4*v + 18. Factor 2/3*w**4 + 0*w - 2/3*w**3 + 0*w**v + 0.
2*w**3*(w - 1)/3
Suppose 24 = 3*l + 3*c, -25*c + 27*c + 5 = 5*l. Suppose 0*d - 2/7*d**2 - 1/7*d**4 + 0 - 3/7*d**l = 0. What is d?
-2, -1, 0
Suppose 17*g - 20*g + 27 = 0. Suppose -9 = -g*o + 6*o. Let 6/5*w**o - 4/5*w**2 - 2/5*w**5 + 0*w + 0 + 0*w**4 = 0. What is w?
-2, 0, 1
Suppose -7*d + 8*d = 9. Suppose i = -d + 11. Factor 7/4*w**2 + 5*w**4 + 0 + i*w**5 + 9/2*w**3 + 1/4*w.
w*(w + 1)*(2*w + 1)**3/4
Factor 1819 + 216*r - 4377 - 39*r**2 + 38*r**2 - 9106.
-(r - 108)**2
Let p = 18 + -16. Solve -2*l**2 - 2*l**p - 2*l**2 + l**2 = 0 for l.
0
Let x = -3/53 - 253/212. Let y = x + 23/12. What is m in -m**2 + 1/3*m**3 + y*m + 0 = 0?
0, 1, 2
Suppose -3*s + o - 1 = -6, 0 = -5*s + o + 5. Suppose s = 4*a, -5*a = 5*u - 2*u - 6. Suppose -3/2*m - 9/2*m**u + 9/2 + 3/2*m**3 = 0. Calculate m.
-1, 1, 3
Let w(x) be the second derivative of x**4/72 - 23*x**3/36 - 2*x**2 - 4*x + 8. Factor w(b).
(b - 24)*(b + 1)/6
Let x = -791597/88 + 67415/8. Let i = 570 + x. Factor -32/11 + i*t + 2/11*t**3 + 14/11*t**2.
2*(t - 1)*(t + 4)**2/11
Let i be -3*((-32)/(-12) + -2). Let v = i + 5. Factor -2*l**2 - 3 + v - 2 - 8*l + 4*l.
-2*(l + 1)**2
Let f(g) be the second derivative of 0 + 0*g**3 - 1/210*g**5 + 1/84*g**4 - 5/2*g**2 + 3*g. Let j(c) be the first derivative of f(c). Factor j(v).
-2*v*(v - 1)/7
Suppose -2*b - 4*s - 28 = -6*b, -3*b + 5*s = -29. Let w = 18 + -13. Factor -4*k**2 + w*k**2 - 1 - k - 6*k**b + 7*k**3.
(k - 1)*(k + 1)**2
Let n(i) = -50*i**3 - 900*i**2 - 850*i + 35. Let m(h) = 61*h**2 + 3*h**3 + 19*h**2 - 2 + 50*h - 27*h**2. Let s(v) = 35*m(v) + 2*n(v). Factor s(c).
5*c*(c + 1)*(c + 10)
Let l(i) = 19*i**2 + 13*i - 6. Let d(n) = 6 - 6*n - 2*n - 20*n**2 - n - 5*n. Let o(p) = 4*d(p) + 5*l(p). Solve o(m) = 0.
-1, 2/5
Let g(f) be the third derivative of f**5/15 + 11*f**4/6 + 20*f**3 + f**2 - 4. Factor g(j).
4*(j + 5)*(j + 6)
Suppose -w - 16*y + 1 = -15*y, 12 = 4*w - 4*y. Factor -8/7 - 2/7*r**w - 8/7*r.
-2*(r + 2)**2/7
Let v = 86 + -82. Let i(z) be the second derivative of 0 - v*z + 1/15*z**3 + 1/105*z**7 - 1/5*z**2 - 1/75*z**6 + 1/15*z**4 - 1/25*z**5. Factor i(y).
2*(y - 1)**3*(y + 1)**2/5
Let r(f) = -2*f**3 + 12*f**2 + 2*f - 15. Let p(c) = -7*c**3 + 37*c**2 + 7*c - 45. Let o(i) = 3*p(i) - 8*r(i). Factor o(m).
-5*(m - 3)*(m - 1)*(m + 1)
Suppose 0 + 15 = -5*q - 5*d, -3*q + 2*d = -16. Suppose 0 = -5*v - 3*u - 5, 2*u + 3 = -q*v - 3. Factor 2/3*y - 2/9*y**v + 0.
-2*y*(y - 3)/9
Let d = 26390/3 - 8796. Suppose -b**2 + d*b**3 + 4/3 + 1/3*b**4 - 4/3*b = 0. What is b?
-2, 1
Let 8 + 4*y**3 + 590*y + 578*y + 18*y**2 - 1144*y = 0. What is y?
-2, -1/2
Let u(y) = -245*y + 245. Let a be u(1). Factor -4/3 + 2/3*w**3 - 2*w + a*w**2.
2*(w - 2)*(w + 1)**2/3
Suppose 0 - 10*t + 19/2*t**2 + 1/2*t**3 = 0. What is t?
-20, 0, 1
Factor 1/4*f**2 + 2*f + 15/4.
(f + 3)*(f + 5)/4
Let x(j) be the second derivative of -j**7/315 + j**6/75 + 3*j**5/50 + j**4/18 + 2*j - 45. Factor x(g).
-2*g**2*(g - 5)*(g + 1)**2/15
Find a, given that -8/7 + 12/7*a - 4/7*a**2 = 0.
1, 2
Let h = 32 - 30. Factor -8*m**2 - 4*m**3 + 4*m**4 + h*m**5 - 2*m**3 - 59*m + 67*m.
2*m*(m - 1)**2*(m + 2)**2
Let y = 91554/19 - 4820. Let x = y - -258/133. Factor -2/7*o**3 + 0 - x*o - 6/7*o**2.
-2*o*(o + 1)*(o + 2)/7
Let p be 84/(-36)*(-6)/91. Factor -2/13*b - p*b**2 + 4/13.
-2*(b - 1)*(b + 2)/13
Let p(f) be the first derivative of -18/5*f**5 - 11/2*f**4 - 5/6*f**6 + 3/2*f**2 - 18 + 2*f - 8/3*f**3. Factor p(z).
-(z + 1)**4*(5*z - 2)
Let i(l) = l - 2. Let z(t) = 2*t - 17. Let v(y) = -5*i(y) + z(y). Let b be v(-3). Factor 2/5*c**3 + 0*c**b - 6/5*c - 4/5.
2*(c - 2)*(c + 1)**2/5
Suppose 2881*z - 2907*z + 23 + 29 = 0. Factor -8/3*n**4 + 0*n + 0*n**z + 0 + 4/3*n**3 + 4/3*n**5.
4*n**3*(n - 1)**2/3
Let r be (-2 - -1)/(1/(-4)). Factor -r*i + 2 + 0*i**2 + 0*i + i**2 + 2.
(i - 2)**2
Let v(s) be the third derivative of 1/30*s**4 - 12*s**2 + 0 + 0*s + 0*s**3 - 1/300*s**5. Let v(u) = 0. What is u?
0, 4
Let a(r) be the second derivative of r**7/378 + 2*r**6/135 + r**5/90 - r**4/27 - r**3/18 + 10*r. Factor a(n).
n*(n - 1)*(n + 1)**2*(n + 3)/9
Let m = -18220 - -200470/11. Factor -m - 32/11*l**2 + 80/11*l.
-2*(4*l - 5)**2/11
Let c = -20150/3 + 6717. Find v, given that 26/3*v + 169/3 + c*v**2 = 0.
-13
Let x(o) = o + 30. Let m be (-2)/14 + (-1950)/70. Let d be x(m). Determine h, given that 1/4*h + 1/2 - 1/4*h**d = 0.
-1, 2
Let q(m) be the second derivative of -m**5/10 - 37*m**4/6 - 323*m**3/3 + 361*m**2 + 46*m. Factor q(c).
-2*(c - 1)*(c + 19)**2
Suppose -3*w + 3 = 3*n, 0 = 4*w - 7*n + 8*n - 13. Let d(q) be the first derivative of 1 - 2/7*q**3 - 1/14*q**w - 2/7*q**2 + 0*q. Solve d(p) = 0 for p.
-2, -1, 0
Let b(f) = -3*f**5 - 23*f**4 + 47*f**3 - 33*f**2 - 4. Let c(w) = 5*w**5 + 46*w**4 - 93*w**3 + 63*w**2 + 7. Let v(a) = 7*b(a) + 4*c(a). Factor v(u).
-u**2*(u - 21)*(u - 1)**2
Factor 12 - 75*l**2 - 9*l**3 + 7*l**3 + 27*l**3 - 4*l.
(l - 3)*(5*l - 2)*(5*l + 2)
Suppose -146*j + 240 = -129 + 77. Factor 4/3*i**3 + 0*i + 8/3*i**j + 0.
4*i**2*(i + 2)/3
Solve -4/3*k**4 + 0 - 4/3*k**3 + 8*k**2 + 0*k = 0 for k.
-3, 0, 2
Factor 96 - 8*u + 1/6*u**2.
(u - 24)**2/6
Let k(w) be the third derivative of -w**6/780 + w**5/390 + 11*w**4/52 + 21*w**3/13 + 289*w**2. Let k(d) = 0. What is d?
-3, 7
Let a(o) = -o**3 + 13*o**2 - 11*o - 11. Let m be a(12). Suppose m - 35 = -17*u. Determine g so that 3/2*g**u + 0 - 3/2*g**4 + 3/2*g**3 - 3/2*g = 0.
-1, 0, 1
Factor 35*l**3 + 31*l + 88*l**4 - 5*l**5 + 10*l**2 - 166*l - 28*l**4 - 456 + 386 + 105*l**3.
-5*(l - 14)*(l - 1)*(l + 1)**3
Let x be (-1 - (-44)/(-12))*(-9)/2. Suppose 6 + x = 9*z. Factor 1/3*l + 0 - 1/3*l**z + 0*l**2.
-l*(l - 1)*(l + 1)/3
Let t(h) be the first derivative of -6 - 4/7*h + 5/7*h**2 + 8/21*h**3 - 3/14*h**4. What is c in t(c) = 0?
-1, 1/3, 2
Factor -5/7*b**2 + 402/7*b - 160/7.
-(b - 80)*(5*b - 2)/7
Let x(m) be the third derivative of 1/42*m**4 - 2/21*m**3 - 4*m**2 - 1/420*m**5 + 0 + 0*m. Find p, given that x(p) = 0.
2
Let z(t) be the first derivative of -5/8*t**2 + 1/12*t**3 + 3/2*t + 9. Find w, given that z(w) = 0.
2, 3
Suppose 1/12*o - 1/2 + 1/2*o**2 - 1/12*o**3 = 0. What is o?
-1, 1, 6
Let l(q) = q**4 + q**3 + 2*q**2 + q - 2. Let o(m) = -15*m**3 - 85*m**2 - 25*m + 110. Let b(z) = -5*l(z) - o(z). Factor b(r).
-5*(r - 5)*(r - 1)*(r + 2)**2
Let j(y) = -16*y**2 + 11*y - 1422. Let b(n) = 3*n**2 - 3*n + 356. Let d(l) = -9*b(l) - 2*j(l). Factor d(q).
5*(q - 8)*(q + 9)
Factor -1/3*l**3 + 5/3*l**2 - 2/3*l - 8/3.
-(l - 4)*(l - 2)*(l + 1)/3
Let w(d) = 16*d - 77. Let g be w(5). Let h(x) be the first derivative of 2/13*x + 5 + 2/39*x**g - 2/13*x**2. Let h(a) = 0. What is a?
1
Suppose 0 = 4*l - 65 - 131. Factor 5*q**3 + 5*q + 0*q + 39*q**2 - l*q**2 + 0*q.
5*q*(q - 1)**2
Suppose -5*x + 3*x = 4*w, 3*x = 6. Let a be 2 - -3*w/(-3). Factor 37 - u**3 - 37 - a*u**2 - 2*u.
-u*(u + 1)*(u + 2)
Let w(l) be the third derivative of 1/30*l**5 - l**3 + 0 + 1/6*l**4 + 0*l + 10*l**2. Let w(c) = 0. Calculate c.
-3, 1
Suppose 3*k**3 + 15*k**2 - 45 - 60 - 99*k - 6*k**2 = 0. What is k?
-7, -1, 5
Let s(x) = 2*x**2 + x - 13. Let r be s(3). Factor -4*v**4 - 5*v + 0 + 14*v + 20*v**3 - 36*v**2 + 19*v - r.
-4*(v - 2)*(v - 1)**3
Suppose 0 = 5*x + 3*h - 6, 3*x - 4*h - 15 = 2*x. Factor 5*f**3 + 7*f**x - 10*f**3.
2*f**3
Let 2304/5*i - 432/5*i**2 + 27/5*i**3 - 4096/5 = 0. Calculate i.
16/3
Factor 5*q**2 + 1/3*q**4 - 8/3*q - 16/3 + 8/3*q**3.
(q - 1)*(q + 1)*(q + 4)**2/3
Let a(c) be the second derivative of c**4/36 + 13*c**3/9 + 25*c**2/6 + c + 3. Factor a(r).
(r + 1)*(r + 25)/3
Let g = 968 - 2872/3. Factor g + 2/3*n**2 - 16/3*n.
2*(n - 4)**2/3
Factor -14/5*b - 12/5*b**2 - 1/5*b**4 + 13/5 + 14/5*b**3.
-(b - 13)*(b - 1)**2*(b + 1)/5
Let u(c) be the third derivative of c**8/13440 - c**7/1120 + c**6/240 + 4*c**5/15 + c**2. Let y(b) be the third derivative of u(b). Factor y(r).
3*(r - 2)*(r - 1)/2
Suppose 210 = -10*z + 2590. Let a be z/36*4/7. Find g such that -8/9*g - a*g**2 + 10/9*g**5 + 26/9*g**4 + 8/9 - 2/9*g**3 = 0.
-2, -1, 2/5, 1
Let q = -173 - -215. Factor -28 + 22*d - 4*d**2 + q*d - 32.
-4*(d - 15)*(d - 1)
Suppose -1 = -4*r + 5*p + 11, -4*p - 8 = -3*r. Let 12*z**2 + 2/3 + r*z**5 - 16/3*z - 8/3*z**3 - 38/3*z**4 = 0. What is z?
-1, 1/4, 1/3, 1
Let p(n) be the first derivative of 2/9*n**3 + 0*n**2 + 0*n + 6 + 