- -37. Determine r so that 3*r - l*r + 3*r + r**g = 0.
0
Let s = -32/69 - -72/23. Factor 22/3*q**2 - 4/3 + s*q**3 + 10/3*q.
2*(q + 1)*(q + 2)*(4*q - 1)/3
Let v(f) be the first derivative of 250/3*f + 10 - 25*f**2 - 1/6*f**4 + 10/3*f**3. Factor v(h).
-2*(h - 5)**3/3
Factor -5/7*g**2 + 16/7 - 79/7*g.
-(g + 16)*(5*g - 1)/7
Let g(j) be the first derivative of 7 + 5/2*j**2 + 10*j - 5/2*j**4 - 20/3*j**3 + 5/6*j**6 + 2*j**5. Solve g(p) = 0.
-2, -1, 1
Let s(g) be the first derivative of -3*g**4/32 - 9*g**3/8 - 9*g**2/2 - 6*g - 264. Factor s(t).
-3*(t + 1)*(t + 4)**2/8
Let v(p) be the first derivative of 5*p**3/3 - 40*p**2 - 840. Factor v(f).
5*f*(f - 16)
Let v(f) be the third derivative of -f**6/540 - f**5/54 - f**4/18 - 71*f**2. Let v(m) = 0. What is m?
-3, -2, 0
Factor 10/7*x + 6/7 + 2/7*x**2 - 2/7*x**3.
-2*(x - 3)*(x + 1)**2/7
Let z(k) be the first derivative of -8*k + 4/3*k**3 + 1/15*k**6 + k**2 + 2/5*k**5 + 2 + k**4. Let u(w) be the first derivative of z(w). Factor u(a).
2*(a + 1)**4
Factor -1/6*l**2 + 47/6*l - 23/3.
-(l - 46)*(l - 1)/6
Suppose 311*b - 27 = 302*b. Let d(s) be the third derivative of 1/120*s**6 + 0*s - 2*s**2 - 2/45*s**5 + 0 + 7/72*s**4 - 1/9*s**b. Factor d(z).
(z - 1)**2*(3*z - 2)/3
Suppose -4*t = 4*k - 32, 12 = -2*k + 3*t + 2*t. Determine l, given that 7*l - l - 2*l + k*l**2 = 0.
-1, 0
Let w be 12/28*77/99. Let n(o) be the second derivative of -o**4 - 10/9*o**3 + 4/3*o**2 + w*o**5 + 14/45*o**6 + 0 + 5*o. Let n(b) = 0. What is b?
-1, 2/7, 1
Suppose 11*w - 9 = 24. Let c be w/5 + (-11520)/(-1050). Find g such that c*g - 27/7*g**2 + 3/7*g**3 - 81/7 = 0.
3
Suppose -8*y - 11 = -131. Suppose 3*b - 1 = 4*i, -5*b + 4 + y = 2*i. Let -1/4*s**3 + 3/2*s**i - 3*s + 2 = 0. Calculate s.
2
Let z(c) be the third derivative of -c**8/168 + 47*c**7/840 - 3*c**6/16 + 13*c**5/60 + c**4/12 + 2*c**2 + 27. Factor z(s).
-s*(s - 2)**3*(8*s + 1)/4
Let z(y) be the third derivative of y**7/140 + y**6/20 + y**5/8 + y**4/8 + 3*y**2 - 43*y. Determine b so that z(b) = 0.
-2, -1, 0
Let t(b) = -32*b + 15. Let g be t(-3). Let s = -108 + g. Factor 1/5*z**2 + 1/5*z**4 + 0*z + 0 - 2/5*z**s.
z**2*(z - 1)**2/5
What is c in 0 + 87/2*c**5 - 91/2*c**3 + 86*c**2 + 2*c - 86*c**4 = 0?
-1, -2/87, 0, 1, 2
Let w(z) be the first derivative of 2*z**3/15 - 18*z**2/5 + 19. Factor w(c).
2*c*(c - 18)/5
Let q(r) be the first derivative of r**6/30 - 2*r**5/5 + 2*r**4 - 16*r**3/3 + 8*r**2 - 11*r - 26. Let w(s) be the first derivative of q(s). Factor w(t).
(t - 2)**4
Let r = 283 + -283. Solve 3/4*s**4 - 1/4*s**3 - 3/4*s**2 - 1/4*s**5 + r + 1/2*s = 0.
-1, 0, 1, 2
Let u = 1443 + -15871/11. Determine q, given that 10/11*q + u*q**3 - 8/11*q**2 - 4/11 = 0.
1, 2
Let v(d) be the second derivative of -d**5/30 - 7*d**4/12 + d**2/2 - 35*d. Let r(p) be the first derivative of v(p). What is f in r(f) = 0?
-7, 0
Let s(c) be the second derivative of -c**7/21 + c**5/10 + 3*c - 61. Suppose s(x) = 0. What is x?
-1, 0, 1
Let s = -472 - -474. Factor 32/7 + 16/7*k + 2/7*k**s.
2*(k + 4)**2/7
Suppose 6*z = -5*y + 7, 5 = y + 6. Factor -5/6*m**3 + 0 + 4/3*m**z + 2/3*m.
-m*(m - 2)*(5*m + 2)/6
Let f(q) be the first derivative of -5*q**3/3 + 85*q**2/2 - 80*q - 294. Factor f(h).
-5*(h - 16)*(h - 1)
Let f(p) be the second derivative of -p**6/15 + p**5/5 + 13*p**4/6 + 10*p**3/3 + 17*p + 1. Suppose f(i) = 0. What is i?
-2, -1, 0, 5
Let w(n) = n**3 + 27*n**2 + 25*n - 22. Let m be w(-26). Solve -3 + 1 + 1 + 3*i**3 - 3 - 3*i**5 - 7*i**m + 11*i**2 = 0.
-2, -1, 2/3, 1
Determine d so that -275*d + 40 + 50*d**2 - 45*d**4 - 285*d**3 + 280*d**2 + 235*d**2 = 0.
-8, 1/3, 1
Let w(v) be the third derivative of v**6/60 + 8*v**5/15 + 15*v**4/4 - 54*v**3 - 1006*v**2. Determine z so that w(z) = 0.
-9, 2
Suppose 40 = 2339*o - 2331*o. Let h(z) be the first derivative of -13 + 1/12*z**3 + 1/4*z**2 - 1/20*z**o - 1/8*z**4 + 0*z. Factor h(t).
-t*(t - 1)*(t + 1)*(t + 2)/4
Let u(f) be the third derivative of -f**7/70 + 5*f**6/8 - 6*f**5/5 + 71*f**2 - 3. Factor u(k).
-3*k**2*(k - 24)*(k - 1)
Suppose -3*f - 2 = 3*q + 1, -2*q + 5*f = -26. Suppose 2*s + 3 + 3 = 0, -q*s = -r + 13. Factor 6*o**r + 6 + 8*o**4 - 9*o**3 + 8*o**4 - 3*o**2 - 25*o**4 + 9*o.
-3*(o - 1)*(o + 1)**2*(o + 2)
Let m(p) be the second derivative of p**6/165 + 2*p**5/55 - p**4/66 - 4*p**3/33 + 56*p. Factor m(s).
2*s*(s - 1)*(s + 1)*(s + 4)/11
Suppose 40 = -9*l - 5. Let k(t) = 3*t**2 - 4*t - 3. Let i(u) = -6*u**2 + 9*u + 7. Let g(v) = l*k(v) - 3*i(v). Suppose g(s) = 0. What is s?
-2/3, 3
Let y(u) be the second derivative of u**7/147 - 13*u**6/105 - 29*u**5/70 - 5*u**4/14 - 274*u. Let y(o) = 0. What is o?
-1, 0, 15
Let x(n) be the first derivative of -n**4/24 - n**3/3 + 5*n**2/4 - 17*n + 6. Let g(v) be the first derivative of x(v). What is a in g(a) = 0?
-5, 1
Let k(a) be the second derivative of a**6/30 + 2*a**5/5 + 4*a**4/3 + 10*a + 2. Find z, given that k(z) = 0.
-4, 0
Let m(j) be the second derivative of -11*j + 0 + 1/12*j**3 - 1/24*j**4 - 1/40*j**5 + 1/4*j**2. Factor m(n).
-(n - 1)*(n + 1)**2/2
Let g(x) be the first derivative of x**6/18 - 8*x**5/15 + 3*x**4/2 - 16*x**3/9 + 5*x**2/6 + 17. Factor g(w).
w*(w - 5)*(w - 1)**3/3
Let c(u) be the first derivative of u**6/54 + u**5/9 - u**4/18 - 10*u**3/27 + u**2/18 + 5*u/9 + 144. What is v in c(v) = 0?
-5, -1, 1
Factor -15/2*y**2 - 27/2*y**3 - 3*y**5 + 0 - 3/2*y - 21/2*y**4.
-3*y*(y + 1)**3*(2*y + 1)/2
Let n = -8 + 32. Suppose -4*q + n = -0*q. Let -q*a**3 + 2*a**4 - 6*a + 0*a**4 - 4*a**3 + 15*a**2 - a**2 = 0. What is a?
0, 1, 3
Suppose -5*a + 17*n + 40 = 14*n, 0 = n + 5. Suppose 12/7*t**2 + 16/7 - 4*t**4 - 6/7*t**a - 34/7*t**3 + 40/7*t = 0. Calculate t.
-2, -1, -2/3, 1
Factor -12/5*f + 2/5*f**2 + 2.
2*(f - 5)*(f - 1)/5
Factor -22982*k - 5*k**3 - 31*k**2 + 0*k**3 + 23050*k - 32.
-(k - 1)*(k + 8)*(5*k - 4)
Let c(h) = -3*h**2 - 28*h + 75. Let y be c(-11). Let x = -1 + 4. Factor y*b**2 + 5*b**3 + 3*b + 12 + 4*b**3 - 13*b**x - 31*b.
-4*(b - 3)*(b - 1)**2
Let k(m) = 1. Let s(v) = v**2 - 47*v - 42. Let j(q) = -30*k(q) + 5*s(q). Determine u, given that j(u) = 0.
-1, 48
Solve -4*y**3 - 472*y - 1372 - 209*y - 84*y**2 + 93*y = 0.
-7
Find g such that -13*g + 12 + 21*g**2 + 8*g**2 - 26*g**2 = 0.
4/3, 3
Let b(d) = -21*d**4 - 18*d**3 + 83*d**2 + 39*d + 13. Let k(o) = 5*o**4 + 4*o**3 - 21*o**2 - 9*o - 3. Let a(m) = -6*b(m) - 26*k(m). Factor a(r).
-4*r**2*(r - 4)*(r + 3)
Let o(f) = -6*f**2 - 5 + 5*f**2 + 2*f**2 + 4 - 2*f**3. Let r(b) = 6*b**3 - 4*b**2 + 2. Let a(w) = 2*o(w) + r(w). Suppose a(n) = 0. What is n?
0, 1
Suppose 9*q = -60*q. Factor 0*m + q - 3/4*m**4 + 9/2*m**3 - 27/4*m**2.
-3*m**2*(m - 3)**2/4
Factor 63/5*a**2 - 3/5 - 12*a.
3*(a - 1)*(21*a + 1)/5
Let q = 18334467/22576240 - -9/110128. Let d = -1/82 + q. Determine u, given that 2/5*u**2 + 0 - d*u = 0.
0, 2
Let a(s) be the second derivative of 0*s**5 + 0 - s - 1/120*s**6 + 0*s**2 + 1/3*s**3 + 0*s**4. Let i(q) be the second derivative of a(q). Solve i(k) = 0 for k.
0
Let g(i) be the second derivative of -i**6/126 - i**5/30 - i**4/21 - 17*i**3/6 - 6*i. Let w(c) be the second derivative of g(c). Factor w(t).
-4*(t + 1)*(5*t + 2)/7
Let b(l) = -l**2 - 243*l + 1242. Let t be b(5). Factor -11*a**3 - 14*a**t - 4*a**4 - 17/2*a - 2 - 1/2*a**5.
-(a + 1)**4*(a + 4)/2
Factor 0*z**2 + 3/4*z**5 + 3/2*z**3 + 0 - 9/4*z**4 + 0*z.
3*z**3*(z - 2)*(z - 1)/4
Find p, given that 51*p**2 + 3 + 6*p - 34*p - 10*p**4 + 5*p**4 - 7 - 2*p**3 - 12*p**4 = 0.
-2, -2/17, 1
Let k be 2024/30 + 427/12810. Let -45/4*s**2 + k - 35/4*s**3 + 135/4*s - 5/4*s**4 = 0. Calculate s.
-3, 2
Let s = -6/437 + 455/1311. Factor 2/3*x**2 - s*x**3 + 1/3*x - 2/3.
-(x - 2)*(x - 1)*(x + 1)/3
Let d = -17 - -88. Factor 41*z - 249 + 20*z + 19*z - 5*z**2 - d.
-5*(z - 8)**2
Solve -200/9*d**3 + 8/9 + 52/3*d**2 - 58/9*d - 10/3*d**5 + 124/9*d**4 = 0 for d.
1/3, 4/5, 1
Suppose -2*n + 4*g + 23 = -3*n, -35 = 3*n - 5*g. Let u = 18 + n. Determine c so that -2/3*c**u + 50/3*c**5 - 30*c**4 + 8/3 - 16*c + 82/3*c**2 = 0.
-1, 2/5, 1
Factor 2/15*t**3 - 44/5*t**2 - 21296/15 + 968/5*t.
2*(t - 22)**3/15
Let k(s) be the first derivative of -3*s**5/10 - 3*s**4 - 21*s**3/2 - 27*s**2/2 + 222. Solve k(t) = 0 for t.
-3, -2, 0
Suppose -560 = -f - 563, 2*i - 5*f = 23. Factor -45/2*b**3 + 12*b**2 + 0 - 2*b + 25/2*b**i.
b*(b - 1)*(5*b - 2)**2/2
Let k(x) be the first derivative