360 + v**5/24 - v**4/4 + v**3/2 - 2*v - 8. Let x(u) be the second derivative of r(u). Solve x(p) = 0.
-6, 1
Let j(t) be the second derivative of -t**5/20 - 89*t**4/6 - 353*t**3/6 - 88*t**2 - 170*t. Let j(a) = 0. What is a?
-176, -1
Let i(t) = -t**2 - 14*t - 8. Let m be i(-6). Determine v, given that 19*v**4 - 55 - 14*v**4 - 80 - m*v**3 + 90*v**2 = 0.
-1, 3
Let a(z) be the first derivative of -2*z**4 + 62*z**3/3 + 11*z**2 - 48*z - 45. Factor a(f).
-2*(f - 8)*(f + 1)*(4*f - 3)
Factor -76/5 + 2*v**2 + 378/5*v.
2*(v + 38)*(5*v - 1)/5
Let q(l) = l**3 + 98*l**2 + 197*l + 483. Let w be q(-96). Factor -16/15 + 4/15*r**2 + 2/15*r**w - 8/15*r.
2*(r - 2)*(r + 2)**2/15
Find r such that 1/2*r**2 + 20449/2 + 143*r = 0.
-143
Let a = -53 - -38. Let f be (-111)/a - 4 - 1. What is j in 4/5*j**5 + 8/5*j**2 - 12/5*j**4 - f*j + 4/5 + 8/5*j**3 = 0?
-1, 1
Suppose 3*y - 23 = 4*r, 3*y = -0*y - 2*r + 29. Factor t**3 - 15 - 5*t**4 + y*t**3 - 23*t + 20*t**2 + 13*t.
-5*(t - 3)*(t - 1)*(t + 1)**2
Let f(t) be the first derivative of t**3/4 + 33*t**2/4 + 363*t/4 + 9. Factor f(l).
3*(l + 11)**2/4
Let c(q) be the first derivative of 15*q**3 + 145*q**2/2 + 30*q + 155. Solve c(l) = 0 for l.
-3, -2/9
Let i(j) be the first derivative of 6*j**2 - 3/4*j**4 + 0*j - 3 + 0*j**3. Factor i(v).
-3*v*(v - 2)*(v + 2)
Let m(z) = z**4 + z**3 - z**2 + z. Let j(g) = -25*g**5 - 27*g**4 + 23*g**3 + 27*g**2 + 8*g. Let l(d) = j(d) - 3*m(d). Let l(v) = 0. Calculate v.
-1, -1/5, 0, 1
Let l(j) be the first derivative of 6/5*j**2 - 26/15*j**3 - 15 + 1/2*j**4 + 0*j. Suppose l(i) = 0. What is i?
0, 3/5, 2
Determine m, given that 0 - 9/5*m**3 + 0*m - 1/5*m**4 + 2*m**2 = 0.
-10, 0, 1
Let r(v) be the second derivative of -29*v + 0 - 1/11*v**3 + 2/11*v**2 - 1/66*v**4 + 3/110*v**5 - 1/165*v**6. What is a in r(a) = 0?
-1, 1, 2
Let q = 34451/1540 + -246/11. Let i(u) be the third derivative of 0*u + 0*u**3 - 1/735*u**7 + 0 - 1/70*u**5 + q*u**6 + 1/84*u**4 + u**2. Factor i(y).
-2*y*(y - 1)**3/7
Let t(x) be the third derivative of x**6/160 - 21*x**5/80 - 45*x**4/32 - 23*x**3/8 + 6*x**2 + 2*x. Factor t(l).
3*(l - 23)*(l + 1)**2/4
Let w(h) be the third derivative of 1/200*h**6 + 0*h - 1/5*h**3 + 13*h**2 + 0*h**5 + 0 - 3/40*h**4. Let w(t) = 0. What is t?
-1, 2
Let r = -2/4797 + 13148/1599. Let f = r + -287/36. Factor -1/4*t**3 + 0*t**2 + f*t + 0.
-t*(t - 1)*(t + 1)/4
Factor 5 + 9*y**2 - 8 + 0 + 21*y**4 + 45*y**3 - 33*y - 15.
3*(y + 1)**3*(7*y - 6)
Let m be 111/24 - (648/54 - (-99)/(-8)). Find w, given that 0*w + 0*w**2 - 3/5*w**m + 0 + 3/5*w**4 + 0*w**3 = 0.
0, 1
Factor 11/10*p**2 + 8/5 - 13/5*p - 1/10*p**3.
-(p - 8)*(p - 2)*(p - 1)/10
Factor 1/4*g**4 - 46656*g + 1944*g**2 + 419904 - 36*g**3.
(g - 36)**4/4
Let p be 536/104 + (-4)/26. Let w(j) = 8*j**3 + 13*j**2 + 41*j + 29. Let x(c) = -c**3 + c**2 - c - 1. Let h(v) = p*x(v) + w(v). Factor h(l).
3*(l + 2)**3
Let o(z) be the second derivative of 1/24*z**4 + 3/2*z**3 + 81/4*z**2 + 45*z + 0. Let o(q) = 0. Calculate q.
-9
Let s(l) be the second derivative of l**6/24 + 37*l**5/16 - 5*l**4/48 - 185*l**3/24 + 2*l - 22. Factor s(h).
5*h*(h - 1)*(h + 1)*(h + 37)/4
Let v = 2 + -7. Let r(d) = -2*d**2 + 4*d + 5. Let o(w) be the first derivative of -w**3/3 + w**2 + 2*w - 1. Let z(g) = v*o(g) + 2*r(g). Factor z(y).
y*(y - 2)
Let w be (10/(-5) - -4) + 3. Find o such that -11 + 432*o**2 - 368*o**4 + 2*o**5 - 86*o**w + 77*o - 53 - 28*o**3 + 35*o = 0.
-4, -1, -2/3, 2/7, 1
Determine j, given that 2108*j**4 - 2113*j**4 + 17*j**3 - 2*j**3 = 0.
0, 3
Solve -52*g - 4/3*g**2 + 160/3 = 0.
-40, 1
Let v(r) be the third derivative of 2*r**2 - 1/6*r**4 + 0*r + 2/3*r**3 - 1/210*r**7 + 0 - 1/20*r**5 + 1/30*r**6. Factor v(u).
-(u - 2)**2*(u - 1)*(u + 1)
Let x(g) be the first derivative of 6*g**5/5 + 19*g**4/4 + 7*g**3 + 9*g**2/2 + g - 144. Suppose x(n) = 0. What is n?
-1, -1/6
Let l(k) = -k**3 + k**2 - k + 3. Let r(y) = -2*y**3 + 3*y**2 - 2*y + 7. Let s = 6 + 19. Let m = s - 32. Let t(a) = m*l(a) + 3*r(a). Factor t(z).
z*(z + 1)**2
Let j = 4579/3046 - 5/1523. Find h such that 6 - j*h**2 + 0*h = 0.
-2, 2
Suppose 0 = 5*p - 4*s - 0*s - 76, 0 = 2*s - 2. Let i be (-2)/p - (-252)/480. Factor -2/15*g**2 - 8/15*g - i.
-2*(g + 1)*(g + 3)/15
Let s(a) be the first derivative of 0*a - 1/1080*a**6 + 5/3*a**3 - 5