t k be 5*(-15)/1050*-4. Factor 2/7*o**3 + 4/7 - 10/7*o + 6/7*o**2 - k*o**4.
-2*(o - 1)**3*(o + 2)/7
Let p(a) be the second derivative of -a**7/840 + a**6/90 - a**5/40 - 23*a**3/6 - 17*a. Let m(q) be the second derivative of p(q). Find i such that m(i) = 0.
0, 1, 3
Let m(h) be the first derivative of -2*h**2 - 28*h + 45. Let s be m(-7). What is n in s*n**2 + 2/3 - 4/3*n**3 - 2/3*n**4 + 4/3*n = 0?
-1, 1
Let r(z) = -5*z**2 - 8*z + 238. Let f(n) = 11*n**2 + 17*n - 475. Let j(d) = 2*f(d) + 5*r(d). Factor j(v).
-3*(v - 8)*(v + 10)
Suppose -11*q + 10 = -4*o - 14*q, q = -5*o + 4. Solve 1/7*g**o - 3/7*g**3 + 1/7*g**4 + 3/7*g - 2/7 = 0.
-1, 1, 2
Let c(l) = -9*l**3 - 15*l**2 - 17*l - 11. Let f(x) = 5*x**3 + 8*x**2 + 9*x + 6. Let u(d) = -6*c(d) - 11*f(d). Let u(h) = 0. Calculate h.
-1, 0, 3
Let j(i) = -8*i + 2. Let g be j(-1). Let o(a) = a**3 - 11*a**2 + 8*a + 22. Let y be o(g). Solve -4*s**2 + 0*s**y + 3*s**2 = 0 for s.
0
Let x be 6/(-4) - 63/(-42). Let n be -3 - -6 - (x - (-51)/18). What is f in n*f**4 - 1/3*f**3 - 1/2*f**2 + 2/3*f + 2/3 = 0?
-1, 2
Let p(b) be the third derivative of b**7/210 + b**5/60 - 18*b**2. Let z(u) = 12*u**3 - 16*u**2 - 6*u. Let i(a) = -5*p(a) - z(a). Factor i(v).
-v*(v - 1)*(v + 3)*(5*v + 2)
Let z(r) be the second derivative of -14*r - 2*r**2 + 0 - 5/6*r**3 + 1/8*r**4. Factor z(k).
(k - 4)*(3*k + 2)/2
Let w(k) be the first derivative of -k**6/9 - 8*k**5/45 + 2*k**4/9 + 4*k**3/9 - k**2/9 - 4*k/9 - 174. What is x in w(x) = 0?
-1, 2/3, 1
Suppose 0 = -6*b - 3*b - 576. Let x = b - -66. Factor 0*p**x - 1/5*p + 0 + 1/5*p**3.
p*(p - 1)*(p + 1)/5
Let v = 295 - 293. Let p(z) be the first derivative of -3/4*z**4 + 0*z**v - 12/5*z**5 + 0*z + 3 + 0*z**3 - 2*z**6. Factor p(n).
-3*n**3*(2*n + 1)**2
Let q be (-2)/7 + (-120)/(-28). Let u(m) = -m**3 - 9*m**2 - 9*m - 1. Let r be u(-8). Solve -2*y + 3*y**5 - 12*y**2 + r*y**3 + 5*y - 12*y**q + 11*y**3 = 0 for y.
0, 1
Let h(j) be the first derivative of -7*j**4 - 17/3*j**2 + 76/9*j**3 + 46/15*j**5 - 5/9*j**6 + 16 + 2*j. Factor h(r).
-2*(r - 1)**4*(5*r - 3)/3
Suppose -5*f + 3 + 2 = g, -5*g - 5 = -5*f. Factor 9 - 25 - 6*o + g*o**2 - 2*o**2 + 12.
-2*(o + 1)*(o + 2)
Let x(u) be the first derivative of -u**4 - 12*u**3 - 28*u**2 + 13. Suppose x(l) = 0. What is l?
-7, -2, 0
Let a(x) be the third derivative of -1/60*x**5 + 0*x + 1/2*x**3 + 0 + 10*x**2 - 1/12*x**4. Determine c, given that a(c) = 0.
-3, 1
Solve f + 0 - 7/10*f**2 = 0.
0, 10/7
Determine y, given that -3/4*y**5 + 0*y + 0 + 3*y**3 - 3*y**2 + 3/4*y**4 = 0.
-2, 0, 1, 2
Let s(i) = i**2 + 7*i + 2. Suppose 5*m + 20 = 5*g - 35, -4*g + 2 = 2*m. Let n be s(m). Factor -n*k**2 + 3*k**2 + 6*k**3 - 4*k**2 - 3*k**4.
-3*k**2*(k - 1)**2
Let h = 19 + 45. Let g be 3*(1 + 1 + -1). Factor 0*s**2 - h + 10*s - g*s**2 - 42*s - s**2.
-4*(s + 4)**2
What is w in -3/7*w**3 + 12/7*w + 18/7*w**2 - 24/7 - 3/7*w**4 = 0?
-2, 1, 2
Let y(i) be the second derivative of -i**7/189 + i**6/135 + 57*i. What is d in y(d) = 0?
0, 1
Factor -15*g**4 + 32*g**3 - 2777*g - 2*g**2 - 10*g**2 + 2*g**5 + 2761*g.
g*(g - 4)*(g - 2)**2*(2*g + 1)
Let q be -3*21/(-18) - (-7)/(-14). Let d be (2/(-4))/(q/20*-5). Determine o so that -d*o**2 + 2*o - 4/3 = 0.
1, 2
Factor 8*r**2 + 2/15 + 122/15*r.
2*(r + 1)*(60*r + 1)/15
Factor 0 + 4*v**3 - 1/2*v**2 + 0*v + 3*v**5 - 13/2*v**4.
v**2*(v - 1)**2*(6*v - 1)/2
Let p(i) be the first derivative of -i**6/45 + 4*i**5/25 - 2*i**4/5 + 4*i**3/9 - i**2/5 + 31. Let p(a) = 0. Calculate a.
0, 1, 3
Let s = -83 + 102. Find l, given that -s - 7*l**3 + l**2 - 20 - l**5 + 8*l - 5*l**4 + 43 = 0.
-2, -1, 1
Let x(g) = -2*g**3 - g**2 + g. Let l(i) = 10*i**3 - 34*i**2 + 6*i. Let d(y) = l(y) + 3*x(y). Determine u so that d(u) = 0.
0, 1/4, 9
Let x(o) be the second derivative of 6/5*o**2 - 9*o - 1/10*o**4 - 5 - 1/5*o**3. Factor x(l).
-6*(l - 1)*(l + 2)/5
Suppose m**5 - m**3 + 248*m**4 + 359*m**3 + 289*m + 612*m**2 - 212*m**4 = 0. What is m?
-17, -1, 0
Suppose 21 = h - 0*h + 3*s, -5*h - 3*s = -45. Let r**3 - 3*r**3 + 2 + r - h*r**2 + 4 + r = 0. Calculate r.
-3, -1, 1
Solve -1/2*t**3 + 1/4*t**5 + 13/2 + 13/2*t**4 - 13*t**2 + 1/4*t = 0 for t.
-26, -1, 1
Let o(c) be the first derivative of 5*c**3/3 + 50*c**2 - 220*c + 347. Factor o(t).
5*(t - 2)*(t + 22)
Suppose -2*d = 5*b - 58, -2*d - 16*b + 14*b + 34 = 0. What is u in -1/2*u**2 + d*u - 81/2 = 0?
9
Factor 0*j**2 + 4*j**2 - 26*j**2 + 5*j**2 + 65*j + 70 + 12*j**2.
-5*(j - 14)*(j + 1)
Factor 1/3*s**3 + 17/3*s + 6*s**2 + 0.
s*(s + 1)*(s + 17)/3
Determine b, given that 118 + 68*b**2 + b**2 - 142 - 15*b**3 - 30*b = 0.
-2/5, 1, 4
Let y be 1190/105 + 9/(-1). Factor -d**4 - 2/3*d - y*d**2 - 8/3*d**3 + 0.
-d*(d + 1)**2*(3*d + 2)/3
Let c(b) be the second derivative of -b**7/357 - 4*b**6/255 + b**5/85 + 2*b**4/17 - 3*b**3/17 - 26*b - 2. Let c(p) = 0. Calculate p.
-3, 0, 1
Factor -24/5*v**4 + 192/5*v - 4/5*v**5 - 32/5*v**3 + 128/5 + 64/5*v**2.
-4*(v - 2)*(v + 2)**4/5
Let c = 19538/3 + -6512. Factor 1/3*n + 1/3*n**2 - c.
(n - 1)*(n + 2)/3
Let s(c) = 5*c**2 + c + 2. Let m(g) = -11*g**2 - g - 4. Let l(k) = 3*m(k) + 7*s(k). Factor l(h).
2*(h + 1)**2
Let a(i) be the third derivative of 1/20*i**5 + 0*i**3 + 2*i**2 + 0 + 0*i - 1/8*i**4. What is h in a(h) = 0?
0, 1
Let g(u) be the first derivative of -6 + 1/36*u**4 - 6*u + 0*u**2 + 1/90*u**6 + 1/30*u**5 + 0*u**3. Let t(j) be the first derivative of g(j). Factor t(q).
q**2*(q + 1)**2/3
Let v be (-24)/(-15) + 4/10. Let w = 5 + -5. Solve u**4 + 4*u**v + 2*u**5 - 5*u**4 + w*u**5 - 2*u = 0.
-1, 0, 1
Let y(k) = k**3 + 25*k**2 + 4*k + 102. Let j be y(-25). Factor 0 - 3/5*t**j + 21/5*t.
-3*t*(t - 7)/5
Let u(x) be the first derivative of -x**5/210 + 4*x**3/21 - 2*x**2 - 9. Let i(r) be the second derivative of u(r). Factor i(d).
-2*(d - 2)*(d + 2)/7
Let m(n) be the first derivative of -3*n**4/4 - n**3 + 3*n**2/2 + 3*n + 104. Factor m(x).
-3*(x - 1)*(x + 1)**2
Suppose 8*u - 3*u = -4*o + 28, 5*u = 4*o - 28. Let 9 + o - 3*k**2 - 4 = 0. What is k?
-2, 2
Let u = 39 + 53. Let b be 9 + -5 - u/24. Let -b + 1/3*d - 1/6*d**2 = 0. Calculate d.
1
Let s(u) = -u**2 + 8*u - 1. Let r(m) be the third derivative of m**4/12 + 30*m**2. Let a(q) = 3*r(q) - s(q). Find p, given that a(p) = 0.
1
Let u(r) be the first derivative of -r**6/330 + r**5/110 - r**4/132 - 3*r + 13. Let o(v) be the first derivative of u(v). Factor o(z).
-z**2*(z - 1)**2/11
Let f = 3911 - 629673/161. Let k = 153/644 - f. Factor 0 - 1/2*l**2 + 1/4*l + k*l**3.
l*(l - 1)**2/4
Suppose -3*r + 0*d - 4*d = -744, 0 = -r + 4*d + 264. Let o = -1761/7 + r. Factor 0 + 0*f - o*f**2 + 3/7*f**4 - 3/7*f**3 + 3/7*f**5.
3*f**2*(f - 1)*(f + 1)**2/7
Find z, given that -1/2*z + 0 + 1/3*z**5 + 7/6*z**2 + 1/6*z**3 - 7/6*z**4 = 0.
-1, 0, 1/2, 1, 3
Let b be (-4)/(-10) - (-23)/5. Suppose -18*v - 28 = -25*v. Factor -g - b*g + 0*g**2 - v - 2*g**2.
-2*(g + 1)*(g + 2)
Solve 20*n**2 + 51*n**3 + 8*n**5 - 99*n**3 - 3*n + 4*n**4 + 8*n**5 + 11*n = 0 for n.
-2, -1/4, 0, 1
Factor 41 - 2*f + 10*f**2 + 10*f - 2*f - 45.
2*(f + 1)*(5*f - 2)
Factor -2/3*q**2 + 20/3*q + 26.
-2*(q - 13)*(q + 3)/3
Let k = 145 - 100. Factor -2*u**4 - 3*u**3 - k*u**5 + 20*u**5 + 24*u**5 + 6*u**4.
-u**3*(u - 3)*(u - 1)
Let z(i) = -i**3 + i**2 - 1. Let h(p) = 23*p**3 - 238*p**2 + 660*p + 183. Let y(w) = h(w) + 3*z(w). Suppose y(s) = 0. What is s?
-1/4, 6
Let u(q) be the first derivative of -2*q**3 - 12*q + 4*q**3 - 3*q**3 - 3 - 6*q**2 - 12. Factor u(l).
-3*(l + 2)**2
Suppose 7*c = -2*l + 3*c - 32, -l - 30 = -5*c. Let j be (112/(-60) - -4) + l/15. Factor -4/5*g**2 + 4/5*g + j - 4/5*g**3.
-4*(g - 1)*(g + 1)**2/5
Let i(w) be the third derivative of 0*w - 1/300*w**5 + 17*w**2 - 49/30*w**3 + 0 + 7/60*w**4. Find y, given that i(y) = 0.
7
Let u(l) = 16*l - 27. Let o(k) = 4*k - 7. Let x(t) = 9*o(t) - 2*u(t). Let i be x(3). Factor -2*b**5 + 55 + 2*b**4 - 55 - 2*b**2 + 2*b**i.
-2*b**2*(b - 1)**2*(b + 1)
Let g(n) = -n**3 + 6*n**2 - n - 2. Let c be g(5). Suppose 2*d + 5*p = -2, 3*d + d - p - c = 0. Solve -3/4*u + 1/2*u**d + 3/4*u**3 - 1/4*u**2 - 1/4 = 0 for u.
-1, -1/2, 1
Suppose -30*g**3 - 6*g**2 + 68*g**3 - 41*g**3 + 24*g = 0. What is g?
-4, 0, 2
Let h = 26281/60 + -438. Let z(q) be the second derivative of -1/24*q**4 + 0 + 0*q**2 - 1/120*q**5 + 5*q + 1/36*q**3 + h*q**6. Factor z(p).
p*(p - 1)*(p + 1)*(3*p - 1)/6
Let b be 2/(-6) + (-418)/6