50. Let t(n) = -n**2 - 10*n + 2. Let m be t(a). Factor -3*o + 0 - 3/2*o**m.
-3*o*(o + 2)/2
Let u(k) = 12*k**3 - 5*k + 8*k**5 + 17*k**2 + 7*k - 20 + 3. Let h(a) = 3*a**5 + 4*a**3 + 6*a**2 + a - 6. Let r(m) = 11*h(m) - 4*u(m). Find c such that r(c) = 0.
-1, 1, 2
Let v(w) = w**4 + w**2 + w + 1. Let l(a) = 21*a**2 + 7*a**4 - 74 + 0*a**4 + 83 + 5*a**4 + 9*a + 12*a**3. Let c(q) = l(q) - 9*v(q). Let c(r) = 0. Calculate r.
-2, 0
Let q(c) = -4*c**3 + c**2 - c - 2. Let z be -3 - (-4 + 2 + 0). Let x be q(z). Let 33*v**4 + 9*v - 12*v**3 + x*v**2 - 8 - 29*v**4 + 3*v = 0. What is v?
-1, 1, 2
Suppose 0*j + 3*j - 15 = 0. Suppose -j*s - 8 = -7*s. Factor -3/2*n**5 + 3*n**2 - 3*n**s + 0 + 0*n**3 + 3/2*n.
-3*n*(n - 1)*(n + 1)**3/2
Let t(b) be the third derivative of b**6/180 + b**5/45 - 7*b**4/36 + 4*b**3/9 + 14*b**2 + 5. Suppose t(n) = 0. Calculate n.
-4, 1
Suppose 441*v - 227*v = 0. Determine j so that 3/5*j**5 + v - 12/5*j**4 + 24/5*j - 9/5*j**3 + 6*j**2 = 0.
-1, 0, 2, 4
Let q(p) be the second derivative of 13*p**7/10080 - p**6/120 - p**5/120 + 3*p**4/4 + 29*p. Let i(j) be the third derivative of q(j). Let i(y) = 0. What is y?
-2/13, 2
Let c(s) = 2*s**3 - 2*s**2 + s - 5. Let d(v) = -v**3 + v**2 - v + 4. Let b(n) = 2*c(n) + 3*d(n). Let m be b(0). Let -4/5 - 6/5*l - 2/5*l**m = 0. Calculate l.
-2, -1
Let s(u) be the third derivative of u**8/840 + 8*u**7/75 + 166*u**6/75 - 112*u**5/5 + 60*u**4 + 3*u**2 + 127. Let s(k) = 0. What is k?
-30, 0, 2
Solve -945*x - 330*x**3 + 810*x**2 + 17 - 5*x**5 + 135 + 253 + 65*x**4 = 0.
1, 3
Let k be (-31)/(-7) - 5*40/50. Factor 9/7*n**2 + k*n**3 + 6/7*n + 0.
3*n*(n + 1)*(n + 2)/7
Let b = 91162/7 + -13023. Factor -4/7 + 1/7*g**2 - b*g**3 + 4/7*g.
-(g - 2)*(g - 1)*(g + 2)/7
Let -1/2*u**2 + 19/2*u + 33 = 0. Calculate u.
-3, 22
Suppose 0 = 413*l - 269 - 557. Let 16/13 + 2/13*f**l - 18/13*f = 0. What is f?
1, 8
Suppose 5*h - 20 = 0, j + 32 = 3*j + 3*h. Find b such that j - b + 5*b**5 - 11*b + 10*b**4 - 10*b**3 + 27*b - 10*b - 20*b**2 = 0.
-2, -1, 1
Let o(h) = -h**2 + 5*h + 2. Let f be o(5). Let b be 0 - (-3 + 3 + -3). Factor 6*z**b + z**f + 3*z - 10*z**3 - 9*z**2 + 9*z.
-4*z*(z - 1)*(z + 3)
Let j(f) be the first derivative of -2*f**7/105 - f**6/5 - 4*f**5/5 - 5*f**4/3 - 2*f**3 + 7*f**2/2 - 12. Let v(u) be the second derivative of j(u). Factor v(k).
-4*(k + 1)**3*(k + 3)
Suppose -3*d = h + 2, 5*d = h + 6 - 20. Find w, given that 0*w + 0*w - 2*w - h*w**2 + 8 - 2*w = 0.
-2, 1
Let x(a) be the first derivative of -1/15*a**3 + 0*a - 2/5*a**2 + 22. Factor x(o).
-o*(o + 4)/5
Solve 3*b**2 - 2*b**3 - 6*b**2 - 281 + 3*b**3 + 285 = 0 for b.
-1, 2
Determine z, given that 1/2*z**4 - 2 + 3/2*z**2 - 2*z + 2*z**3 = 0.
-2, -1, 1
Let p be 3*16/(-3)*(-24)/144. Factor 2*l**2 - 2/3*l**4 - 4/3*l**3 - 8/3 + p*l.
-2*(l - 1)**2*(l + 2)**2/3
Let m(h) be the first derivative of h**2/2 - 13*h - 3. Let o be m(14). Factor -1 - o - 2*i**3 + 6*i**2 - 6.
-2*(i - 2)**2*(i + 1)
Suppose -1/2*o**2 + 1 - 1/2*o = 0. What is o?
-2, 1
Let z be ((-7)/(-385))/(0 - (-3)/30). Suppose z*f**2 + 4/11*f - 6/11 = 0. What is f?
-3, 1
Let w = 40029 + -40029. Factor -2/11*t**2 + 0 - 8/11*t**3 - 6/11*t**4 + w*t.
-2*t**2*(t + 1)*(3*t + 1)/11
Suppose -39*s + 6*s = 0. Factor 0 + s*d + 4/7*d**2 - 2/7*d**3 - 2/7*d**4.
-2*d**2*(d - 1)*(d + 2)/7
Let q be ((180/27)/(-5))/((70/(-24))/5). Factor -24/7*l**3 + 4/7*l**4 + 0 - q*l + 36/7*l**2.
4*l*(l - 4)*(l - 1)**2/7
Let k(b) = -2*b**3 - 10*b**2 + b + 3. Let w be k(-8). Let s = w - 5683/15. Factor -4/15 + 4/15*i**2 - 2/15*i**3 + s*i.
-2*(i - 2)*(i - 1)*(i + 1)/15
Suppose -3*k - 14 = -29. Let c be 4 + -1 - (6 - k). Let -3 - w**2 - 8*w + 4*w**c + 15 + 20*w = 0. Calculate w.
-2
Let l be (4/(-21))/(-16 + 14). Let -2/21 - l*i**2 + 4/21*i = 0. What is i?
1
Factor -361 + 847*b**2 + b - 848*b**2 + 37*b.
-(b - 19)**2
Let w(k) be the first derivative of -k**6/120 - k**5/30 - k**4/24 + 9*k**2/2 + 15. Let p(t) be the second derivative of w(t). Determine v, given that p(v) = 0.
-1, 0
Let d(y) be the first derivative of -y**7/1260 + y**6/720 + 5*y**2 - 5. Let v(x) be the second derivative of d(x). Factor v(m).
-m**3*(m - 1)/6
Let o(s) = s**3 - 3*s**2 + s - 1. Let q be o(3). Suppose -q*i = 3*i + 2*m - 70, 60 = 5*i + 4*m. Factor 17*n + i*n - 11*n - 8 + 6*n**2.
2*(n + 4)*(3*n - 1)
Let f(j) = -5*j + 6. Let y be f(-2). Suppose 2*t - y = t. Factor -2*s**5 + 8*s**3 - 12 + 4*s**4 + 12 - t*s**2.
-2*s**2*(s - 2)**2*(s + 2)
Let u be 600/(-420)*(-4)/10. Factor -u*z + 2/7 - 2/7*z**2 + 4/7*z**3.
2*(z - 1)*(z + 1)*(2*z - 1)/7
Let k(h) be the second derivative of 2/3*h**2 - 1/18*h**4 + 1/9*h**3 - 7*h + 0. What is v in k(v) = 0?
-1, 2
Let q(o) be the second derivative of -o**5/390 + o**4/52 - 2*o**3/39 - 4*o**2 - 22*o. Let p(t) be the first derivative of q(t). Factor p(a).
-2*(a - 2)*(a - 1)/13
Solve -9/2*o + 3*o**2 - 7 + 1/2*o**3 = 0 for o.
-7, -1, 2
Let j(w) = -110*w**2 + 110*w + 220. Let d(z) = -5*z**2 + 5*z + 10. Let f be 3/(-2)*32/(-24). Let v(b) = f*j(b) - 45*d(b). Determine y, given that v(y) = 0.
-1, 2
Let f be (1 - -2) + 3 + -5. Let s be f/4 + 45/12. Let -2 + s*i**2 - 3*i - 4*i**2 + 4 + i**2 = 0. Calculate i.
1, 2
Suppose 0 = -0*o + 9*o - 189. Suppose 5*x - 31 + o = 0. Solve -x*v**3 - 1/2*v**4 - v - 5/2*v**2 + 0 = 0.
-2, -1, 0
Let w(s) = s**4 + 14*s**3 + 29*s**2 + 44*s + 18. Let l(u) = u**3 + u. Let k(v) = 5*l(v) - w(v). Factor k(f).
-(f + 1)*(f + 2)*(f + 3)**2
Let u be (32/48*(-3)/39)/(3/(-81)). Factor -2/13*v**2 - 20/13*v - u.
-2*(v + 1)*(v + 9)/13
Let o(w) be the second derivative of -2*w**7/21 + 2*w**6/5 + 3*w**5 + 17*w**4/3 + 4*w**3 + 79*w + 2. Suppose o(z) = 0. Calculate z.
-1, 0, 6
Let y(z) be the second derivative of 0*z**2 + 16/105*z**6 + 0*z**4 - 6*z + 0 + 18/7*z**3 - 18/35*z**5 - 2/147*z**7. Find k, given that y(k) = 0.
-1, 0, 3
Let g = 132/893 - 2/47. Factor -2/19*z**3 + g*z**4 + 0*z**2 + 0*z + 0.
2*z**3*(z - 1)/19
Let h = 62/11 + -175/33. Let p(g) be the first derivative of 1/9*g**3 + 4 - 1/3*g**2 + h*g. Determine q, given that p(q) = 0.
1
Let 0 + 1/6*x**5 + 0*x + 0*x**2 + 1/3*x**4 - 1/2*x**3 = 0. Calculate x.
-3, 0, 1
Suppose -42 - 6 = -4*g. Find k such that 2*k + 11*k**2 - g*k**3 + 13 - 4 - 10 = 0.
-1/3, 1/4, 1
Factor 3*s**2 + 43/3*s - 10/3.
(s + 5)*(9*s - 2)/3
Suppose c = -2977*b + 2973*b - 34, 2*b + 12 = -3*c. Solve 8/3*h**c - 8/3 - 2/3*h + 2/3*h**3 = 0.
-4, -1, 1
Let i(w) be the first derivative of -4*w**3/3 - 30*w**2 - 56*w - 153. Find l such that i(l) = 0.
-14, -1
Suppose -84*o + 75*o = -18. Let r(p) be the second derivative of 0*p**o + 0 - 5/18*p**4 - p - 2/15*p**5 - 1/45*p**6 - 2/9*p**3. Solve r(d) = 0.
-2, -1, 0
Suppose 0 = -3*j + 24. Suppose 4*c - 18 = 5*a, -5*c + j = -3*a + 4*a. Determine h so that -3*h**4 + 2*h**5 + 7*h - 3*h**5 - 7*h - c*h**3 = 0.
-2, -1, 0
Let n = 135 - 78. Let y = n + -54. Factor 0*l - 2/5*l**4 - 4/5*l**y - 2/5*l**2 + 0.
-2*l**2*(l + 1)**2/5
Suppose 2*m - 5 = -5*l - 3*m, m + 14 = 4*l. Suppose -q + 29 = l*q - 3*t, -5*q = -4*t - 36. Factor 14*a - 8*a + 4*a**4 - 10*a**3 - 8*a + q*a**2.
2*a*(a - 1)**2*(2*a - 1)
Solve -4/7*h**3 + 0*h + 36/7*h**2 + 0 = 0.
0, 9
Let w(g) be the first derivative of 4*g**5/25 + 8*g**4/5 - 176*g**3/15 + 96*g**2/5 - 162. Let w(r) = 0. Calculate r.
-12, 0, 2
Let d = -3 + 17. Let m = d + -11. Suppose -w**3 + 12*w**2 - 2*w**3 - 3*w**2 + 0*w**m - 9*w + 3 = 0. Calculate w.
1
Let x = 7244 + -28851/4. Find h such that x + 4*h**3 + 45/2*h**2 + 50*h + 1/4*h**4 = 0.
-5, -1
Let i(f) be the third derivative of -f**8/1344 + f**7/168 - 3*f**6/160 + 7*f**5/240 - f**4/48 - 93*f**2 - 1. Let i(l) = 0. Calculate l.
0, 1, 2
Let q(i) be the second derivative of -5*i**4/42 - 4*i**3/9 + 4*i**2/21 - 42*i. Factor q(m).
-2*(m + 2)*(15*m - 2)/21
Let l(i) = i**5 + i**4 - i**2 + 2*i. Let s(c) = -2*c**5 + 32*c**4 + 76*c**3 - 748*c**2 + 1114*c - 484. Let r(f) = -4*l(f) - s(f). Suppose r(p) = 0. Calculate p.
-11, 1, 2
Suppose -3 - 7466*a**2 + 7450*a**2 - 11 - 29*a - a**3 = 0. Calculate a.
-14, -1
Suppose -4*c = 5*b - 51, -14*b = -15*c + 10*c + 3. Factor 6/13*u**2 + 10/13*u**b - 4/13*u + 0.
2*u*(u + 1)*(5*u - 2)/13
Let k(a) = 3*a**2 + 142*a + 1583. Let d(l) = 3*l**2 + 141*l + 1584. Let q(n) = -4*d(n) + 3*k(n). Determine y, given that q(y) = 0.
-23
Let b = 2/15499 - -15495/30998. Factor 867/2*y + b*y**3 + 4913/2 + 51/2*y**2.
(y + 17)**3