1/4 + v*d + 1/4*d**2 = 0.
-1, 1
Let x(n) be the second derivative of n**8/17640 - n**6/1260 - n**5/630 + 4*n**3/3 - 2*n. Let t(o) be the second derivative of x(o). Factor t(z).
2*z*(z - 2)*(z + 1)**2/21
Let c(y) be the second derivative of y**4/3 - 208*y**3/3 + 5408*y**2 + 307*y. Factor c(s).
4*(s - 52)**2
Let y(n) be the second derivative of 3*n**5/140 + 9*n**4/14 + 33*n**3/14 + 24*n**2/7 - 122*n. Solve y(h) = 0 for h.
-16, -1
Let i be (-168)/(-70)*10/4. Suppose 2*m - 2 = r - i, 3*r - 4*m - 10 = 0. Factor -3*v**r + 4 + 4*v**2 + 2*v - 7*v.
(v - 4)*(v - 1)
Let z(k) be the third derivative of k**6/540 - 2*k**5/135 + k**4/27 - 2*k**2 - 15*k. Factor z(w).
2*w*(w - 2)**2/9
Suppose -4*f = -2*f - 4*f - 4*f. Find n, given that f + 0*n**2 + 2/7*n**4 + 8/7*n - 6/7*n**3 = 0.
-1, 0, 2
Factor 0 + 14/5*m**2 + 6/5*m + 2*m**3 + 2/5*m**4.
2*m*(m + 1)**2*(m + 3)/5
Let g(q) be the third derivative of -q**8/1008 + q**7/315 + q**6/120 - 2*q**5/45 + q**4/18 - 108*q**2 - 1. Suppose g(b) = 0. Calculate b.
-2, 0, 1, 2
Let w(q) be the second derivative of 6*q**6/35 + 11*q**5/14 + 19*q**4/14 + q**3 + q**2/7 - 60*q. Factor w(p).
2*(p + 1)**3*(18*p + 1)/7
Let -490 + 15*h**2 - 95*h**2 + 385*h + 41*h**3 - 36*h**3 = 0. What is h?
2, 7
Let a(c) = -4*c + 8. Let o(s) = -s**3 + 4*s**2 - 4*s. Let h be o(3). Let r(z) = -z**2 - 5*z + 9. Let q(i) = h*a(i) + 4*r(i). Factor q(l).
-4*(l - 1)*(l + 3)
Let f(n) be the first derivative of -32/7*n - 2/21*n**3 + 8/7*n**2 - 13. What is j in f(j) = 0?
4
Let f = -215355/11 - -19579. Factor 8/11*v**2 - f*v + 6/11.
2*(v - 1)*(4*v - 3)/11
Let q = 4615 + -4612. Find o such that 1/2 + 15/2*o**2 - 13/2*o**q + 2*o**4 - 7/2*o = 0.
1/4, 1
Solve 2/9*i**4 + 44/3*i**3 + 0*i + 0 + 242*i**2 = 0.
-33, 0
Let k(p) be the second derivative of p**5/10 + 29*p**4/6 - 10*p**3 - 120*p - 1. Let k(s) = 0. What is s?
-30, 0, 1
Let h(f) be the second derivative of 0 + 1/25*f**5 - 9*f + 1/5*f**6 - 3/35*f**7 - 1/5*f**2 + 7/15*f**3 - 7/15*f**4. Determine a, given that h(a) = 0.
-1, 1/3, 1
Let c be (-22)/6 - (-29)/(-87) - -8. Let h(k) be the first derivative of -1/4*k**c + 1/2*k**2 + 0*k**3 + 0*k - 5. Factor h(v).
-v*(v - 1)*(v + 1)
Solve -6 - 291/5*f - 57/5*f**2 = 0.
-5, -2/19
Let l(m) be the first derivative of -45*m**4/4 - 122*m**3 + 357*m**2/2 + 54*m - 112. Factor l(n).
-3*(n - 1)*(n + 9)*(15*n + 2)
Let x(n) be the second derivative of n**7/420 - n**6/90 - n**5/60 + n**4/6 - 5*n**3/3 - 3*n. Let o(j) be the second derivative of x(j). Factor o(l).
2*(l - 2)*(l - 1)*(l + 1)
Let u(i) be the third derivative of -i**5/30 + i**4/6 - i**3/3 + 39*i**2. Determine k so that u(k) = 0.
1
Let o(s) = -s**2 - s - 1. Let u(i) = -i**2 + 5*i - 3. Let g(k) = -k**2 + 4*k - 2. Let n(d) = 4*g(d) - 5*u(d). Let q(z) = -n(z) + o(z). Factor q(h).
-2*(h - 2)**2
Let g(n) be the second derivative of 0*n**2 + 0 - 2*n - 1/12*n**4 + 1/12*n**3 + 1/40*n**5. Factor g(q).
q*(q - 1)**2/2
Suppose 0 = -75*x + 78*x - 5*l - 1, x - l = 1. Factor -2/3*o**x - 8/3 + 8/3*o.
-2*(o - 2)**2/3
Let v(s) = 17*s**3 - 93*s**2 + 213*s - 37. Let m(w) = -w**3 - w**2 - w + 1. Let z(p) = 5*m(p) + v(p). Find f such that z(f) = 0.
1/6, 4
Let k(r) be the third derivative of r**7/1260 + r**6/36 + 5*r**5/12 + r**4/6 + 10*r**2. Let t(x) be the second derivative of k(x). Determine f so that t(f) = 0.
-5
Let u = -11692 + 11694. What is x in -16/9 + 2/9*x**u - 4/9*x = 0?
-2, 4
Let s(m) = 4*m**3 - 33*m**2 + 75*m - 32. Let a(f) = -2*f**3 + 17*f**2 - 37*f + 16. Let j(y) = -14*a(y) - 6*s(y). Suppose j(c) = 0. What is c?
1, 8
Let 75/4*o**2 + 33/4 + 51/2*o + 3/2*o**3 = 0. What is o?
-11, -1, -1/2
Let z = -25703/8 + 3213. Determine h, given that 0 + 1/8*h - 3/8*h**3 - z*h**2 + 1/8*h**4 + 1/4*h**5 = 0.
-1, 0, 1/2, 1
Let v(k) be the third derivative of 0*k - 3*k**4 - 1/5*k**6 - 11/10*k**5 - 1/70*k**7 + 0 - 9/2*k**3 + 3*k**2. Factor v(x).
-3*(x + 1)**2*(x + 3)**2
Let b(h) be the second derivative of -h**4/12 - 2*h**3/3 - 3*h**2/2 + 6*h - 4. Determine o so that b(o) = 0.
-3, -1
Suppose 0 = 215*p - 210*p. Let h(x) be the second derivative of 0*x**3 + 1/28*x**4 - x + 0*x**2 + p. What is c in h(c) = 0?
0
Let a(i) be the first derivative of -1/14*i**4 + 0*i**2 + 0*i - 2/21*i**3 + 41. Factor a(r).
-2*r**2*(r + 1)/7
Let q = 38 + -17. Let s = 33 - q. What is z in 2*z - 6*z**2 + s*z**2 + z**3 - 3*z**2 = 0?
-2, -1, 0
Let w(o) be the third derivative of o**7/1365 - 7*o**6/780 + 7*o**5/195 - 2*o**4/39 + 179*o**2. Factor w(g).
2*g*(g - 4)*(g - 2)*(g - 1)/13
What is o in 5*o**3 + 45*o + 1/4*o**4 + 81/4 + 59/2*o**2 = 0?
-9, -1
Suppose c + 32 = 4*v + 5*c, 5*c = -3*v + 30. Suppose 0 = -4*r - r - 15, -23 = -4*g + v*r. Factor -j**2 - 3*j**3 + 12*j**g + j**2 - 12*j.
-3*j*(j - 2)**2
Let d be 164/287*14/4. Let z(c) = -c**3 + 4*c**2 + c - 1. Let x be z(4). Let -1/6*w**5 + 0 - 1/3*w**4 + 0*w**d + 0*w - 1/6*w**x = 0. Calculate w.
-1, 0
Let f(y) be the third derivative of y**8/6720 - y**7/420 + y**6/80 - y**5/30 - y**4/2 + 10*y**2. Let t(o) be the second derivative of f(o). Factor t(s).
(s - 4)*(s - 1)**2
Let j be (48/28)/((-1408)/(-2240)). Factor 26/11*c**2 + j*c**4 + 58/11*c**3 + 0 - 2/11*c.
2*c*(c + 1)**2*(15*c - 1)/11
What is p in 1/6*p**5 + 1/3*p**4 - 5/6*p**3 - 5/3*p**2 + 2/3*p + 4/3 = 0?
-2, -1, 1, 2
Let x(u) be the first derivative of -1/8*u**4 + 0*u - 1/5*u**5 + 0*u**2 - 1/12*u**6 + 4 + 0*u**3. Factor x(q).
-q**3*(q + 1)**2/2
Let -9/2*d + 3/4*d**3 + 0 + 15/4*d**2 = 0. Calculate d.
-6, 0, 1
Let t be ((-20)/35)/(((-8)/(-14))/(-2)). Suppose -2*o + 17 = t*o - 5*b, -13 = -3*o + 4*b. Factor 15/4*i**2 + 7/4*i**o + 1/4*i**4 + 0 + 9/4*i.
i*(i + 1)*(i + 3)**2/4
Let y(q) be the first derivative of 12 - q**3 + 0*q**2 - 1/5*q**5 + 0*q + q**4. Factor y(p).
-p**2*(p - 3)*(p - 1)
Let d = 40 + -61. Let c = d - -24. Factor 3*z**3 - 6*z**2 - 3*z**3 + 0*z**3 - 2*z**c - 4*z.
-2*z*(z + 1)*(z + 2)
Let z(l) be the second derivative of l**7/7 - 34*l**6/15 + 137*l**5/10 - 41*l**4 + 188*l**3/3 - 40*l**2 + 40*l. Let z(g) = 0. What is g?
1/3, 2, 5
Let p(f) be the second derivative of 5*f**9/2016 + f**8/140 + f**7/560 - f**6/120 - 7*f**3/2 + 4*f. Let m(a) be the second derivative of p(a). Factor m(g).
3*g**2*(g + 1)**2*(5*g - 2)/2
Let j(m) = -14*m**2 - 88*m - 392. Let u(l) = -108 - 153 - 9*l**2 - 10*l - 49*l. Let d(s) = 5*j(s) - 8*u(s). Factor d(x).
2*(x + 8)**2
Let s be 0/(-9) + (-25)/(-5). Let z(g) be the second derivative of -1/60*g**s + 1/18*g**3 + 1/6*g**2 - 1/36*g**4 + 5*g + 0. Find f, given that z(f) = 0.
-1, 1
Let u(m) = m**2 - 1. Let n(p) = -5*p**2 + 0*p**2 + 0 - p**2 - 3. Let g(r) = n(r) + 9*u(r). Factor g(j).
3*(j - 2)*(j + 2)
Let h(z) = -z**2 - 7*z. Let i be h(-7). Suppose -g - 5*f = -23, -g - 3*f + 11 = -f. What is l in l**g + 2*l**3 - 3*l**2 + i*l**3 = 0?
0, 1
Let v(f) be the first derivative of 0*f + 1/10*f**2 - 7 + 1/15*f**3. Let v(a) = 0. Calculate a.
-1, 0
Let a(v) be the third derivative of 13/60*v**6 + 2/35*v**7 + 13*v**2 + 1/168*v**8 + 0 + 0*v**3 + 1/3*v**4 + 2/5*v**5 + 0*v. Factor a(p).
2*p*(p + 1)**2*(p + 2)**2
Factor 5*j**2 - 240 + 8*j**2 - 5*j**2 + 0*j**2 - 3*j**2 - 110*j.
5*(j - 24)*(j + 2)
Let a be -1*6*(-10)/15. Suppose 0*q**a - 6*q + 13*q + q + 2*q**4 - 6*q**3 = 0. Calculate q.
-1, 0, 2
Let p = -168/17 + 1463/136. Let d(x) be the first derivative of 11/4*x**2 + x + p*x**4 + 5 + 8/3*x**3. Let d(z) = 0. Calculate z.
-1, -2/7
Suppose -60*n = -62*n + 14, -4*h = -4*n + 16. Solve 0 + 1/4*u**h + 1/2*u**2 - 3/4*u = 0.
-3, 0, 1
Determine z so that 43*z**3 + 37*z**3 + 11*z**5 + 35*z**3 + 149*z**3 - 27*z**5 - 188*z**2 - 92*z**4 + 32*z = 0.
-8, 0, 1/4, 1
Suppose -8 + 4*k**4 - 6*k**3 + k**4 + 6*k**2 + 4*k**4 - 10*k - 26*k + 35*k**3 = 0. Calculate k.
-2, -2/9, 1
Let u = -571/35 + 117/7. Let z = -1/97 + 199/485. Find q, given that z*q + u*q**2 + 0 = 0.
-1, 0
Let t = 83 - 170. Let k be 6/(-27) - t/27. Factor 6 + k*x**2 - 2 - 13 + 6*x.
3*(x - 1)*(x + 3)
Let t(i) = -i**3 - 36*i**2 + 101*i. Let q(n) = -3*n**3 - 90*n**2 + 252*n. Let x(k) = 5*q(k) - 12*t(k). Factor x(o).
-3*o*(o - 2)*(o + 8)
Let g(h) be the first derivative of 4/9*h**3 - h**2 + 2/3*h + 16. Find l such that g(l) = 0.
1/2, 1
Let b(v) = -3*v**3 - 2*v**2 - 8*v. Let j = 4 - 1. Let x = j - 8. Let z(k) = 2*k**3 + k**2 + 5*k. Let d(t) = x*b(t) - 8*z(t). Factor d(n).
-n**2*(n - 2)
Let n(p) be the third derivative of -p**8/2