6
Let c(a) be the third derivative of a**5/300 - 3*a**4/10 - 37*a**3/30 - 6*a**2 - 4*a + 60. Solve c(n) = 0.
-1, 37
Let m(l) be the second derivative of 1/21*l**4 + 0 - 84*l - 6/7*l**2 + 4/21*l**3. What is i in m(i) = 0?
-3, 1
Let h(i) be the second derivative of i**5/40 - 11*i**4/8 + 67*i**3/6 + 42*i**2 - 2*i - 34. Suppose h(t) = 0. Calculate t.
-1, 6, 28
Let p(f) = -f**3 - 9*f**2 - 18*f + 5. Let v be p(-6). Solve -60*t + v*t**2 - 52 + 5 - 18 = 0 for t.
-1, 13
Let l(t) be the second derivative of 1/6*t**4 - 4*t - 1/15*t**6 - 2*t**5 + 0*t**2 - 7 + 20/3*t**3. Suppose l(h) = 0. What is h?
-20, -1, 0, 1
Let k(h) = -h + 23. Let z be k(9). Suppose 0 = -0*o - z*o + 56. Suppose -429*g + 119*g**2 - 39*g**2 - 4*g**3 + 409*g - 105*g**o - g**3 = 0. What is g?
-1, 0, 2/7, 2/3
Factor 1/2*w**2 - 39/2 - 19*w.
(w - 39)*(w + 1)/2
Suppose 1211*j + 12 = 1217*j. Let l(q) be the second derivative of -29*q - 1/8*q**j + 0 + 0*q**3 + 1/48*q**4. Let l(r) = 0. What is r?
-1, 1
Let x(c) = -9*c**2 - 679*c - 12574. Let d be x(-33). Factor 0 + 6*b - d*b**2 - 11/2*b**3.
-b*(b + 6)*(11*b - 2)/2
Let q(t) be the third derivative of t**6/48 - 7*t**5/2 + 275*t**4/16 - 205*t**3/6 + 171*t**2. Factor q(u).
5*(u - 82)*(u - 1)**2/2
Factor 0*s**3 + 0 + 9*s**4 + 0*s - 3/4*s**5 + 0*s**2.
-3*s**4*(s - 12)/4
Determine t so that 93/4*t - 15/4*t**3 - 9/2 - 3*t**2 = 0.
-3, 1/5, 2
Let f(w) be the third derivative of w**6/300 - w**5/25 - 3*w**4/20 + 18*w**3/5 + 664*w**2 + 1. Factor f(s).
2*(s - 6)*(s - 3)*(s + 3)/5
Determine l, given that 94/3*l + 556/9 + 2/9*l**2 = 0.
-139, -2
Suppose 91*l + 97156 = 97429. Factor 1/3 + 10*p**2 + 3*p**5 + 11*p**4 + l*p + 46/3*p**3.
(p + 1)**3*(3*p + 1)**2/3
Let k(c) be the second derivative of 2*c**7/21 + 16*c**6/5 + 66*c**5/5 + 64*c**4/3 + 14*c**3 + 894*c. Let k(z) = 0. What is z?
-21, -1, 0
Let g(z) be the second derivative of -19*z**4/12 + 191*z**3/12 - 5*z**2/4 - 1067*z. Determine i so that g(i) = 0.
1/38, 5
Let d be (9/15)/((-3)/(-30)). Suppose -3*x - 6 = 0, -3*m + d = -2*m - 2*x. Factor 4*w + 7*w - 7*w - 2*w**3 + 2*w**m + 0*w.
-2*w*(w - 2)*(w + 1)
Let c(t) be the second derivative of t**5/10 + 17*t**4/6 - t**3/6 - 7*t**2 + 26*t. Let r be c(-17). Find x, given that -r*x - 3 - 22 + 2*x**2 + 7*x + 9 = 0.
-4, 2
Let u(c) be the third derivative of c**6/80 - 29*c**5/4 + 863*c**4/16 - 287*c**3/2 - 2*c**2 + 3109*c. Factor u(j).
3*(j - 287)*(j - 2)*(j - 1)/2
Let d = 228/845 + -818/9295. Determine y so that 4/11*y - 2/11*y**3 + 0 + d*y**2 = 0.
-1, 0, 2
Let k(z) be the first derivative of -27/32*z**4 - 96 - 1/48*z**6 + 0*z - 9/40*z**5 + 0*z**2 - 9/8*z**3. Factor k(s).
-s**2*(s + 3)**3/8
Suppose 0 - 63845*s + 61585/2*s**2 + 5/2*s**4 + 560*s**3 = 0. Calculate s.
-113, 0, 2
Suppose 2*n - 7378 = 5*y - 0*n, 3*y + n = -4429. Let b be 2/(-12)*y/328. Solve 49/4*u**4 - b*u**2 - 35/2*u**3 + 5*u + 1 = 0 for u.
-2/7, 1
Let l(q) be the first derivative of -33 + 167 + 6*q**3 - 15*q**2 + q**3 - 2*q**3 - 6*q**3. Factor l(m).
-3*m*(m + 10)
Factor 0 + 429*u**2 + 1143/8*u + 9/8*u**3.
3*u*(u + 381)*(3*u + 1)/8
Let i be (-2 - 0)*(-327)/218. Let p(f) be the second derivative of -56*f**4 - 49/5*f**5 - 32*f**2 + 21*f + 0 + 72*f**i. Let p(s) = 0. What is s?
-4, 2/7
Let s = 565 + -566. Let z be (s - -2)*(-84)/(-28). Factor -1/10*t**z + 1/10*t + 0 + 0*t**2.
-t*(t - 1)*(t + 1)/10
Factor 0 - 81/7*v + 18/7*v**4 - 18/7*v**2 + 80/7*v**3 + 1/7*v**5.
v*(v - 1)*(v + 1)*(v + 9)**2/7
Let p(f) = -30*f - 13. Let d be p(-1). Factor 39*z**2 - 81*z**2 + 43*z**2 - d*z.
z*(z - 17)
Let v(s) = -s**2 + 3*s + 13. Let a be v(5). Find y such that 11*y**5 + 16*y**5 + 3*y**4 + 99*y**4 + 79*y**3 - 48*y**a + 53*y**3 - 24*y**2 = 0.
-2, 0, 2/9
Suppose 1338 = 82*t + 141*t. Let l(c) be the third derivative of -1/420*c**t - 3*c**2 - 1/210*c**5 + 1/42*c**4 + 0 + 0*c**3 + 0*c. Factor l(r).
-2*r*(r - 1)*(r + 2)/7
Let k be (-538)/732 - 190/(-228). Let j = k - -104/183. Factor -j*z**3 - 10/3*z - 4/3 - 8/3*z**2.
-2*(z + 1)**2*(z + 2)/3
Let q = -224 - -231. Solve -q*h**3 + 3*h**4 - 12*h**3 - 4*h - 4*h**2 - 3*h**5 + h**4 + 26*h**3 = 0.
-1, -2/3, 0, 1, 2
Let r be 7 + -3 - (-918)/(-368). Let c = -1/184 + r. Factor 9/2*d**2 - c*d**4 + 3*d + 0 + 0*d**3.
-3*d*(d - 2)*(d + 1)**2/2
Let q(p) = -4*p**3 + 8*p - 2. Let s be q(-3). Let v = 414/5 - s. Let 3/5*b**2 + 0 + 0*b + 1/5*b**4 + v*b**3 = 0. Calculate b.
-3, -1, 0
Suppose 4*h - 25 = 5*h. Let o be 1*(4 + -3) - (h - 1). Determine i so that 4*i**2 + 12*i**5 - 8*i + 44*i**3 - 21*i**4 + 8*i**4 + o*i**4 + 30*i**4 = 0.
-2, -1, 0, 1/3
Factor -81*i**3 - 19052*i**2 - 47*i - 504 + 968*i - 3*i**4 + 18719*i**2.
-3*(i - 1)**2*(i + 8)*(i + 21)
Let f(x) = 18*x**2 + 21*x - 125. Let s(w) = -110*w**2 - 125*w + 750. Let d(v) = -11*v**2 + 97*v + 22. Let i be d(9). Let q(o) = i*s(o) + 25*f(o). Factor q(p).
5*(p + 5)*(2*p - 5)
Let x(q) be the second derivative of q**4/20 + 73*q**3/2 - 549*q**2/5 - 29*q - 10. Factor x(v).
3*(v - 1)*(v + 366)/5
Let h(u) = u**3 - 20*u**2 - 9*u - 10. Let x be h(20). Let o be (-589)/x + 3/(-5). Let -5/2*d - 20*d**4 + 5/2*d**3 + 10*d**5 + 25/2*d**2 - o = 0. What is d?
-1/2, 1
Find r such that -34*r**3 + r**3 + 385*r - 27*r**3 - 200*r**2 - 68*r**3 + 10 - 67*r**3 = 0.
-2, -1/39, 1
Let s(i) be the first derivative of -2*i**6/3 - 1264*i**5/5 - 37446*i**4 - 7888624*i**3/3 - 77900162*i**2 + 68. Determine u, given that s(u) = 0.
-79, 0
Let a = 157 + -122. Find p such that -15 - a*p**2 + 3 - 15*p**3 + 32 = 0.
-2, -1, 2/3
Suppose -1848*t = 61946 - 61946. Factor 0 - 20/7*r**3 + t*r**2 + 0*r - 4/7*r**4.
-4*r**3*(r + 5)/7
Let h be 6 - (-27*(-4)/300)/(5/50). What is z in h*z + 3/5*z**2 + 12/5 = 0?
-2
Let w(f) be the first derivative of 0*f**3 - 16/5*f**5 + 0*f**2 - 7/6*f**6 - f**4 + 71 + 0*f. Factor w(x).
-x**3*(x + 2)*(7*x + 2)
Let x(s) = 4*s**2 - 464*s + 13450. Let o(a) be the first derivative of a - 283. Let l(t) = -6*o(t) - x(t). Find g such that l(g) = 0.
58
Factor 9*o**3 + 164*o + 13*o**3 + 51 + 8*o**3 + 117 + 48*o**2 - 26*o**3.
4*(o + 2)*(o + 3)*(o + 7)
Let y(d) be the second derivative of -d**4/42 + 214*d**3/21 - 3*d + 865. Find q such that y(q) = 0.
0, 214
Let w(t) = -t**2 - 10*t - 9. Let u be w(-13). Let a = 52 + u. Let a*b**2 - 7 - 1 + 4 = 0. What is b?
-1, 1
Factor 106 + 41 - 20*o + 3*o**2 - 35*o + 13*o.
3*(o - 7)**2
Let j(s) = 3*s**4 + s**3 - s**2 - s + 1. Let q(y) = -56*y**4 - 2496*y**3 - 7418*y**2 - 7420*y - 2499. Let v(b) = -76*j(b) - 4*q(b). Find o, given that v(o) = 0.
-1, 2480
Let l(t) be the first derivative of t**3/6 - 203*t**2/4 - 102*t + 1142. Factor l(u).
(u - 204)*(u + 1)/2
Factor -268/17*w + 8978/17 + 2/17*w**2.
2*(w - 67)**2/17
Let w = 55 + -47. Suppose -w = 4*h - 6*h. Factor 4*j**4 + j**5 + 4*j**h + 4*j**4 + j**2 - j**3 - 13*j**4.
j**2*(j - 1)**2*(j + 1)
What is p in -27*p**3 + 13/2*p**4 + 21/2 + 47*p**2 - 1/2*p**5 - 73/2*p = 0?
1, 3, 7
Let z(a) be the first derivative of -a**4 - 32*a**3/3 + 30*a**2 + 216*a + 1933. Factor z(o).
-4*(o - 3)*(o + 2)*(o + 9)
Factor -469/2 - 53/4*z + 1/4*z**2.
(z - 67)*(z + 14)/4
Let o(y) be the third derivative of y**7/350 - 33*y**6/200 + 81*y**5/20 - 2187*y**4/40 + 2187*y**3/5 - 710*y**2 + 2*y + 2. Determine t, given that o(t) = 0.
6, 9
Find a, given that 945 + 219*a + 0*a**2 + 2*a**2 + a**2 + 501*a + 483 = 0.
-238, -2
Let m = -5 - -7. Let f = 1181286/13 - 90868. Determine b, given that 4/13*b**3 + 0*b**m - 2/13*b**5 + 0 + 0*b + f*b**4 = 0.
-1, 0, 2
Let l = 34 + -33. Let i be (1 - -3 - -4) + l. Determine k, given that -i*k - 6 + 8 - 3*k**5 - 8 + 6*k**2 + 12*k**3 = 0.
-1, 1, 2
Let d = 1008 - 69. Let c = -1515 - -2454. Solve -4*s**3 + d + 12*s**2 - 8*s - c = 0.
0, 1, 2
Suppose -792 - 319*w**4 - 66*w**4 - 3192*w**3 - 2414*w - 758*w + 35*w**5 - 423*w**4 - 39*w**5 - 4768*w**2 = 0. What is w?
-198, -1
Let b = -429364 - -429366. Solve -b + 2/9*h**2 - 16/9*h = 0 for h.
-1, 9
Let a be 0/(-2)*3/(-9). Factor 4*x**2 - 17*x + a + x + 2*x**3 - 16 + 8*x.
2*(x - 2)*(x + 2)**2
Suppose 2433*z + 48 = 2449*z. What is u in -5/9*u - 2/9*u**2 + 1/9*u**z + 2/3 = 0?
-2, 1, 3
Let h be -7*(1590/35 - 46). What is d in 1/2*d**4 - h*d + 0 + 3/2*d**3 - 3*d**2 = 0?
-4, -1, 0, 2
Let r be 6144/(-1584)*39/(-52). Suppose 30/11 - r*y + 2/11*y**2 = 0. Calculate y.
1, 15
Solve -3/5*s**2 - 378/5 - 27*s = 0 for s.
-42, -3
Let b = -6 + 6. Suppose 0 = w + 3, -2*p + 16 = -0*