 q**2 - 1. Let c(f) = -2*m(f) + o(f). Let u(x) be the first derivative of c(x). Factor u(v).
-3*(v - 6)**2
Let o be ((-117)/6)/13 - (-1 + -2) - 1. Factor 1/3 + o*s + 1/6*s**2.
(s + 1)*(s + 2)/6
Let v(z) be the second derivative of 0 - 2/9*z**2 + 0*z**3 + 19*z + 0*z**5 - 2/135*z**6 + 2/27*z**4. Factor v(j).
-4*(j - 1)**2*(j + 1)**2/9
Let y be (-38 + 4026/99)*(-1)/(-92)*3. Factor 6/23*o**2 + 0*o + y*o**3 + 0.
2*o**2*(o + 3)/23
Let t be 6/(((-30)/140)/((-6)/231)). Let d = -2/563 - -1148/6193. Find a such that -d*a + t*a**5 + 18/11*a**3 - 2/11*a**2 - 2*a**4 + 0 = 0.
-1/4, 0, 1
Let m(w) = 3*w**3 + 10*w**2 + 13*w + 4. Let b(r) = -7*r**3 - 22*r**2 - 27*r - 7. Let z(c) = -6*b(c) - 15*m(c). Find k, given that z(k) = 0.
-3, -2, -1
Factor -116/3*q**2 - 356/9*q - 40/3 + 4/9*q**4 - 12*q**3.
4*(q - 30)*(q + 1)**3/9
Let t(a) be the third derivative of 1/180*a**5 + 0 + 0*a**3 + 0*a + 1/360*a**6 + 1/216*a**4 + 1/1890*a**7 + 5*a**2. Factor t(g).
g*(g + 1)**3/9
Let s = 5682 - 5680. Find p such that 24/7 + 52/7*p - 20/7*p**s = 0.
-2/5, 3
Let o = -2829 + 2833. Let t(f) be the second derivative of -1/3*f**o + 6*f + 0 + 8/3*f**3 - 8*f**2. Factor t(c).
-4*(c - 2)**2
Factor 760/3*c - 800 + 2/9*c**3 - 128/9*c**2.
2*(c - 30)**2*(c - 4)/9
Suppose 0 = -5*d - 10 + 50. Factor -d*k + 135*k**2 + 45*k**3 + 20*k + 123*k + 5*k**4.
5*k*(k + 3)**3
Factor 0 - 1/4*c**3 - 3/4*c**2 + 0*c.
-c**2*(c + 3)/4
Let c(d) be the first derivative of -2*d**3/3 - d**2 + 24*d - 4. Determine a, given that c(a) = 0.
-4, 3
Let a(u) be the first derivative of u**6/12 + 29*u**5/10 + 28*u**4 + 98*u**3/3 + 284. Factor a(p).
p**2*(p + 1)*(p + 14)**2/2
Let g = 2/4983 - -19906/64779. Let 14/13*a - 6/13*a**3 + 4/13*a**2 + g = 0. Calculate a.
-1, -1/3, 2
Let y(q) be the second derivative of -2 + q - 2*q**2 + 22/9*q**3 + 4/9*q**4. Let y(z) = 0. What is z?
-3, 1/4
Solve -33*s**2 + 110 + 75*s - 18*s**2 - 190*s + 56*s**2 = 0.
1, 22
Let p be 5 - (14/2 + 192/(-72)). Let 2/3*k - p*k**2 + 0 = 0. Calculate k.
0, 1
Let t = -822 - -4113/5. Let l(m) = m**2 + 6*m - 7. Let j be l(-7). Suppose -t*i**4 + 0*i**3 + 1/5*i**5 + j + 4/5*i**2 + 0*i = 0. What is i?
-1, 0, 2
Let o = -314/565 - -108/113. Find c, given that o*c**4 + 39/5*c**2 + 8/5*c + 17/5*c**3 - 16/5 = 0.
-4, -1, 1/2
Suppose -3*k + 21 = 3*m, -6 - 4 = -m - 4*k. Let x(z) be the third derivative of 0 + 1/40*z**m + 0*z + 2*z**3 + 0*z**4 - 3/20*z**5 - 7*z**2. Factor x(t).
3*(t - 2)**2*(t + 1)
Let f(a) be the first derivative of -a**5 + 20*a**4 + 60*a**3 + 691. Factor f(w).
-5*w**2*(w - 18)*(w + 2)
Let u(s) = -s**2 + 5*s - 6. Let a(r) = 6*r**2 - 26*r + 31. Let n = -40 + 38. Let l(y) = n*a(y) - 11*u(y). Solve l(z) = 0.
-4, 1
Let -96/7*g**2 + 4*g**3 + 14 - 4*g - 2/7*g**4 = 0. Calculate g.
-1, 1, 7
Let r(b) = -9*b**2 - 34*b - 65. Let g(q) = -3*q**2 - 11*q - 22. Let h(o) = -11*g(o) + 4*r(o). Determine t, given that h(t) = 0.
-3, -2
Suppose -110/9 + 14/9*y**2 - 98/9*y + 2/9*y**3 = 0. Calculate y.
-11, -1, 5
Let q(m) = m**2 + 28*m - 204. Let x be q(-34). Let c(a) be the first derivative of 2/9*a**3 + 7 + x*a - 2/3*a**2. Factor c(v).
2*v*(v - 2)/3
Let h = 3031 - 3031. Factor h + 0*j - 3/2*j**2 - 3/4*j**4 - 9/4*j**3.
-3*j**2*(j + 1)*(j + 2)/4
Let n = 292 - 285. Suppose 5*t - y - 165 = -0*y, -y + 132 = 4*t. Suppose -t*s + 11 - 28*s**2 - 11*s**3 + 6*s**3 + n = 0. Calculate s.
-3, 2/5
Suppose 3*m - 104*s - 5 = -103*s, 4*m = -3*s + 24. Factor 3/5*l**5 + 3/5*l**4 + 3/5*l - 6/5*l**2 + 3/5 - 6/5*l**m.
3*(l - 1)**2*(l + 1)**3/5
Suppose -39*d = -60*d + 42. Determine f so that -6/7*f**d + 6/7 - 3/7*f + 3/7*f**3 = 0.
-1, 1, 2
Let f(a) be the second derivative of 9*a**5/140 - 85*a**4/14 - 118*a**3/7 + 348*a**2/7 - 594*a. Factor f(v).
3*(v - 58)*(v + 2)*(3*v - 2)/7
Let k be (-100)/6*9/6. Let n = -23 - k. Suppose 0*q + 0 - 3/4*q**n = 0. What is q?
0
Let j = -8 + 12. Suppose 0 = -4*t + 2*c + 234, -272 = -5*t - j*c + 40. Find q such that 14*q**4 + 9*q + 44*q + 86*q**2 - 5*q + t*q**3 + 8 = 0.
-2, -1, -2/7
Let s(r) be the first derivative of -16 - 45/2*r**4 + 8/5*r - 64/5*r**2 + 38*r**3. Suppose s(z) = 0. Calculate z.
2/15, 1
Let o(w) be the second derivative of -w**6/6 - 13*w**5/4 - 205*w**4/12 - 235*w**3/6 - 45*w**2 + 271*w. Factor o(p).
-5*(p + 1)**2*(p + 2)*(p + 9)
Let y be (-180)/(-40) - (-3 - -15)/3. Let o(c) be the second derivative of 0 + 1/12*c**4 + 0*c**3 - 8*c - y*c**2. Determine g so that o(g) = 0.
-1, 1
Let d = 228 + -1113/5. Suppose 30*n + 6 = 32*n. Solve -6/5*f + 0 + 27/5*f**2 - 3*f**n + 21/5*f**5 - d*f**4 = 0.
-1, 0, 2/7, 1
Let j(d) be the first derivative of -d**7/42 + d**6/15 + d**5/20 - d**4/6 - 8*d - 4. Let q(t) be the first derivative of j(t). Factor q(h).
-h**2*(h - 2)*(h - 1)*(h + 1)
Let o be 21*(15/(-9))/5. Let n(f) = 16*f**3 + 18*f**2 + 2*f - 7. Let r(v) = -5*v**3 - 6*v**2 - v + 2. Let i(u) = o*r(u) - 2*n(u). Factor i(l).
3*l*(l + 1)**2
Let t(o) = -o**3 + 11*o**2 + 25*o + 8. Suppose -9 + 51 = -3*b. Let z = b - -9. Let d(j) = j**3 + j**2 - j. Let h(f) = z*d(f) - t(f). Factor h(y).
-4*(y + 1)**2*(y + 2)
Let k(h) be the second derivative of 1/147*h**7 + 0*h**2 - 1/14*h**4 - 1/14*h**5 - 1/105*h**6 + 9*h + 0 + 0*h**3. Determine b so that k(b) = 0.
-1, 0, 3
Let r(p) be the second derivative of p**7/21 + p**6/5 - 2*p**4/3 - 54*p. Solve r(b) = 0.
-2, 0, 1
Let -1/10*k**3 + 0 + 12/5*k - k**2 = 0. What is k?
-12, 0, 2
Let x(m) = 4*m**5 - m**4 - 5*m**3 + 2*m**2 + 4*m - 1. Let y(l) = -l - 4*l + 2*l**5 + l**3 + 4*l - 3*l**5. Let c(s) = x(s) + 3*y(s). Factor c(r).
(r - 1)**3*(r + 1)**2
Suppose -41*z + 39*z = -4. Suppose 4*v - 3*v = -z*b, 5*v - b = 0. Suppose -4/3*o**4 + 4/3*o**2 - 2/3*o + 2/3*o**5 + 0*o**3 + v = 0. Calculate o.
-1, 0, 1
Let b = -9 + 19. Suppose -4*o - o + b = 0. Let 6*g + 5 - 4 - 5 + g**o - 3*g**2 = 0. What is g?
1, 2
Let z(c) be the third derivative of 24*c**2 - 1/720*c**6 + 1/90*c**5 + 0*c - 1/1260*c**7 + 0*c**3 + 1/36*c**4 + 0. Solve z(m) = 0 for m.
-2, -1, 0, 2
Let i(r) be the first derivative of 9*r**4 - 208*r**3/3 + 66*r**2 + 40*r - 107. Find l such that i(l) = 0.
-2/9, 1, 5
Suppose -5*f + 15 = 0, f + 2*f = 4*q - 15. Let b(x) = -x**3 + 5*x**2 + 6*x. Let p be b(q). Suppose 4/7*u**2 + p*u + 0*u**3 - 2/7 - 2/7*u**4 = 0. Calculate u.
-1, 1
Let x(t) be the first derivative of 5*t**8/1344 + t**7/120 + t**6/240 - 13*t**2/2 - 15. Let b(u) be the second derivative of x(u). Let b(o) = 0. What is o?
-1, -2/5, 0
Let t be -5 + (-26)/(-4) + (-14)/(-4). Let a(q) = -q**2 + 3*q + 12. Let c be a(t). Solve -3/5*i + 3/5*i**3 + 3/5*i**c - 3/5 = 0 for i.
-1, 1
Let u be 37/154 - (-47)/1034. Factor -u*q**2 + 0*q + 2/7.
-2*(q - 1)*(q + 1)/7
Let j = -6 - -11. Suppose z = 4*o + o + 17, 4*z = -j*o - 7. Let 0*d + 6 + 5*d + 3*d - 4*d - 2*d**z = 0. Calculate d.
-1, 3
Let i(p) be the second derivative of -p**6/24 - 19*p**5/16 - 25*p**4/3 + 125*p**3/6 - p + 32. Factor i(r).
-5*r*(r - 1)*(r + 10)**2/4
Find g such that 1/3*g**5 - 8/3*g**2 + 2/3*g**4 + 0 - 4/3*g**3 + 0*g = 0.
-2, 0, 2
Let d(h) = -3*h - 7. Let u be d(-4). Suppose u*i - 4*i = 2. Factor 4*k**4 + 2*k**3 + 6*k**5 - 10*k**5 - i*k**3.
-4*k**4*(k - 1)
Factor 85*y**2 + 32*y**4 + 198*y**3 - 58*y**3 + 50*y**2 + 29*y**4 - 56*y**4.
5*y**2*(y + 1)*(y + 27)
Let o(b) be the first derivative of -25/3*b**3 + 20*b - 25/2*b**6 - 30*b**2 + b**5 + 135/4*b**4 + 9. Determine g so that o(g) = 0.
-1, 2/5, 2/3, 1
Let u be (-24)/16*64/(-12). Solve 7*i**2 - 2*i**2 - 3 - i**2 + u*i - 9 = 0.
-3, 1
Determine n so that -11/4*n + 1/4*n**2 + 5/2 = 0.
1, 10
Factor 0 - 2/5*d - 2/5*d**3 - 4/5*d**2.
-2*d*(d + 1)**2/5
Let x(v) be the second derivative of v**7/1680 - v**6/360 - 4*v**3/3 + 8*v. Let b(s) be the second derivative of x(s). Factor b(k).
k**2*(k - 2)/2
Let x(h) be the second derivative of h**8/30240 + h**7/11340 + 4*h**4/3 + 4*h. Let m(k) be the third derivative of x(k). Let m(c) = 0. What is c?
-1, 0
Let j(w) be the third derivative of -w**5/450 - w**4/20 + 2*w**3/9 + 7*w**2 + 1. Factor j(n).
-2*(n - 1)*(n + 10)/15
Find q, given that 37*q + 18 - 15*q**3 + 14*q + 5*q**2 - 11*q + 2 = 0.
-1, -2/3, 2
Let d(a) be the second derivative of -a**4/2 - 241*a**3/3 + 162*a**2 + 264*a. Factor d(l).
-2*(l + 81)*(3*l - 2)
Let k be (38/57)/(2/(-15)). Let z(p) = p**3 + 5*p**2 + 2*p + 10. Let o be z(k). Solve 1/7*h**2 + 0 + o*h = 0 for h.
0
Suppose 26 = 3*x - 4*c - 0*c, 2*x 