*3
Let p(m) be the first derivative of m**4/2 + 8*m**3/3 + 4*m**2 - 135. Let p(o) = 0. Calculate o.
-2, 0
Suppose -2*c + t + 3*t = -24, 4*c = -2*t + 28. Let r be (16/20)/(c/60). Factor -7*h**4 - r*h**3 + h**4 + 8*h**4.
2*h**3*(h - 3)
Suppose 3*f + 24 = 6*f. Let o be (1 - 2) + (f - 5). Factor 69 - 69 + 2*r**o.
2*r**2
Let z(v) be the first derivative of 13 - 1/10*v**6 - 1/5*v**2 - 13/25*v**5 - 19/20*v**4 - 11/15*v**3 + 0*v. Find x such that z(x) = 0.
-2, -1, -1/3, 0
Let o(v) = 3*v**4 + 9*v**3 - 4. Suppose 5*a = c - 6, -3*c + 4*a - 3 - 1 = 0. Let m(d) = 1. Let r(h) = c*m(h) - o(h). Determine n so that r(n) = 0.
-3, 0
Find f, given that 356/7*f - 1/7*f**2 - 31684/7 = 0.
178
Let j(z) be the second derivative of z**7/840 + z**6/90 + z**5/40 - 3*z**3/2 - 15*z. Let u(l) be the second derivative of j(l). What is r in u(r) = 0?
-3, -1, 0
Let i(g) be the third derivative of g**8/392 + g**7/490 - g**6/20 - 19*g**5/140 - 3*g**4/28 + g**2 + 5*g. Suppose i(o) = 0. Calculate o.
-2, -1, -1/2, 0, 3
Let m(y) be the third derivative of -y**8/26880 - y**7/1680 - y**6/320 - 17*y**4/24 + 4*y**2. Let l(r) be the second derivative of m(r). Factor l(h).
-h*(h + 3)**2/4
Let p(l) = 2*l**3 - l - 1. Let o be p(-1). Let h be (-8)/(-3) + o/3. Determine x, given that -3*x - 3*x**2 + 4*x + 4*x**h + 0*x = 0.
-1, 0
Let r(f) = 4*f**5 + 4*f**4 + 2*f**3. Let s(p) = 9*p**5 + 7*p**4 + 2*p**3 - p**2. Let o(c) = 5*r(c) - 2*s(c). Factor o(a).
2*a**2*(a + 1)**3
Let o(t) be the third derivative of 1/16*t**4 + 0*t + 29*t**2 + 5/24*t**3 + 1/240*t**5 + 0. Find a such that o(a) = 0.
-5, -1
Factor -3*s**3 + 7*s**3 + 2*s + 4*s**2 - 4*s + 139 - 94*s + 5.
4*(s - 3)*(s - 2)*(s + 6)
Let m be (-88)/286 + (-142)/(-39). Factor 0 - 4*q**3 - m*q**2 - 2/3*q**4 + 0*q.
-2*q**2*(q + 1)*(q + 5)/3
Let q(z) be the second derivative of -z**5/20 + z**4/4 + z**3 - 4*z**2 + 32*z. Find t, given that q(t) = 0.
-2, 1, 4
Let u = -94 + 96. Factor -y - 2 + 2*y - u*y**2 + y**2 + 2*y**2.
(y - 1)*(y + 2)
Let r(a) be the second derivative of -5*a**7/112 - 27*a**6/40 + 213*a**5/160 - 3*a**4/8 - 2*a + 14. Let r(i) = 0. What is i?
-12, 0, 1/5, 1
Let d(n) be the second derivative of 4*n**6/3 + 9*n**5/5 - 3*n**4 - 10*n**3/3 + 6*n**2 + 32*n - 1. Find k such that d(k) = 0.
-1, 1/2, 3/5
Let b(m) be the first derivative of -3 + 2*m**2 + 3/40*m**4 + 1/200*m**6 - 1/10*m**3 - 3/100*m**5 + 0*m. Let z(i) be the second derivative of b(i). Factor z(g).
3*(g - 1)**3/5
Let m(v) be the second derivative of -1/30*v**5 - 1/120*v**6 + 0 + 0*v**4 - 2*v + 0*v**3 + 5/2*v**2. Let y(z) be the first derivative of m(z). Factor y(d).
-d**2*(d + 2)
Let s = 4220 + -4218. Determine u, given that -u + 9/2*u**3 + 5/2*u**5 + 1/2*u**s - 13/2*u**4 + 0 = 0.
-2/5, 0, 1
Suppose -22 + 19 = -x. Suppose x*m - 6*m + 3 = 0. Let n(p) = -4*p**2 + 4*p + 2. Let c(v) = v**2. Let t(g) = m*n(g) + 6*c(g). Solve t(q) = 0.
-1
Let q be (-12)/(-5) + 4/(-10). Let s be (-34)/(-14) - (-42)/(-28)*8/(-21). Determine n so that 2/3*n - 2/3 - 1/6*n**s + 1/6*n**q = 0.
-2, 1, 2
Let m(f) = f - 1. Let d be m(6). Suppose 47 + 19 = 22*g. Factor -2/5*s**d + 0*s**g + 0*s**2 + 0 + 2/5*s**4 + 0*s.
-2*s**4*(s - 1)/5
Factor -3*m**3 + 8*m**2 - 27*m + 65*m + 6 - 25*m + 0*m**3 + 4*m**3.
(m + 1)**2*(m + 6)
Determine m so that 0 + 1/2*m**3 - 6*m**2 + 11/2*m = 0.
0, 1, 11
Suppose -4*z - 3*z + 168 = 0. Let o be ((-6)/8)/(z/(-160)). Let k(i) = -i**2 + i - 2. Let t(l) = l**2. Let b(s) = o*k(s) + 10*t(s). What is f in b(f) = 0?
-2, 1
Let l(d) be the first derivative of -24 - 1/6*d**3 + 2*d + 0*d**2. What is g in l(g) = 0?
-2, 2
Let g(s) be the first derivative of s**4/4 - s**3 + 3*s**2/2 + 16*s - 19. Let k(q) be the first derivative of g(q). Let k(n) = 0. Calculate n.
1
Let n(d) = -d**2 + 633*d - 10472. Let o be n(17). Solve -3/5*q**2 + 9/5*q + o = 0.
0, 3
Let b(t) = t**4 - t**3 - t**2 - t - 1. Let q(s) = 8*s**4 - 13*s**3 - 3*s**2 - 3*s - 3. Let f(g) = -3*b(g) + q(g). Factor f(o).
5*o**3*(o - 2)
Let d(m) = 2*m**2 + 90*m + 794. Let x be d(-33). Solve 1/5*i - 2/5*i**x - 1/5*i**3 + 2/5 = 0 for i.
-2, -1, 1
Let a = -1007 + 1009. Let x = -17 - -24. Factor 6*p + 3 + 3*p**2 + x*p**2 - 7*p**a.
3*(p + 1)**2
Let j(s) be the first derivative of 2/55*s**5 + 2/11*s**3 + 0*s + 0*s**2 + 2/11*s**4 + 18. Find w such that j(w) = 0.
-3, -1, 0
Suppose 0 = -249*p + 321*p - 216. What is w in 0*w**p - 2/3 - 3*w + 4/3*w**4 - 11/3*w**2 = 0?
-1, -1/2, 2
Suppose k + 2*b = 11, 0 = -3*k + 8*k - 4*b - 27. Let v be 2398/2002 + (-3)/k. What is h in 0 - 6/13*h**3 + v*h**4 - 16/13*h**2 + 8/13*h + 4/13*h**5 = 0?
-2, 0, 1/2, 1
Factor 1/2*l**3 + 1089 + 957/2*l - 32*l**2.
(l - 33)**2*(l + 2)/2
Suppose 2*j = -2*t - 4, 5*j - 2*t - 22 + 4 = 0. Let y be 17 + -18 + j*2. Factor 3*m**y - 7*m**3 + 16*m**2 - 2 - 12*m + 2.
-4*m*(m - 3)*(m - 1)
Let f(t) = 3*t**3 - 103*t**2 - 71*t + 37. Let z be f(35). Factor 3/4*q**z - 3/2*q + 0 - 9/4*q**4 + 3*q**3.
-3*q*(q - 1)**2*(3*q + 2)/4
Determine t so that 7/2*t + 3 + 1/2*t**2 = 0.
-6, -1
Let w = 2567/20295 + 7/369. Let v = w - -36/55. Solve -3/5 - v*q - 1/5*q**2 = 0.
-3, -1
Let x be 66/385*56/18. Let 0 - x*o - 2/15*o**2 = 0. Calculate o.
-4, 0
Let n = -43 + 46. Let c(a) be the first derivative of -3/5*a + 2 + 2/5*a**2 - 1/15*a**n. Suppose c(p) = 0. What is p?
1, 3
Let k(a) be the third derivative of -a**5/330 - 7*a**4/66 - 49*a**3/33 - a**2 - 10*a. Let k(r) = 0. Calculate r.
-7
Let 32/7*a**3 - 816/7*a**2 - 52/7 - 414/7*a = 0. What is a?
-1/4, 26
Let j be ((-101)/16 - -2) + 4. Let q = 1/48 - j. Factor 1/6*b + q - 1/6*b**2.
-(b - 2)*(b + 1)/6
Let o(j) = 4*j**2 + 8*j + 6. Let m be (2 + 25/(-10))*2. Let t(f) = 1. Let l(c) = m*o(c) + 6*t(c). Factor l(b).
-4*b*(b + 2)
Let v be 1/((-10)/(-4))*25. Let i be (-2)/8 - v/(-40). Determine a so that -2/5*a**5 - 16/5*a**3 + 0 + i*a - 8/5*a**2 - 2*a**4 = 0.
-2, -1, 0
Let o = 71 - 59. Let 160*l + o - 73*l - 3*l**2 - 78*l = 0. What is l?
-1, 4
Let h(b) be the first derivative of -b**5/25 + 2*b**3/15 - b/5 - 74. Suppose h(u) = 0. What is u?
-1, 1
Let p = -131 - -186. Let f be 4/1 + (-160)/p. Factor -6/11*l**2 - 14/11*l + f.
-2*(l + 3)*(3*l - 2)/11
Let h(t) = t**4 - t**3 + t**2 - 1. Let c(s) = 4*s**4 + 167*s**3 + 9579*s**2 + 175446*s - 185196. Let f(i) = 4*c(i) - 12*h(i). What is y in f(y) = 0?
-57, 1
Let n = -73/119 - -25/17. Let b = -23/14 + 31/14. Factor -n*h + 2/7*h**2 + b.
2*(h - 2)*(h - 1)/7
Solve 7/2*w**3 + 0*w - 1/4*w**4 - 13/4*w**2 + 0 = 0 for w.
0, 1, 13
Let j(i) = i**3 + 7*i**2 + 7*i + 2. Let o be j(-5). Suppose -1 = -o*t + 16*t. Determine s, given that t + 2 + 1 - 10*s + 8*s**2 - 2*s**3 = 0.
1, 2
Let w = 584/1725 + -3/575. Let i(l) be the first derivative of w*l**6 + 0*l + 4/3*l**3 + 0*l**4 - 2 - 4/5*l**5 - l**2. Let i(q) = 0. What is q?
-1, 0, 1
Factor -2/5*q**4 - 6 - 96/5*q**2 + 36/5*q**3 + 92/5*q.
-2*(q - 15)*(q - 1)**3/5
Let m be (-5 - -11) + (-4)/(4/(-3)). Factor 29*w**2 + 12*w - 154*w**3 + m*w**2 + 148*w**3 - 14 + 18*w.
-2*(w - 7)*(w + 1)*(3*w - 1)
Suppose 2*f - g = 7, -5*f = -0*g + 4*g - 24. Factor 5*z**2 - 76*z**4 + 28*z**4 + 3*z**f.
-5*z**2*(3*z - 1)*(3*z + 1)
Suppose u - 2*u = 0. Suppose u = 2*m - 3*x + 2, -3*x = 5*m + 2*x - 20. Factor -9*b - b**m - 2*b**2 - 3 + 3*b.
-3*(b + 1)**2
Let l(f) = f**2 + f - 1. Let j(s) = 5*s**4 + 35*s**3 + 79*s**2 + 49*s - 4. Let b(m) = -j(m) + 4*l(m). Factor b(d).
-5*d*(d + 1)*(d + 3)**2
Let y = -79/58 + 4185/986. Let s = y - -8317/34. Solve -s*j**2 - 6 + 507/2*j**4 + 78*j**3 - 78*j = 0 for j.
-1, -2/13, 1
Let c(f) be the third derivative of f**8/840 + f**7/175 - 11*f**6/150 - 3*f**5/5 - 9*f**4/20 + 9*f**3 + 81*f**2. Factor c(n).
2*(n - 5)*(n - 1)*(n + 3)**3/5
Let u(p) = 209*p - 6060. Let s be u(29). Factor -s - 4/3*o - 1/3*o**2.
-(o + 1)*(o + 3)/3
Suppose 6*f - 21 - 9 = 0. Factor -4 + 12*z**3 - 6*z**2 - 4*z - 4*z**3 + 14*z**2 - 4*z**f - 4*z**4.
-4*(z - 1)**2*(z + 1)**3
Factor 8*m - 16*m - 16 + 2*m**2 + 5*m**2 - 8*m**2.
-(m + 4)**2
Let s = 17433 + -17430. Find f such that -4/5*f**s - 4/5*f**2 + 0 + 0*f = 0.
-1, 0
Let o be -3 + 13 - (28/8 + -4). Let -27/2*j**3 + o*j**2 + 6 + 30*j = 0. What is j?
-1, -2/9, 2
Let s(a) = 2*a - 1 - 5*a + 2*a + a**2. Suppose -w = -4*p + 24, -25*p - 2*w = -27*p + 18. Let o(m) = 9*m**2 - 13*m - 5. Let l(n) = p*s(n) - o(n). Solve l(b) = 0.
0, 2
Let q(w) be the first derivative of -w**4/54 - 4*w**3/27 + 41*