 Calculate u.
-5, 0, 2/9, 1
Let k(x) be the second derivative of -x**6/195 + 2*x**4/39 - 3429*x. Factor k(q).
-2*q**2*(q - 2)*(q + 2)/13
Let i(q) be the third derivative of -1/84*q**6 - 138*q**2 + 0 + 0*q + 0*q**3 - 1/735*q**7 + 1/35*q**5 + 0*q**4. Find p such that i(p) = 0.
-6, 0, 1
Let f(z) be the second derivative of 0 + 16/45*z**3 + 17/15*z**2 - 317*z - 1/90*z**4. Factor f(c).
-2*(c - 17)*(c + 1)/15
Let v(a) be the second derivative of -1/30*a**6 + 26/3*a**4 - 33 + 18*a**3 + 23/20*a**5 - a + 0*a**2. Solve v(w) = 0.
-2, 0, 27
Suppose 88 + 215 + 59*p - 157*p - p**2 = 0. Calculate p.
-101, 3
Let h(f) be the third derivative of 25*f**4/24 + 329*f**3/6 + 5*f**2 - 5*f. Let k be h(-13). What is z in -4/5*z**3 + 3/5*z**2 + 0 + 1/5*z**k + 0*z = 0?
0, 1, 3
Let y(l) be the third derivative of -4/3*l**3 - 1/60*l**5 + 0*l**4 + 1/360*l**6 + 0 + 0*l - 3*l**2. Let g(j) be the first derivative of y(j). Factor g(z).
z*(z - 2)
Let g(m) = 2. Let p(s) = -3*s**2 - 8*s - 13. Let o(t) = -2*g(t) - p(t). Let d = 4 + -2. Let n(w) = w**2 + w. Let x(f) = d*n(f) - o(f). What is h in x(h) = 0?
-3
Let a(p) = 42*p**2 - 136*p - 565. Let k(b) = 16*b**2 - 68*b - 282. Let q(w) = -2*a(w) + 5*k(w). Solve q(y) = 0 for y.
-10, -7
Factor 61/3 + 1/3*j**2 - 62/3*j.
(j - 61)*(j - 1)/3
Let v(k) be the first derivative of k**6/180 - k**4/36 - 9*k**2/2 - 2*k - 39. Let o(u) be the second derivative of v(u). Factor o(x).
2*x*(x - 1)*(x + 1)/3
Let j = 28985 - 28978. Factor -k**4 + j*k + 1/3*k**5 - 2*k**3 + 3 + 10/3*k**2.
(k - 3)**2*(k + 1)**3/3
Let h(f) be the second derivative of 3*f**5/160 + 15*f**4/16 + 77*f**3/16 - 81*f**2/4 - 2*f - 109. Factor h(a).
3*(a - 1)*(a + 4)*(a + 27)/8
Let i be ((-24115)/4823)/((3/9)/((-2)/10)). Factor -1/4*r**i - r**2 - 1/2 - 5/4*r.
-(r + 1)**2*(r + 2)/4
Let q(y) = 3*y**2 - 31*y - 268. Let j be q(-10). Suppose -6*z - 330 = -j. Let 2/13*d**3 - 2/13*d + 6/13 - 6/13*d**z = 0. Calculate d.
-1, 1, 3
Let p(x) be the second derivative of 17*x**3/3 - 33*x**2 - 2*x + 299. Let j be p(2). Solve -5/4*i + 1/4*i**j - 3/2 = 0 for i.
-1, 6
Let i(v) be the third derivative of 1/30*v**5 + 0*v + 10 + v**4 - 4*v**2 + 0*v**3. Factor i(n).
2*n*(n + 12)
Let l(d) be the first derivative of 2*d**3/9 + 120*d**2 + 714*d + 5720. Suppose l(s) = 0. Calculate s.
-357, -3
Suppose 0 = y + 2*f - 3*f, -4*f = 3*y - 14. Let y*r**2 + 51 - 15 - 1467*r + 1429*r = 0. Calculate r.
1, 18
Let q be 2 + (-77242)/14 - (-12)/42. Let a = 71745/13 + q. Factor -a + 20/13*h - 2/13*h**2.
-2*(h - 5)**2/13
Let i = 1016 + -1014. Suppose 3*b + i = 2*x, -60*b - 3 = -58*b - 3*x. Factor -2/3*o**3 + 2/3*o + 0 + b*o**2.
-2*o*(o - 1)*(o + 1)/3
Let r be (-4)/2 - (40/5 + -14). Factor 2 + 2*d**3 - d + 7*d**5 + 13*d**5 - r*d**2 - 21*d**5 + 2*d**4.
-(d - 2)*(d - 1)**2*(d + 1)**2
Suppose -3*p - n = n - 21, 34 = 5*p + 3*n. Factor -x**p - 24*x - 2*x**3 + 6*x**3 - 16*x**3 + 44*x**2 + 5*x**5 - 12*x**4.
4*x*(x - 3)*(x - 1)**2*(x + 2)
Let l(i) be the second derivative of 3*i**5/20 - 2*i**4 - 513*i**3/2 - 7563*i. Factor l(z).
3*z*(z - 27)*(z + 19)
Let x = 366196/2380105 - 2/183085. Solve x*b**3 + 28/13*b + 14/13*b**2 + 16/13 = 0.
-4, -2, -1
Let t(f) be the third derivative of -f**8/1848 - f**7/1155 + 23*f**6/660 - 13*f**5/110 + 3*f**4/22 + 2541*f**2. Find y such that t(y) = 0.
-6, 0, 1, 3
Suppose 1260 = -62*a + 44*a. Let j be 0 - a/8 - (18 - 13). Find v, given that -j*v**4 + v + 0 + 3*v**2 - 1/4*v**3 = 0.
-2/3, -2/5, 0, 1
Let y(g) be the first derivative of -2*g**5/15 - 10*g**4 - 232*g**3/9 + 108. What is w in y(w) = 0?
-58, -2, 0
Let k(m) be the second derivative of -3 + 1/48*m**3 - 4*m - 7/16*m**2 - 1/160*m**5 + 7/96*m**4. Factor k(p).
-(p - 7)*(p - 1)*(p + 1)/8
Suppose -7*w + 94 = -81. Let z(f) = -5*f**4 - 50*f**2 + 25*f + 5. Let n(g) = g**3 - g**2 - 1. Let y(m) = w*n(m) - z(m). Solve y(r) = 0.
-3, -2, -1, 1
Suppose -2*v + 2 + 2 = 0. Let r be 35 - v*6/(-4). What is j in -10*j**3 + r*j**3 - 48*j + 36*j**2 - 10 - 6 = 0?
-2, -2/7, 1
Suppose 20*r = -46 - 101 + 207. Factor 6*m**2 - 2/3*m**r + 40/3 - 16*m.
-2*(m - 5)*(m - 2)**2/3
Let m(k) = -16*k**2 - 6368*k + 5088032. Let w(i) = 45*i**2 + 19106*i - 15264099. Let n(b) = -17*m(b) - 6*w(b). Factor n(t).
2*(t - 1595)**2
Suppose j + 5*t - 88 = 0, -431 = -4*j + 5*t - 79. Let k = 113 - j. Factor g**2 - k*g**3 + 24*g**3 - 4*g + 3*g**2 + 0*g.
-g*(g - 2)**2
Factor 75/2*i - 9 - 11/2*i**2 - 2*i**3.
-(i - 3)*(i + 6)*(4*i - 1)/2
Suppose 257 = 2*v - 233. Suppose -250*f + v*f + 55 = 0. Factor f*z**2 - 12 - 16*z + 0*z**2 + 16*z**3 + 4*z**4 + z**2 - 4*z**2.
4*(z - 1)*(z + 1)**2*(z + 3)
Let z(o) be the first derivative of o**4/12 - 86*o**3/9 + 555*o**2/2 + 2700*o + 1240. Factor z(q).
(q - 45)**2*(q + 4)/3
Factor 16/5 + 32/5*c**4 - 88/5*c**3 - 4/5*c**5 + 112/5*c**2 - 68/5*c.
-4*(c - 4)*(c - 1)**4/5
Let q = 124505/497988 + -2/124497. Factor q*r**4 + 21/4*r**2 + 3/2 - 19/4*r - 9/4*r**3.
(r - 6)*(r - 1)**3/4
Suppose 3*o = 5*c + 12, 73*o - 81*o + 32 = 0. Let d(v) be the first derivative of 3/20*v**4 + 0*v + c*v**2 - 1/5*v**3 - 13. Factor d(g).
3*g**2*(g - 1)/5
Let k(o) be the first derivative of o**6/15 + 32*o**5/25 + 6*o**4/5 - 92*o**3/15 - 13*o**2/5 + 12*o + 1802. Determine a, given that k(a) = 0.
-15, -2, -1, 1
Let r(g) be the third derivative of -g**7/420 + 31*g**6/48 - 5*g**5/4 - 155*g**4/12 + 154*g**3/3 + 185*g**2 - 19*g. Suppose r(b) = 0. What is b?
-2, 1, 2, 154
Let y(i) be the third derivative of i**8/336 - 79*i**7/105 + 31*i**6/8 + i**5/15 - 155*i**4/6 - 2*i**2 + 3*i - 401. Factor y(k).
k*(k - 155)*(k - 2)**2*(k + 1)
Factor -1/6*i**2 - 32258/3 - 254/3*i.
-(i + 254)**2/6
Suppose -a + 3*z = -18, 14*z = 3*a + 15*z - 44. Let w be (-35)/a - -1 - (-7 - -5). Suppose 2/3*d - w*d**3 - 2/3*d**2 + 2/3 = 0. Calculate d.
-1, 1
Let g(d) = 2*d**3 + 10*d**2 - 4*d - 6. Let r(w) = -w**2 + w + 1. Suppose -11*o - 21 + 32 = 0. Suppose -30 = 7*u - 12*u. Let k(c) = o*g(c) + u*r(c). Factor k(x).
2*x*(x + 1)**2
Let k(y) = 8*y**4 + 46*y**3 + 5*y**2 - 19*y. Let c(v) = 3*v**4 + 15*v**3 + 2*v**2 - 6*v. Suppose 21*l - 18*l + 21 = 0. Let d(i) = l*c(i) + 2*k(i). Factor d(q).
-q*(q + 1)*(q + 2)*(5*q - 2)
Let k(c) be the third derivative of 1/126*c**7 - 184*c**2 + 0*c**3 + 0 + 0*c**5 + 1/60*c**6 + 1/1008*c**8 + 0*c**4 + 0*c. Factor k(b).
b**3*(b + 2)*(b + 3)/3
Suppose 32 + 2*a**2 - 1/4*a**5 - 1/4*a**4 - 40*a + 13/2*a**3 = 0. Calculate a.
-4, 1, 2, 4
Let d(i) be the second derivative of -i**7/420 + i**6/12 - 5*i**5/6 - 51*i**2/2 + 5*i - 1. Let f(x) be the first derivative of d(x). Factor f(o).
-o**2*(o - 10)**2/2
Let s(n) be the first derivative of n**5/40 - 13*n**4/16 + 25*n**2/2 - 4*n + 176. Let q(o) be the second derivative of s(o). Factor q(f).
3*f*(f - 13)/2
Solve 5*c**2 + 7*c**2 - 1644*c - 2380161 + 6704661 + 10944*c - 7*c**2 = 0.
-930
Let l(r) be the third derivative of r**5/360 + 487*r**4/24 + 237169*r**3/4 - 4*r**2 + 391. Suppose l(f) = 0. Calculate f.
-1461
Suppose 41 = -324*j - 39 + 80. Let g(v) be the first derivative of -8*v**2 + 32/3*v**3 + 22 + 21*v**4 + j*v. Factor g(f).
4*f*(3*f + 2)*(7*f - 2)
Let a(p) = 3*p**2 + 5*p - 6. Let s be a(1). Let 194*x**2 + 30*x - 176*x**2 - 17 + 2*x**3 - 35 + s = 0. Calculate x.
-5, 1
Let h = 1/30 - -79/30. Let w be (-112)/(-210)*(-2 + 0)*125/(-50). Let w - h*y + 2/3*y**2 = 0. Calculate y.
2
Let l(j) = -j**2 - 25*j - 30. Let d be l(-13). Let t be ((-2)/56*9)/((-108)/d). Find q, given that t*q**2 + 3/8 - 3/4*q = 0.
1
Factor v - 1/2*v**5 + 0 + 3/2*v**3 + 1/2*v**4 - 5/2*v**2.
-v*(v - 1)**3*(v + 2)/2
Let y(n) be the third derivative of -2*n**7/525 + 101*n**5/75 - 40*n**3/3 - 2*n**2 - 95*n. Suppose y(r) = 0. Calculate r.
-10, -1, 1, 10
Determine k so that 28/3*k**2 - 19 - 1/6*k**3 + 59/6*k = 0.
-2, 1, 57
Let k(h) = 33*h**2 - 695*h + 8. Let u(z) = -26*z**2 + 695*z - 6. Let y(v) = -3*k(v) - 4*u(v). Determine c, given that y(c) = 0.
0, 139
Let -72/11*g**2 - 2/11*g**3 - 156/11 + 230/11*g = 0. What is g?
-39, 1, 2
Let b(m) be the third derivative of -m**5/12 + 1535*m**4/12 + 1025*m**3/2 + 2*m**2 - 280. Factor b(d).
-5*(d - 615)*(d + 1)
Let -25 - 37*j**2 + 7*j + 130*j**2 - 25 - 7*j**3 - j**4 - 10 - 32*j**2 = 0. What is j?
-12, -1, 1, 5
Let v(k) be the second derivative of -k**5/16 - 175*k**4/48 - 80*k**3/3 - 155*k**2/2 + 105*k - 6. Determine h, given that v(h) = 0.
-31, -2
Let q(o) be the thir