1
Suppose 0 = 3*g, 5*g - 11 - 9 = -2*k. Let n be ((-42)/15 - -4) + (-4)/k. Solve -4/5 + 2/5*f**3 + n*f**2 - 2/5*f = 0 for f.
-2, -1, 1
Let v(a) be the third derivative of a**8/3360 + a**7/1260 - 5*a**4/4 + 22*a**2. Let d(z) be the second derivative of v(z). Factor d(b).
2*b**2*(b + 1)
Let c(k) = -6 + 6 - 34*k**2 - 43*k**3 - 8*k - 12*k**4 - 2 + 9*k**3. Let t(m) = m. Let j(u) = c(u) - 6*t(u). Determine x, given that j(x) = 0.
-1, -1/2, -1/3
Let a(f) = -17*f**2 - 51*f + 47. Let o(y) = -8*y**2 - 24*y + 23. Let c(d) = 3*a(d) - 7*o(d). Factor c(n).
5*(n - 1)*(n + 4)
Let n(t) be the third derivative of -1/240*t**5 + 0 + 30*t**2 + 0*t - 1/3*t**3 + 1/16*t**4. Factor n(l).
-(l - 4)*(l - 2)/4
Suppose 9/2 + 3/2*u**2 - 25/4*u + 1/4*u**3 = 0. What is u?
-9, 1, 2
Let x(u) be the first derivative of u**7/280 - u**6/5 + 18*u**5/5 - 17*u**3/3 - 34. Let d(a) be the third derivative of x(a). Determine f, given that d(f) = 0.
0, 12
Let y(a) be the first derivative of -a**6/1620 - a**5/540 + 5*a**3 - 23. Let h(o) be the third derivative of y(o). What is i in h(i) = 0?
-1, 0
Let j(k) be the second derivative of k**6/45 - 2*k**5/15 + k**4/6 + 4*k**3/9 - 4*k**2/3 + 174*k - 2. Find z, given that j(z) = 0.
-1, 1, 2
Let w(d) be the third derivative of -d**5/140 - 3*d**4/28 - 5*d**3/14 + 16*d**2. Determine i, given that w(i) = 0.
-5, -1
Let u(h) be the second derivative of 17*h - 17/65*h**5 + 0 + 3/13*h**3 - 1/13*h**6 + 25/273*h**7 + 7/39*h**4 + 1/13*h**2. Suppose u(g) = 0. Calculate g.
-1, -1/5, 1
Let b(s) be the second derivative of s**4/4 - 4*s**3 + 18*s**2 - 22*s. Factor b(j).
3*(j - 6)*(j - 2)
Find g such that -62/15*g**2 + 0 + 2/15*g**3 + 4*g = 0.
0, 1, 30
Let u be (-10)/(-20)*(-1 - -1) + 4. Let m be -4 - 17*u/(-16). Suppose -m - 3/4*i**2 - i = 0. Calculate i.
-1, -1/3
Let m(x) = x**3 + 8*x**2 + 39*x - 53. Let c(i) = -4*i**2 - 20*i + 26. Let d(n) = -5*c(n) - 2*m(n). Determine w, given that d(w) = 0.
-3, 1, 4
Let r(l) = 13*l**3 - 2*l - 1. Let w be r(-1). Let m = 17 + w. Factor 2*a**3 - 4*a - 2*a**2 + 0*a**5 + 2*a**4 - 2*a**m + 4*a.
-2*a**2*(a - 1)**2*(a + 1)
Let t(a) be the second derivative of a**7/84 - 23*a**6/60 + 4*a**5 - 37*a**4/3 - 20*a**3/3 + 100*a**2 + 269*a - 2. What is k in t(k) = 0?
-1, 2, 10
Let a(z) be the third derivative of z**6/200 + z**5/100 - z**4/8 + 3*z**3/10 - 293*z**2. Factor a(w).
3*(w - 1)**2*(w + 3)/5
Let m(j) be the first derivative of -5/6*j**3 - 5/6*j**4 + 11*j - 13 + 1/4*j**5 + 5*j**2. Let c(d) be the first derivative of m(d). Factor c(x).
5*(x - 2)*(x - 1)*(x + 1)
Let n = 18 - 9. Suppose -2*d + 3 = -n. Determine p, given that 0*p + 8*p - 7*p**2 - d*p**3 - p**2 = 0.
-2, 0, 2/3
Suppose -4*r = -8, -105*k - 2*r = -106*k - 2. Factor 0 + 1/7*v**k - 1/7*v**4 + 3/7*v**3 - 3/7*v.
-v*(v - 3)*(v - 1)*(v + 1)/7
Let s be 2/(-16)*1 - 625/(-200). Suppose 2 + 7/4*v**s + 5*v - 13/2*v**2 = 0. What is v?
-2/7, 2
Solve 184*l**4 + 166*l**2 - 4*l**5 + 54*l**2 - 200*l + 11*l**3 - 212*l**4 + l**3 = 0 for l.
-5, 0, 1, 2
Suppose 15*m**2 + 25*m + 353 - 181 - 182 = 0. What is m?
-2, 1/3
Let n(b) be the second derivative of b**4/48 + 13*b**3/24 + 11*b**2/4 - 888*b. Factor n(j).
(j + 2)*(j + 11)/4
Let o be 2 + ((-20)/140 - 2/(-9)). Let s = o + -13/7. Factor s - 2/9*h**3 + 2/9*h - 2/9*h**2.
-2*(h - 1)*(h + 1)**2/9
Let q(a) be the first derivative of -a**7/210 + 2*a**6/45 + 11*a**5/30 + a**4 - 16*a**3/3 - 19. Let y(s) be the third derivative of q(s). Factor y(w).
-4*(w - 6)*(w + 1)**2
Let p = -23715/13 + 1827. Let 6/13*a**4 + 42/13*a - p + 38/13*a**2 - 34/13*a**3 = 0. What is a?
-1, 2/3, 3
Let l(m) be the third derivative of -m**7/1890 - 11*m**6/1080 - 11*m**5/540 + 59*m**4/216 - 2*m**3/3 - 2*m**2 + 75*m. Factor l(s).
-(s - 1)**2*(s + 4)*(s + 9)/9
Let t be ((-7)/(-18))/(245/420). Factor -1/6 + t*h**3 - h**2 + 2/3*h - 1/6*h**4.
-(h - 1)**4/6
Let s(x) be the third derivative of x**6/240 - 7*x**5/60 - 5*x**4/16 + 6*x**2 + 2*x. Suppose s(p) = 0. What is p?
-1, 0, 15
Let u = -7924/605 + 4/605. Let q = -1828/143 - u. Factor 0*f**2 + 2/13*f**4 + q*f - 2/13 - 4/13*f**3.
2*(f - 1)**3*(f + 1)/13
Find c such that 330*c - 3*c**2 + 0*c**2 - 38212 + 38547 - 2*c**2 = 0.
-1, 67
Factor 36*l - 11*l + 4*l**2 - 15*l - 14*l - l**3.
-l*(l - 2)**2
Determine z so that 27*z**4 - 108*z**2 + 0 + 231/2*z**3 + 3/2*z**5 - 486*z = 0.
-9, -2, 0, 2
Let j = -5239/10 - -525. Find c, given that -6/5*c**4 - 2/5*c + 6/5*c**2 + j*c**3 + 0 - 7/10*c**5 = 0.
-2, -1, 0, 2/7, 1
Let p(x) be the third derivative of 2*x**7/105 + x**6/5 - x**5/5 - 28*x**4/3 - 32*x**3 - 227*x**2. Factor p(w).
4*(w - 3)*(w + 1)*(w + 4)**2
Let j(d) be the third derivative of 0 + 33*d**2 + 0*d + 5/24*d**4 + 1/12*d**5 - 5/3*d**3. Factor j(r).
5*(r - 1)*(r + 2)
Let y(h) be the second derivative of -h**5/50 - 97*h**4/30 - 2303*h**3/15 + 2401*h**2/5 + 327*h. What is n in y(n) = 0?
-49, 1
Suppose 0 = -0*n + 5*n + 2*v - 34, -2*n - v + 13 = 0. Find b such that -2 - 13*b**3 - 4*b**5 - 5 + 16*b**4 - n*b**2 + 20*b - 3*b**3 - 1 = 0.
-1, 1, 2
Let z be (-4)/(-22)*253/115. Factor 4/5*b**2 - 2/5*b**3 - z*b + 0.
-2*b*(b - 1)**2/5
Let l = -368/13 - -3338/117. Factor -l*c**2 + 0*c + 2/9.
-2*(c - 1)*(c + 1)/9
Let x be -2*7/(84/(-18)). Suppose 9 = -s + 4*h, -5*h + 15 = -0. Factor 21/4*v**s - 3/4*v + x*v**4 + 0 + 3/2*v**2.
3*v*(v + 1)**2*(4*v - 1)/4
Let y(i) be the third derivative of 11*i**5/90 + i**4/3 + i**3/9 + 2*i**2 - 73*i. Factor y(x).
2*(x + 1)*(11*x + 1)/3
Let r = -743 - -14863/20. Let w(b) be the third derivative of -1/8*b**4 + 1/70*b**7 + 0*b**3 + r*b**5 + 6*b**2 + 0 + 0*b - 3/40*b**6. Factor w(u).
3*u*(u - 1)**3
Let h(z) = 4*z**2 + 25*z. Let f(n) = 2*n**2 + 13*n. Let u(t) = -t - 20. Let v be u(-10). Let x(s) = v*f(s) + 6*h(s). Factor x(g).
4*g*(g + 5)
Suppose 0*f - 25 = -3*o - f, -5*f - 5 = 2*o. Let b(j) = -j - 1. Let p(r) = -r**2 - 34*r - 322. Let m(z) = o*b(z) + 5*p(z). Factor m(s).
-5*(s + 18)**2
Let k(g) be the second derivative of -1/50*g**6 - 1/10*g**3 + 0 + 3/50*g**5 - 1/70*g**7 + 22*g + 1/10*g**4 - 3/10*g**2. Factor k(a).
-3*(a - 1)**2*(a + 1)**3/5
Let 10*q + 112/5*q**2 + 58/5*q**3 - 4/5 = 0. Calculate q.
-1, 2/29
Factor 13*t - 37/4*t**2 + 7/4*t**3 - 3.
(t - 3)*(t - 2)*(7*t - 2)/4
Let -146*m**3 + 146*m**3 + 5*m**2 - 2*m**4 - 3*m**4 = 0. What is m?
-1, 0, 1
Let j(s) be the third derivative of -s**8/168 - 4*s**7/105 + s**6/20 + 3*s**5/5 + s**2 + 68. What is o in j(o) = 0?
-3, 0, 2
Suppose -t + 117 = 5*c, 0 = 3*c + 2*t - 42 - 31. Suppose -c*w + 47*w = 23*w. What is y in 1/4*y**2 + w*y + 0*y**3 - 1/4*y**4 + 0 = 0?
-1, 0, 1
Let t(l) be the third derivative of -l**3 + 1/60*l**5 + 0*l - 1/225*l**6 + 0 + 3*l**2 - 1/60*l**4. Let k(r) be the first derivative of t(r). Factor k(g).
-2*(g - 1)*(4*g - 1)/5
Let p be (-9)/(-30)*2 + 14/10. Let l(y) be the second derivative of 5*y + 3/2*y**3 + 0 + 1/4*y**4 + 3*y**p. Factor l(o).
3*(o + 1)*(o + 2)
Let c(m) be the first derivative of -4*m**3/3 + 154*m**2 + 312*m + 392. Factor c(j).
-4*(j - 78)*(j + 1)
Let d(t) be the first derivative of 2*t**3/5 + 16*t**2 + 104*t/5 + 93. Factor d(l).
2*(l + 26)*(3*l + 2)/5
Let m(l) be the third derivative of l**8/560 + 11*l**7/840 + l**6/30 + l**5/30 + 15*l**3/2 + 39*l**2. Let i(j) be the first derivative of m(j). Factor i(g).
g*(g + 1)*(g + 2)*(3*g + 2)
Let r(o) = 3. Let p(k) = 4*k**2 - 16*k + 16. Let q(s) = p(s) - 12*r(s). Factor q(a).
4*(a - 5)*(a + 1)
Let v = -216684051/436 + 496982. Let h = 2/109 + v. Let h + 1/2*y + 1/4*y**2 = 0. What is y?
-1
Let w be -1*(0 + 1)*-14. Let g = w + -12. Factor h + h + 4*h**2 + 6*h - 6*h**3 + g*h**3.
-4*h*(h - 2)*(h + 1)
Let s(q) be the first derivative of -q**9/3024 + q**8/1680 + q**7/840 - q**6/360 - 13*q**3/3 + 24. Let p(f) be the third derivative of s(f). Factor p(o).
-o**2*(o - 1)**2*(o + 1)
Determine n, given that 70/3*n + 2/3*n**3 - 26/3*n**2 + 98/3 = 0.
-1, 7
Suppose 7*r - 18 - 10 = 0. Let g be (r - 1) + (13 - 13). Factor 0*f + g*f**2 - 15/2*f**3 + 0.
-3*f**2*(5*f - 2)/2
Let a(b) be the third derivative of b**7/7560 + b**6/1080 + 5*b**4/4 - 12*b**2. Let k(z) be the second derivative of a(z). Factor k(j).
j*(j + 2)/3
Let y(p) be the second derivative of -p**5/60 - p**4/12 - p**3/6 + 3*p**2/2 + 11*p. Let c(r) be the first derivative of y(r). Suppose c(n) = 0. What is n?
-1
Let g(k) be the first derivative of -k**4/6 - k**3/3 +