*f**2 + 1/78*f**4 + 1/13*f**3 - 3*f. Factor m(p).
2*(p + 1)*(p + 2)/13
Let u(y) be the first derivative of -4*y**3/27 - 77*y**2/3 + 232*y/9 - 845. Solve u(x) = 0.
-116, 1/2
Suppose -3*o = 3, y - 2*o - 7 = -3*o. Factor -4*l**5 + 23 - y*l**4 + 8*l**2 - 23 + 4*l.
-4*l*(l - 1)*(l + 1)**3
What is v in 1/7*v**4 - 15/7*v**2 + 32/7*v - 16/7 - 2/7*v**3 = 0?
-4, 1, 4
Let h = -470 - -472. Let z(g) be the second derivative of 0 - 2*g**h + 5*g - 1/12*g**4 + 2/3*g**3. Let z(b) = 0. What is b?
2
Let m(c) be the first derivative of c**3/5 - 45*c**2 + 3375*c + 223. Let m(t) = 0. Calculate t.
75
Let n(a) be the third derivative of a**5/135 + 41*a**4/108 - 7*a**3/9 + 2*a**2 + 30. Find t, given that n(t) = 0.
-21, 1/2
Factor 162 - 27*k**2 - 21*k**3 - 3*k**4 + 37*k + 42*k + 0*k + 2*k.
-3*(k - 2)*(k + 3)**3
Suppose 7*p + 18 = -66. Let t(y) = 2*y**4 - 12*y**3 - 18*y**2 - 4*y - 12. Let m(w) = w**3 + w**2 + 1. Let k(i) = p*m(i) - t(i). Suppose k(g) = 0. Calculate g.
-1, 0, 2
Let k = 2023 - 2023. Let -6/5*t**3 + 0 + k*t + 6/5*t**2 = 0. What is t?
0, 1
Let c(b) be the first derivative of -16 - 1/2*b**3 - 15/4*b**2 + 9*b. Factor c(u).
-3*(u - 1)*(u + 6)/2
Let q be (-1518)/(-8) + (-2)/(-8). Let -40 + 44*n**3 - 300*n + 440*n**4 - 149*n**3 + q*n**4 + 405*n**5 - 590*n**2 = 0. What is n?
-1, -2/3, -2/9, 1
Find f, given that -2/11*f**2 - 24/11*f + 0 = 0.
-12, 0
Let m(r) = 2*r**3 - 50*r**2 - 232*r + 4. Let s be m(29). Solve 6 + s*u + 2/3*u**2 = 0.
-3
Let d = 246481/42 - 11737/2. Solve -4/21*p**3 + 8/21*p**2 + 4/21*p - d*p**4 - 2/7 = 0.
-3, -1, 1
Factor 22*i**2 + 200*i - 40*i**2 + 10*i**2 + 2000 + 13*i**2.
5*(i + 20)**2
Suppose -8 = -2*l - 0. Let n = 312 - 310. Find x such that 2*x**3 + 0 + 0*x - 4/3*x**n - 2/3*x**l = 0.
0, 1, 2
Suppose -16*k + 45*k + 19*k = 96. Factor -5/2*o**4 - 10*o - 5/2 - 15*o**k - 10*o**3.
-5*(o + 1)**4/2
Factor -491*z**3 - 1064*z + 4*z**4 + 959*z**3 - 980 - 48*z**2 - 428*z**3.
4*(z - 5)*(z + 1)*(z + 7)**2
Let o(x) be the first derivative of x**3/7 - 6*x**2/7 + 141. Factor o(u).
3*u*(u - 4)/7
Let m(a) be the first derivative of 5*a**4/4 + 20*a**3/3 + 218. Factor m(n).
5*n**2*(n + 4)
Let p(m) be the third derivative of -m**6/120 + 29*m**5/60 - 65*m**4/8 - 75*m**3/2 + 29*m**2 + 3*m. Find r such that p(r) = 0.
-1, 15
Let q = 756 - 754. Determine i, given that 0*i**q + 0 + 2/5*i**5 + 0*i**4 + 2/5*i - 4/5*i**3 = 0.
-1, 0, 1
Let n(t) = -t**2 + 7*t + 2. Let s be n(4). Let o = 18 - s. What is v in -3*v**5 - 5*v**3 + 5*v**5 + 9*v + v**4 - v - v**5 - v**2 - o = 0?
-2, 1
Let o = -59 + 59. Let j(y) be the first derivative of -7 + 1/4*y**4 + 0*y - 1/2*y**2 + o*y**3. Determine b, given that j(b) = 0.
-1, 0, 1
Let d = -1/392 + 397/1960. Factor 0 - 3/5*w - d*w**2.
-w*(w + 3)/5
Let u(d) be the second derivative of d**6/15 - 7*d**5/20 + d**4/12 + 7*d**3/6 - 3*d**2/2 - d + 13. Solve u(x) = 0.
-1, 1/2, 1, 3
Let v(l) be the first derivative of l**7/168 - l**6/72 - l**5/6 + 5*l**4/6 - 23*l**3/3 + 28. Let y(m) be the third derivative of v(m). Factor y(i).
5*(i - 2)*(i - 1)*(i + 2)
Let -9/5*t - 19/5*t**2 + 2 = 0. What is t?
-1, 10/19
Determine l, given that 36*l + 16*l**2 + 0*l**2 - 96 - 20*l**2 + 16 = 0.
4, 5
Let q(k) = 14*k**3 + 79*k**2 + 14*k + 18. Let c(w) = 29*w**3 + 159*w**2 + 29*w + 33. Let f(r) = 6*c(r) - 11*q(r). Factor f(b).
5*b*(b + 4)*(4*b + 1)
Let f(r) be the first derivative of -r**3/7 + 9*r**2/7 + 48*r/7 + 13. Suppose f(p) = 0. Calculate p.
-2, 8
Let w(h) be the first derivative of 2*h**4/9 - h**3/3 - h**2/3 + 20*h + 17. Let c(q) be the first derivative of w(q). Factor c(u).
2*(u - 1)*(4*u + 1)/3
Let q be 0 - -9*1/(-3). Let v be q*(2/(-18) - 22/99). Factor 1/4*r**2 - v + 0*r.
(r - 2)*(r + 2)/4
Factor 3/2*p**2 + 9/2*p + 0.
3*p*(p + 3)/2
Let u(d) be the first derivative of -4*d**3/3 + 58*d**2 - 216*d + 258. Solve u(a) = 0 for a.
2, 27
Let n = 2864/5291 + 2/481. Let x be 49/(-33) - 1180/(-708). Find h such that -x*h**2 + n*h**3 + 0 - 6/11*h**4 + 0*h + 2/11*h**5 = 0.
0, 1
Let s be 20 - 36/27*(-6)/(-4). Factor -s*p**3 - 5*p**2 + 4*p**2 + 19*p**3 - 5*p**5 + p**4 + 4*p**5.
-p**2*(p - 1)**2*(p + 1)
Suppose 2*t = l - 6, l = 5*t - 0*t + 12. Let w(n) be the first derivative of 1/10*n**5 - 1/6*n**3 + 7 + 1/4*n**l - 1/8*n**4 + 0*n. Find q such that w(q) = 0.
-1, 0, 1
Let f be (-1 + 3)/(((-10)/(-2))/20). Factor f*d + 0 - 2 + 6 - 2 - 8*d**3 - 2*d**2.
-2*(d - 1)*(d + 1)*(4*d + 1)
Let a(u) be the third derivative of -1/9*u**3 + 2/945*u**7 + 0 - 2*u**2 + 0*u - 1/60*u**6 + 1/108*u**4 + 1/30*u**5. What is g in a(g) = 0?
-1/2, 1, 3
Determine m so that 6*m - 9594*m**2 + 9592*m**2 - 30*m + m**3 = 0.
-4, 0, 6
Let c be 216/(-144) + 6/4. Let l(q) be the third derivative of c - 9/20*q**5 + 1/8*q**6 - 1/70*q**7 - 5*q**2 + 0*q - q**3 + 7/8*q**4. Find h such that l(h) = 0.
1, 2
What is v in -48/7*v**2 - 51/7*v - 12/7 - 9/7*v**3 = 0?
-4, -1, -1/3
Let n be ((-25)/(-15))/((-700)/(-504)). Factor -n*y + 1/5*y**2 + 9/5.
(y - 3)**2/5
Let o(l) be the first derivative of -l**4/10 - 48*l**3/5 - 1728*l**2/5 - 27648*l/5 + 187. Factor o(f).
-2*(f + 24)**3/5
Let x(d) be the third derivative of d**6/360 - d**4/6 + 17*d**3/6 + 17*d**2. Let y(s) be the first derivative of x(s). Solve y(u) = 0.
-2, 2
Let m(l) be the first derivative of -l**4/4 - 7*l**3 + 3*l**2/2 + 66*l + 49. Let b be m(-21). Factor 4/7*n + 0 + 2/7*n**b - 6/7*n**2.
2*n*(n - 2)*(n - 1)/7
Let o = 75 - -19. Let k = -91 + o. Factor -2/11*a - 2/11 + 2/11*a**2 + 2/11*a**k.
2*(a - 1)*(a + 1)**2/11
Let v(k) = -3*k**4 + 75*k**3 - 60*k**2 + 6*k - 12. Let f(d) = -d**4 + 2*d**3 + d**2 + d - 2. Let b(c) = -6*f(c) + v(c). Suppose b(l) = 0. What is l?
-22, 0, 1
Let n = -111 - -216. Let w be 3/(-9) + 575/n. Suppose w*o**2 - 30/7*o**3 + 9/7*o**5 - 3/7*o - 6/7*o**4 - 6/7 = 0. What is o?
-2, -1/3, 1
Suppose 4*c = -c + 3*g - 17, 3*c = -g - 13. Let a be ((-1)/(-2))/((-3)/c). Factor -8/9*v**2 + 0 - 8/9*v + a*v**3.
2*v*(v - 2)*(3*v + 2)/9
Let v(l) = -l**3 + 3*l**2 + 4*l. Let d(c) = -2*c**3 + 5*c**2 + 8*c. Let s(b) = -6*d(b) + 11*v(b). Suppose s(n) = 0. What is n?
-4, 0, 1
Let d(a) = a**2 + 2*a**2 - 2*a**2 - 2. Let b(y) = -11. Let l(j) = -5. Let z(f) = -6*b(f) + 13*l(f). Let s(h) = d(h) + 2*z(h). Let s(v) = 0. What is v?
0
Let j(v) be the second derivative of -1/75*v**6 + 0*v**4 + 0*v**3 + 0*v**2 + 13*v + 0 - 1/50*v**5. Factor j(z).
-2*z**3*(z + 1)/5
Let z be (-9)/(117/13) + 116/20. Let n = 2773 - 13817/5. Determine s so that -n - 3/5*s**2 + z*s = 0.
4
Let c = -19 - -24. Suppose c*t = 20, 0*t + 4*t - 14 = i. What is z in -15 - 4*z - z**i + 15 - z**2 = 0?
-2, 0
Let u(o) be the third derivative of -o**5/180 + 13*o**4/36 + 3*o**3/2 - 58*o**2. Factor u(c).
-(c - 27)*(c + 1)/3
Let i = 290 - 287. Let s(m) be the first derivative of 4*m - m**2 - 2/3*m**3 + i. Determine b, given that s(b) = 0.
-2, 1
Let p(j) be the third derivative of -5*j**8/336 - 5*j**7/42 - 5*j**6/12 - 5*j**5/6 - 25*j**4/24 - 5*j**3/6 - 68*j**2 + 3*j. What is k in p(k) = 0?
-1
Let v(b) be the second derivative of -b**6/480 - b**5/20 - b**4/2 - 11*b**3/6 + 15*b. Let w(i) be the second derivative of v(i). Solve w(z) = 0.
-4
Let s = -10169/30 - -339. Let i(z) be the third derivative of 0 - 1/105*z**7 - s*z**5 + 1/30*z**6 + 0*z**3 + z**2 + 0*z + 0*z**4. Find q such that i(q) = 0.
0, 1
Suppose -60 + 61 - 61 = -30*d. Factor 15/2*j**3 + 3 + 3/2*j**4 + 21/2*j + 27/2*j**d.
3*(j + 1)**3*(j + 2)/2
Suppose 4 = n + 2. Let x be -2 + (12/(-2))/(-1). Let -15*t + 2*t + n*t**2 - x + 11*t = 0. What is t?
-1, 2
Let r = 5 - -1. Let t be 6 + -6 + r/2. Factor c**2 - 1 + 2*c + 0*c - 3*c**3 - t*c + 4*c**3.
(c - 1)*(c + 1)**2
What is u in -u**2 + 2*u**2 - 7*u**2 + 200*u - 404 + 2*u**2 + 208*u = 0?
1, 101
Let g(c) be the first derivative of -3/8*c**4 + 29 + 0*c - c**3 + 0*c**2. Determine m, given that g(m) = 0.
-2, 0
Let z(q) be the first derivative of q**9/1512 - q**8/420 + q**6/90 - q**5/60 + 10*q**3/3 - 12. Let n(g) be the third derivative of z(g). Solve n(m) = 0.
-1, 0, 1
Let m be ((-216)/144)/((-2)/(8/(-2))). Let p be (-3)/(-30)*5*m/(-12). Factor -1/4*w + p + 1/8*w**2.
(w - 1)**2/8
Let n(b) be the second derivative of -2*b**6/45 + b**4/3 + 4*b**3/9 + 5*b. Find k, given that n(k) = 0.
-1, 0, 2
Let i(g) be the second derivative of -g**4/20 + 2*g**3/5 + 289*g. Factor i(q).
-3*q*(q - 4)/5
Let m(v) be the first derivative of v**