 What is m?
-2, -1, 3
Let p(q) = 2*q**4 - 2*q**3 + 2*q - 2. Let s(n) = -10*n**4 + 9*n**3 - n**2 - 9*n + 11. Let z(d) = 11*p(d) + 2*s(d). What is l in z(l) = 0?
-1, 0, 1, 2
Let q(i) be the third derivative of -1/12*i**5 - 1/24*i**4 + 0*i**3 + 3*i**2 + 0*i + 0 - 23/480*i**6 - 1/120*i**7. Determine w so that q(w) = 0.
-2, -1, -2/7, 0
Suppose 4*n + 17 = 3*b, -b + 16 = 3*b - 4*n. Let j be -2 + (-4)/b + 3. Suppose -q**4 - q**3 + q**2 - j + 5 + q**5 = 0. What is q?
-1, 0, 1
Let q = 760/427 + -4/61. Factor 0 + 12/7*k**2 - q*k**3 - 4/7*k + 4/7*k**4.
4*k*(k - 1)**3/7
Let d(l) be the first derivative of -l**7/420 - l**6/36 - 2*l**5/15 - l**4/3 - 5*l**3/3 + 1. Let n(s) be the third derivative of d(s). Factor n(q).
-2*(q + 1)*(q + 2)**2
Let i(f) = -15*f + 45. Let h be i(3). Find u such that 3/2*u**2 - 3/2*u + 9/2*u**3 + h - 3*u**5 - 3/2*u**4 = 0.
-1, 0, 1/2, 1
Let t(u) be the third derivative of u**8/84 - 8*u**7/105 + u**6/5 - 4*u**5/15 + u**4/6 + 12*u**2. Factor t(j).
4*j*(j - 1)**4
Let a = -8 + 8. Let a*j**2 + 9 - j + 0*j**2 - 5*j + j**2 = 0. Calculate j.
3
Suppose 3*v - 25 + 1 = 5*b, 3*b + 18 = 3*v. Factor -4*q**3 + 4*q**4 - q**2 - 5*q**v + 12*q**3.
q**2*(q + 1)*(4*q - 1)
Let i(h) = 16*h**2 + 52*h + 36. Let x(m) = -m - 1. Let a(p) = i(p) + 24*x(p). Factor a(c).
4*(c + 1)*(4*c + 3)
Let j be -1 - 1/(-2) - (-20)/20. Factor j*g + 0 - 1/2*g**2.
-g*(g - 1)/2
Solve -8 - 3*g - 2*g - 4*g + 2 - 3*g**2 = 0 for g.
-2, -1
Let 0*i**4 - 2/11*i**5 + 0*i**2 + 0 + 0*i + 2/11*i**3 = 0. What is i?
-1, 0, 1
Let g(i) be the third derivative of 2/27*i**3 + 8*i**2 + 0 - 1/270*i**5 + 0*i - 1/108*i**4. Factor g(t).
-2*(t - 1)*(t + 2)/9
Let c(g) = g**3 + g**2 + g + 5. Let s be c(0). Let p(r) = -r**2 + r + 2. Let w(x) = 2*x**2 - x - 3. Let j(d) = s*p(d) + 3*w(d). Factor j(k).
(k + 1)**2
Let o be -4*(0 + (-3)/6). Suppose -4*y + 2 = 2*u, 0 = -5*y - 5*u - 2 - 3. Factor a**y - 4*a**2 + a**3 + 0*a**3 + o*a.
a*(a - 2)*(a - 1)
Let o(l) = 5*l**5 - 4*l**4 - 2*l**3 + l. Let q(m) = -4*m**5 + 4*m**4 + 3*m**3 - m**2 - 2*m. Let d(s) = 3*o(s) + 4*q(s). Factor d(b).
-b*(b - 5)*(b - 1)*(b + 1)**2
Solve -2*a**3 + 4*a**2 - 6*a**3 + 6*a**3 = 0 for a.
0, 2
Suppose 0 = -g + v + 5, 5 = -5*g - 6*v + v. Let -x**3 + x**3 + x**3 - 2*x**g - x + 2*x = 0. Calculate x.
0, 1
Let f be 1 + 2 - (2 + 0). Suppose f = 3*z + 5*r - 1, 0 = -5*r - 10. Factor z - 8*g + 7*g**2 - 2 + g**2.
2*(2*g - 1)**2
Find n, given that -20*n - 14*n**4 + 12*n**2 - 13*n**4 + 4*n**3 + 8 + 23*n**4 = 0.
-2, 1
Find u, given that 8/7*u**3 - 4*u**2 + 0 + 4/7*u**4 + 16/7*u = 0.
-4, 0, 1
Let d be (-10)/(-4)*(-2 - (-564)/270). Factor d*v**2 + 8/9 - 10/9*v.
2*(v - 4)*(v - 1)/9
Let t(h) be the second derivative of -h**7/147 - 4*h**6/105 - 3*h**5/35 - 2*h**4/21 - h**3/21 + 16*h. Determine v, given that t(v) = 0.
-1, 0
Factor -6/5*x**3 - 1/5*x + 4/5*x**2 + 0 + 4/5*x**4 - 1/5*x**5.
-x*(x - 1)**4/5
Let h(l) = 6*l**2 + 17*l - 23. Let b(z) = -3*z**2 - 8*z + 11. Let g(o) = -5*b(o) - 2*h(o). Factor g(u).
3*(u - 1)*(u + 3)
Let u be 0 + 52/16 - 3. Determine g, given that -1/4*g**3 + u*g - 1/4*g**2 + 1/4 = 0.
-1, 1
Let l = 62 + -32. Let m be ((-8)/l)/((-2)/3). Factor 0 + 4/5*z**2 + 2/5*z + m*z**3.
2*z*(z + 1)**2/5
Let b(o) = o**3 + 6*o**2 + 5*o - 6. Let n be b(-5). Let m be (-1)/2 + (-15)/n. Factor 5*j + j - m*j - 2 - 2*j**2.
-2*(j - 1)**2
Suppose -5*h = 3 - 18. Factor 38*x**4 + 9*x**5 + 5*x**5 + 15*x**3 - 4*x + 13*x**h + 2*x**2 + 2*x**3.
2*x*(x + 1)**3*(7*x - 2)
Let x(c) be the third derivative of -c**6/180 + c**5/30 - c**4/12 + c**3/9 + 22*c**2. Solve x(w) = 0.
1
Suppose -2*n = -6 - 4. Suppose -n*w - g = -3, w - 2*g + 9 = 3. Find o such that -1/3*o + 1/3*o**3 + 1/3*o**4 - 1/3*o**2 + w = 0.
-1, 0, 1
Find q such that -8/7*q**2 + 8/7*q - 2/7 = 0.
1/2
Suppose 3*n - 4*s - 14 = 0, 12 = -4*n + 6*n - 4*s. Let p(h) be the first derivative of -2/45*h**5 - 5 + 0*h - 2/9*h**3 + 1/6*h**4 + 1/9*h**n. Factor p(w).
-2*w*(w - 1)**3/9
Let d(h) be the first derivative of -h**6 - 3*h**5 - 3*h**4 - h**3 - 2. What is w in d(w) = 0?
-1, -1/2, 0
Find h such that 0*h**2 + 0 + 0*h + 3/4*h**3 = 0.
0
Let p be (-4)/12 - (-37)/3. Factor 10*f**5 - 14*f**4 - 8*f**5 + p*f**3 + 6*f**4 + 2*f - 8*f**2.
2*f*(f - 1)**4
Let b(l) = -12*l**4 - 25*l**3 + l**2. Let v(u) = 8*u**4 + 17*u**3 - u**2. Let h(t) = -5*b(t) - 7*v(t). Determine o so that h(o) = 0.
-1, -1/2, 0
Let x(g) be the first derivative of -7/4*g**4 + 7 + 0*g - 4*g**3 + 2*g**2. Factor x(k).
-k*(k + 2)*(7*k - 2)
Let j(s) be the second derivative of 1/60*s**6 - 4*s + 0*s**2 + 0*s**5 + 1/24*s**3 - 1/24*s**4 - 1/168*s**7 + 0. Determine n so that j(n) = 0.
-1, 0, 1
Let p = 52 + -49. Let u(r) be the first derivative of -3/4*r**4 + 3/2*r**2 + 3*r + 2 - r**p. Factor u(s).
-3*(s - 1)*(s + 1)**2
Let v be 14/4 - 7/(-14). Suppose 3*z + 5*x + 4 - 11 = 0, -v*x - 8 = -z. Let -1/4*g**z - 1/4*g**3 + 1/4*g**2 + 1/4*g**5 + 0 + 0*g = 0. Calculate g.
-1, 0, 1
Let p = 117 + -1754/15. Let n(i) be the third derivative of 2*i**2 + 0 + 0*i + p*i**3 + 1/150*i**5 + 1/30*i**4. Factor n(q).
2*(q + 1)**2/5
Let j(r) be the first derivative of 2/21*r**6 + 0*r**4 + 0*r**3 - 2/35*r**5 + 0*r**2 + 2 + 0*r. Factor j(c).
2*c**4*(2*c - 1)/7
Let m(d) be the third derivative of d**5/30 + d**4/2 + 5*d**3/3 - 6*d**2. Find n, given that m(n) = 0.
-5, -1
Let o(p) = 0 - p**4 + p**5 + p**4 + p**3 + 1. Let q(m) = m**5 - 4*m**4 + m**3 + 3. Let g(f) = 3*o(f) - q(f). Factor g(y).
2*y**3*(y + 1)**2
Let d(j) be the first derivative of -4*j**5/5 + 4*j**4 - 20*j**3/3 + 4*j**2 - 5. Factor d(t).
-4*t*(t - 2)*(t - 1)**2
Let b(u) be the third derivative of 0 - 1/60*u**5 + 1/48*u**6 - 2*u**2 + 1/6*u**3 + 0*u - 5/48*u**4. Let b(k) = 0. Calculate k.
-1, 2/5, 1
Let h = 78 + -75. Let 18/5*t**h + 3/5*t**5 + 12/5*t**2 + 12/5*t**4 + 3/5*t + 0 = 0. Calculate t.
-1, 0
Let b(a) be the third derivative of -a**6/540 + a**5/60 - a**4/18 + 7*a**3/6 - 6*a**2. Let v(t) be the first derivative of b(t). Let v(o) = 0. Calculate o.
1, 2
Let n(g) = 5*g**2 - g - 6. Let c(w) = -11*w**2 + 2*w + 13. Let o be 3/(-2 + 15/9). Let a(d) = o*n(d) - 4*c(d). Factor a(h).
-(h - 2)*(h + 1)
Let h(o) be the first derivative of -o**4/16 - o**3/6 - 8. Factor h(f).
-f**2*(f + 2)/4
Let r(f) be the third derivative of f**6/780 + f**5/195 - f**4/39 - 8*f**3/39 - 10*f**2. Determine b so that r(b) = 0.
-2, 2
Let z be 50/18 + 4/18. Let s(j) be the third derivative of 0*j**z + 1/180*j**5 + j**2 + 1/72*j**4 + 0 + 0*j. Factor s(o).
o*(o + 1)/3
Factor 7*u - 12 - 3*u - 4*u**3 + 16*u - 4*u**2.
-4*(u - 1)**2*(u + 3)
Let t(p) = p**3 + 2*p**2 + 2*p. Let w = 25 + -81. Let q = w + 35. Let x(z) = 4*z**3 + 7*z**2 + 7*z. Let o(l) = q*t(l) + 6*x(l). Factor o(m).
3*m**3
What is c in 92/13*c**3 + 0 - 34/13*c**2 + 24/13*c**5 - 86/13*c**4 + 4/13*c = 0?
0, 1/4, 1/3, 1, 2
Factor -5/4*j - 3/4 + 11/4*j**2 - 3/4*j**3.
-(j - 3)*(j - 1)*(3*j + 1)/4
Find h such that -11*h**2 + h**4 + 6*h**3 - 3*h**4 + 7*h**2 = 0.
0, 1, 2
Let q(w) be the second derivative of w**6/40 + 3*w**5/16 + 7*w**4/16 + 3*w**3/8 + 2*w. Factor q(i).
3*i*(i + 1)**2*(i + 3)/4
Let y = -363 + 747/2. Solve -11/2*f - y*f**2 - 17/2*f**3 - 5/2*f**4 - 1 = 0.
-1, -2/5
Let z(j) = 4*j**3 + 5*j**2 + 4*j. Let b(c) = -9*c**3 - 11*c**2 - 9*c. Let y(r) = 6*b(r) + 14*z(r). Suppose y(i) = 0. Calculate i.
-1, 0
Suppose -i + 4 + 0 = 0. Factor -31*s**i + 32*s**4 + 0*s**2 - s**3 - s**2 + s**5.
s**2*(s - 1)*(s + 1)**2
Suppose 9*s = 4*s + 80. Let x be 2/s*(-4)/(-2). Let 0 + x*g**2 + 0*g = 0. What is g?
0
Suppose -2*d + 11 = -3*w, d = -2*d - w + 11. Factor 0*o**2 + 0*o - 2/5*o**d + 0*o**3 + 0 - 2/5*o**5.
-2*o**4*(o + 1)/5
Suppose 5*v - 6*v = v. Factor 2/3*u + v - 2/3*u**3 - 2/3*u**4 + 2/3*u**2.
-2*u*(u - 1)*(u + 1)**2/3
Suppose -270/7*c**2 - 324/7 - 6/7*c**4 - 66/7*c**3 - 486/7*c = 0. What is c?
-3, -2
Let d = 551/585 + 11/65. Factor 2/3*x**2 - d*x + 4/9.
2*(x - 1)*(3*x - 2)/9
Let f(z) be the third derivative of z**6/80 - 3*z**5/20 + 9*z**4/16 - 5*z**2 - z. Factor f(x).
3*x*(x - 3)**2/2
Let k(t) be the third derivative of t**5/80 + 3*t**4/16 + 9*t**3/8 - 3*t**2. Solve k(h) = 0 for h.
-3
Let j(f) be the third derivative of -f**5/12 + 5*f**4/4 - 15*f**3/2 - 23*f**2. Factor j(o).
-5*(o - 3)**2
Let n(t) = -10*t**4 - 10*t**3 + 40*t**2 + 65*t + 20. Let k(v) = 10*v**4 + 11*v**3 - 39*v**2 - 65*v - 19. Let l(r) = -5*k(r) - 6*n(r).