45, -1, 1
Let s(d) be the first derivative of d**4/14 - 2*d**3/21 - 5*d**2/7 - 6*d/7 + 54. Determine q, given that s(q) = 0.
-1, 3
Suppose -4*t = 9 + 3. Let a be 22/44 + t/(-2). Factor 8*h**2 + 28*h**3 - 2*h + 144*h**4 + a*h - 124*h**4.
4*h**2*(h + 1)*(5*h + 2)
Let g(z) be the second derivative of 0*z**5 + 1/40*z**6 + 0*z**2 - 4*z + 0*z**3 + 0 + 0*z**4. What is k in g(k) = 0?
0
Let r(s) be the first derivative of s**5 + 5*s**4 - 55*s**3/3 + 15*s**2 - 105. Suppose r(n) = 0. Calculate n.
-6, 0, 1
Suppose -54 = -29*o - 9 + 13. Suppose 2/7*z**4 + 6/7*z**o - 8/7*z**3 - 8/7 + 8/7*z = 0. Calculate z.
-1, 1, 2
Let o(p) = -p**3 + p**2 + p - 1. Let y(l) = 4*l**3 - 2*l**2 - 8*l + 8. Let g(a) = -1. Let c(n) = -4*g(n) - 2*y(n). Let m(i) = -3*c(i) + 21*o(i). Factor m(v).
3*(v - 1)**2*(v + 5)
Let h be 4/40*-4 + (-96)/(-15). Suppose -s = -5*c + 6 + 12, 3*s - 3*c + h = 0. Let -4/3*o**2 + 2*o - 4/3*o**3 - 2/3*o**5 + s*o**4 - 2/3 = 0. Calculate o.
-1, 1
Let r(i) = -i**2 + 6*i - 4. Let l be r(4). Suppose -l*h + 19 = -1. Factor -h*m**3 - m + 10*m + 3*m**3 - 11*m - 4*m**2.
-2*m*(m + 1)**2
Let c(s) be the third derivative of -s**6/120 - 7*s**5/15 - 25*s**4/24 + 9*s**3 + s**2 - 7. Let c(z) = 0. Calculate z.
-27, -2, 1
Let g(w) be the second derivative of 15*w + 25/11*w**2 + 1/66*w**4 + 0 - 10/33*w**3. Factor g(p).
2*(p - 5)**2/11
Let u = 6764 + -13527/2. Determine h, given that -2*h - u*h**2 - 2 = 0.
-2
Let i(p) be the third derivative of -p**8/1680 - p**7/315 + 7*p**6/180 - 2*p**5/15 + p**4/6 + 4*p**2. Let w(t) be the second derivative of i(t). Factor w(o).
-4*(o - 1)**2*(o + 4)
Let t(q) = -2*q - 4. Let c be t(-2). Let z(l) be the second derivative of 1/8*l**4 - l**2 + 3*l + c + 1/40*l**5 + 0*l**3. Factor z(u).
(u - 1)*(u + 2)**2/2
Let d(p) = 0*p**4 + p**3 - 5*p**4 + p + 2*p**2 + 6*p**4 - p**2. Let i(k) = -4*k**3 - 4*k**2. Let m(v) = -4*d(v) - 2*i(v). Factor m(w).
-4*w*(w - 1)**2*(w + 1)
Suppose 0 = -8*l + 10*l - 32. Suppose 4*r - 24 = -l. Find n, given that -n**2 + 7/2*n - 1/2*n**3 - r = 0.
-4, 1
Let k(s) be the third derivative of 0*s**3 + 4*s**2 - 1/15*s**4 - 1/150*s**5 + 0*s + 0. Find m, given that k(m) = 0.
-4, 0
Suppose 4*j - 20 = 0, 10*z + 5*j = 12*z + 21. Let 2/3*s**z + 0 - 2/9*s**3 - 4/9*s = 0. What is s?
0, 1, 2
Suppose 0 = -18*y - 18*y + 56*y - 9*y. Find s such that 2/7*s**5 - 6/7*s**2 + y - 10/7*s**4 + 0*s + 2*s**3 = 0.
0, 1, 3
Let y(n) = 3*n + 55. Let f be y(-17). Factor 5*g + 4*g**3 + f*g**3 - 4*g**3 + 4*g**2 - 13*g.
4*g*(g - 1)*(g + 2)
Let o(z) be the first derivative of z**7/210 - z**6/150 - z**5/50 + 4*z - 9. Let w(x) be the first derivative of o(x). Solve w(c) = 0 for c.
-1, 0, 2
Suppose 4*f - 7*f + 486 = -3*t, t = -2*f + 333. Suppose 5*q + 155 = f. What is d in 8/7*d**q + 4/7*d**3 - 8/7 - 4/7*d = 0?
-2, -1, 1
Suppose -37 + 13 = -24*c. Let b be (c/9)/(28/63). What is r in 0*r + 0 - b*r**2 - 1/4*r**3 = 0?
-1, 0
Let m be (1 - 8)/((-14)/4). Determine n, given that 0 + 6/11*n**3 - 2/11*n + 4/11*n**4 + 0*n**m = 0.
-1, 0, 1/2
Let f(j) be the first derivative of -6 + 0*j**2 + 9/20*j**4 + 0*j**3 + 0*j + 3/25*j**5. Factor f(x).
3*x**3*(x + 3)/5
Let q(v) be the second derivative of -v**5/5 + 7*v**4/3 + 16*v**3/3 - 140*v. Factor q(p).
-4*p*(p - 8)*(p + 1)
Let n(c) be the third derivative of 9*c**2 + 0*c**3 + 0 - 1/108*c**4 - 1/270*c**5 + 0*c. Factor n(y).
-2*y*(y + 1)/9
Let w(a) be the third derivative of a**9/60480 + a**8/26880 - a**4/6 + 14*a**2. Let u(x) be the second derivative of w(x). Factor u(r).
r**3*(r + 1)/4
Let f(d) be the third derivative of d**10/50400 - 7*d**5/60 + 29*d**2. Let u(v) be the third derivative of f(v). Let u(r) = 0. Calculate r.
0
Let u(b) be the second derivative of b**5/5 + 110*b**4 + 24200*b**3 + 2662000*b**2 - 127*b. Factor u(g).
4*(g + 110)**3
Suppose 2*r + r = 0. Suppose -3*x + 5 + 1 = r. Factor -36 + 4*n**3 + x*n + 5*n**2 + n**4 + 36.
n*(n + 1)**2*(n + 2)
Let m be 6193/165 + 2/(-10). Factor -m*n + 16/3*n**2 + 196/3.
4*(2*n - 7)**2/3
Let q = 2238 + -2236. Factor 0*a + 9/2*a**3 + 0 + 0*a**q - 3/2*a**4.
-3*a**3*(a - 3)/2
Let i be ((-3)/20)/(175/20 + -9). Factor 0 - 3/5*m**2 + 1/5*m + i*m**3 - 1/5*m**4.
-m*(m - 1)**3/5
Let o = -104/79 - -37519/28440. Let v(z) be the third derivative of 0*z**4 - 1/1260*z**7 + o*z**5 + 0*z**3 + 0 + 0*z**6 + 0*z - z**2. Factor v(n).
-n**2*(n - 1)*(n + 1)/6
Let u(m) be the third derivative of m**5/4 + 55*m**4/48 + 63*m**2. Find f such that u(f) = 0.
-11/6, 0
Let a(l) be the third derivative of 7*l**7/40 - 189*l**6/160 + 233*l**5/80 - 111*l**4/32 + 9*l**3/4 + 2*l**2 + 13. Find k such that a(k) = 0.
3/7, 1, 2
Let i(f) be the third derivative of f**4 - 6*f**3 - 7*f**2. Let c(h) = h**2 - 24*h + 36. Let b(r) = 4*c(r) + 3*i(r). Factor b(y).
4*(y - 3)**2
Let q = 15 - -48. Let g be 0 + 3/(-9) - (-30)/q. Factor -g*b + 0 + 2/7*b**2 - 1/7*b**3.
-b*(b - 1)**2/7
Let k(m) = m**3 - m**2 + m. Let s(g) = g**5 + 6*g**4 + 5*g**3 + 12*g**2 - 6*g. Let z(n) = 30*k(n) + 5*s(n). Factor z(f).
5*f**2*(f + 1)*(f + 2)*(f + 3)
Let m(g) be the second derivative of -g**5/190 - 15*g**4/38 - 477*g. Factor m(j).
-2*j**2*(j + 45)/19
Find t such that -24/7 - 2*t - 2/7*t**2 = 0.
-4, -3
Let f(u) be the third derivative of -u**7/980 + u**6/252 - u**5/210 + u**3/2 - 3*u**2. Let c(h) be the first derivative of f(h). Suppose c(k) = 0. Calculate k.
0, 2/3, 1
Let c(i) be the third derivative of 5/144*i**4 - 1/24*i**5 + 5/12*i**3 + 21*i**2 + 0*i - 1/144*i**6 + 0. Suppose c(z) = 0. What is z?
-3, -1, 1
Let c(n) be the third derivative of n**8/168 - n**6/10 - 4*n**5/15 - n**4/4 - 85*n**2. Factor c(m).
2*m*(m - 3)*(m + 1)**3
Let f(b) = b**2 + 11*b + 18. Let k be f(-9). Suppose -5*c + 21 - 11 = k. Factor 4*y + y - 3*y**c + y.
-3*y*(y - 2)
Let m(b) be the second derivative of 0 + 43*b + 33/16*b**2 + 1/32*b**4 - 3/4*b**3. Determine u so that m(u) = 0.
1, 11
Solve -1/3*h**4 - 31/3*h**3 + 48 + 172/3*h**2 - 284/3*h = 0.
-36, 1, 2
Let h(x) = -x - 2. Let c be h(-4). Let l be (2 + 6/(-9))*(1 + 2). Factor -4*q + 2*q**c - l*q**2 + 9 + 3*q**2 - 6.
(q - 3)*(q - 1)
Let y(h) be the second derivative of h**7/630 - h**6/270 - 2*h**5/45 + 2*h**4/9 - 13*h**3/6 + 18*h. Let l(k) be the second derivative of y(k). Factor l(r).
4*(r - 2)*(r - 1)*(r + 2)/3
Factor 35*h**3 - 21*h**3 + h**5 - 17*h**3 + 2*h**2.
h**2*(h - 1)**2*(h + 2)
Let t(c) be the second derivative of -c**4/12 + 19*c**3/6 + 60*c**2 - 713*c. Suppose t(d) = 0. Calculate d.
-5, 24
Let n(p) be the second derivative of 0 + 1/25*p**5 - 1/30*p**3 - 3*p + 1/20*p**4 + 0*p**2. Factor n(y).
y*(y + 1)*(4*y - 1)/5
Let v(a) be the first derivative of -2*a**5/35 - a**4/14 + 8*a**3/21 + 4*a**2/7 - 74. Factor v(f).
-2*f*(f - 2)*(f + 1)*(f + 2)/7
Let k(h) = 145*h - 325. Let n(v) = -v**2 + 72*v - 163. Let q(y) = -2*k(y) + 5*n(y). Factor q(i).
-5*(i - 11)*(i - 3)
Let k = 97 + -90. Let r be 2/k + 1 + (-3)/3. Factor 18/7 + r*n**2 + 12/7*n.
2*(n + 3)**2/7
Suppose -11*o + 5/2*o**2 + 4 = 0. Calculate o.
2/5, 4
Let q(b) = 62*b - 867. Let z be q(14). Let y(k) be the first derivative of 0*k + 1/13*k**2 + z + 2/39*k**3. Factor y(u).
2*u*(u + 1)/13
Let l(j) = -2*j**5 - 10*j**4 - 19*j**3 - 11*j**2 - 5*j - 5. Let g(f) = f**5 + 5*f**4 + 9*f**3 + 5*f**2 + 2*f + 2. Let b(r) = 5*g(r) + 2*l(r). Solve b(h) = 0.
-3, -1, 0
Let b(d) = -1588*d**2 - 244*d - 9. Let z(g) = -4767*g**2 - 731*g - 27. Let r(c) = -11*b(c) + 4*z(c). Factor r(v).
-(40*v + 3)**2
Let h be 5/(25/15)*1/(-1). Let z be h*(-3)/(-18) + 45/66. Factor 2/11*o**3 + z*o**4 + 0 - 2/11*o**2 - 2/11*o.
2*o*(o - 1)*(o + 1)**2/11
Suppose -3/4*o**5 + 0*o + 0*o**2 + 0 - 3/2*o**3 - 9/4*o**4 = 0. What is o?
-2, -1, 0
Suppose 4*l = -1058 + 102. Let x = l - -242. Suppose 0*f + 4/7*f**x + 0 + 2/7*f**4 - 6/7*f**2 = 0. What is f?
-3, 0, 1
Let q(j) be the third derivative of j**6/30 - 34*j**5/15 + 6*j**2 - 2. Factor q(u).
4*u**2*(u - 34)
Let n = 31 + -26. Suppose 62 + n = 5*g - 3*w, -3*g - 5*w = -47. Find j, given that 6*j**3 - 44*j**2 - 24*j**4 + 10*j**2 + 46*j**3 + 16*j + 4*j**5 - g*j**2 = 0.
0, 1, 2
Let y = -15623 + 15623. Solve y - 2/11*u**2 - 2/11*u = 0.
-1, 0
Let l(n) = n**2 + n. Suppose 2 + 13 = 5*b. Let z(r) = -6*r**2 - r + 9. Let t(m) = b*z(m) + 21*l(m). Let t(k) = 0. Calculate k.
-3
Let q = -242/7 + 3160/91. Let p = q + 42/65. Factor p - 2/5*s - 2/5*s**2.
-2*(s - 1)*(s + 2)/5
Suppose -21