19
Let c be -6*(1*(-6)/9 - 0). Factor -31*a - a**3 + 8*a**2 - 3*a**4 + c*a**4 - 9 - 5*a**3 + 37*a.
(a - 3)**2*(a - 1)*(a + 1)
Let p(a) be the second derivative of -21*a - 1/6*a**3 - 1/10*a**5 - 1/60*a**6 + 0*a**2 + 0 - 5/24*a**4. Solve p(j) = 0.
-2, -1, 0
Let f(g) be the second derivative of -g**5/140 + g**4/12 - 18*g**2/7 - 336*g. Let f(h) = 0. Calculate h.
-2, 3, 6
Let k(m) = 3*m**2 - 8*m - 5 - 7 - 4*m**2 + 3. Let g(u) = -1. Let j(f) = -14*g(f) - 2*k(f). Factor j(h).
2*(h + 4)**2
Suppose 4*o + 2*w = -10, -8*o + w = -3*o - 5. Suppose -5*p = 2*i - 4, 4*i + 5*p - 8 = -o. Solve -3/5*b**3 - 2/5 - 23/5*b**i + 9/5*b**4 - 13/5*b = 0.
-1, -1/3, 2
Let a(j) be the first derivative of -j**4/48 - j**3/4 - 5*j**2/8 - 33*j - 34. Let d(u) be the first derivative of a(u). Determine t, given that d(t) = 0.
-5, -1
Let i(p) = -9*p**2 + 44*p + 23. Let q(b) = -b**2 + 2*b + 1. Let u(y) = -i(y) + 5*q(y). Let u(d) = 0. Calculate d.
-1/2, 9
Let n(y) be the second derivative of -y**5/10 + 17*y**4/2 - 33*y**3 + 49*y**2 - 7*y + 1. Solve n(t) = 0 for t.
1, 49
Factor 0*d + 0 + 15/4*d**2 - 1/4*d**3.
-d**2*(d - 15)/4
Let i(h) = -135*h - 1485. Let r be i(-11). Let f(b) be the second derivative of 5*b + 1/2*b**2 + r + 0*b**4 - 1/40*b**5 + 1/4*b**3. Factor f(m).
-(m - 2)*(m + 1)**2/2
Let k(o) be the third derivative of 10201*o**5/180 + 101*o**4/12 + o**3/2 - 26*o**2 - 2*o. Let k(q) = 0. What is q?
-3/101
Find h, given that 9*h**4 + 40*h**2 + 28*h + 5*h**5 - 108*h - 29*h**3 - 49*h**4 + 104*h**3 = 0.
-1, 0, 1, 4
Let b be 1/(-2)*(24/(-3) + 8). Let n be b - 0 - (-1)/2. Factor 0 + 1/4*u**5 + 1/2*u**2 + 0*u - n*u**4 - 1/4*u**3.
u**2*(u - 2)*(u - 1)*(u + 1)/4
Let x(g) be the first derivative of g**4/5 - 8*g**3/3 - 104*g**2/5 - 224*g/5 + 57. Determine z so that x(z) = 0.
-2, 14
Let s be (-3)/21 - ((-90)/(-21))/(-2). Determine n, given that -2*n**3 - 4 - n**2 - 4*n**2 + 5*n**s + 6*n = 0.
-2, 1
Let l(o) be the second derivative of -5/3*o**3 + 5/12*o**4 + 0 + 5/2*o**2 - 23*o. Suppose l(k) = 0. Calculate k.
1
Let a(x) be the second derivative of -5*x**7/42 + x**6/3 + 7*x**5/4 + 5*x**4/3 - 25*x + 3. Factor a(s).
-5*s**2*(s - 4)*(s + 1)**2
Let b(k) be the second derivative of k**4/30 - 16*k**2/5 + 3*k. Determine l, given that b(l) = 0.
-4, 4
Let x(w) be the first derivative of w**7/2800 + w**6/1800 - w**5/1200 + w**3/3 - 2. Let m(a) be the third derivative of x(a). Factor m(u).
u*(u + 1)*(3*u - 1)/10
Let g be ((-48)/(-10) + -6)/(84/(-80)). Factor -8/7*k**2 - g*k + 0 - 2/7*k**3.
-2*k*(k + 2)**2/7
Suppose 0 = -2*c + c - 4*r + 30, c + 2*r = 22. Let t = -10 + c. Factor -t*y - 3 + 2*y - 12*y**3 - 4*y + 21*y**2.
-3*(y - 1)**2*(4*y + 1)
Suppose 26*g - 29*g = -9. Suppose 2*s = -q + s + g, 3*q - 13 = -s. Let 0 + 2/3*m**3 + 4/9*m**4 - 2/3*m**q + 0*m - 4/9*m**2 = 0. Calculate m.
-1, 0, 2/3, 1
Let i(d) be the first derivative of 4*d**3/3 + 40*d**2 - 115. Determine n so that i(n) = 0.
-20, 0
Factor 134/5*p**2 + 6666/5*p - 20402/15 + 2/15*p**3.
2*(p - 1)*(p + 101)**2/15
Let m(g) be the third derivative of 0*g - 1/126*g**7 + 18*g**2 + 1/30*g**6 + 0 + 2/9*g**3 - 1/6*g**4 + 1/180*g**5. Determine p, given that m(p) = 0.
-1, 2/5, 1, 2
Factor 6/17*m**2 + 2/17*m**3 + 0*m + 0.
2*m**2*(m + 3)/17
Let j = -20113 + 20209. Factor 24*h + 3/2*h**2 + j.
3*(h + 8)**2/2
Let y(u) be the third derivative of -7*u**6/540 - 17*u**5/135 + 47*u**4/108 - 2*u**3/9 - 17*u**2 - 11. Factor y(w).
-2*(w - 1)*(w + 6)*(7*w - 1)/9
Let t(h) be the second derivative of -8/9*h**3 - 4/3*h**2 + 11/18*h**4 - 7/45*h**6 + 13/30*h**5 + 6*h - 5/63*h**7 + 0. What is o in t(o) = 0?
-2, -1, -2/5, 1
Let t(l) = -8*l**2 - 2*l + 4. Let q be t(0). Let i(f) be the first derivative of 1/20*f**q + 4 - 2/5*f - 4/15*f**3 + 1/2*f**2. Solve i(b) = 0 for b.
1, 2
Suppose 106*i + 54*i - 429 = 17*i. Factor -6/7*v - 9/7*v**i + 0 + 15/7*v**2.
-3*v*(v - 1)*(3*v - 2)/7
Let l(c) be the second derivative of 0 - 1/42*c**4 - 29*c + 5/21*c**3 + 6/7*c**2. Determine k so that l(k) = 0.
-1, 6
Let v(s) be the second derivative of -s**5/4 + 15*s**4/4 - 270*s**2 - 54*s. Find d such that v(d) = 0.
-3, 6
Let y(b) be the second derivative of b**6/135 - 4*b**5/45 - 7*b**4/18 + 8*b**3/27 + 20*b**2/9 + 34*b - 7. Suppose y(v) = 0. Calculate v.
-2, -1, 1, 10
Let j = -561 + 565. Let s(q) be the second derivative of 0*q**3 - q + 0*q**2 + 1/210*q**6 + 0 + 1/140*q**5 + 0*q**j. What is i in s(i) = 0?
-1, 0
Let q(g) be the third derivative of g**5/60 - 25*g**4/6 + 1250*g**3/3 + 31*g**2. Solve q(n) = 0.
50
Suppose 0 = 2*b - 4*m - 24, b + 9 = -2*m - 3*m. Let q be (b - 2) + (7 - 8). Factor -9/2 - 15/2*w - 3/2*w**2 + 3/2*w**q.
3*(w - 3)*(w + 1)**2/2
Let q(l) be the first derivative of -5*l**4/8 + 55*l**3/2 - 1815*l**2/4 + 6655*l/2 - 64. Factor q(i).
-5*(i - 11)**3/2
Suppose z + 7 = 5*f - 4*f, 0 = f + 3*z + 13. Factor -2*o + 4*o - o**f - 20 + 20.
-o*(o - 2)
Let u = -38 + 54. Suppose 6*n - 4*n - 3*x = u, 5*n + 4*x = 17. Factor 18 - 12*w + w**2 - 7*w**2 + n*w**2 + 3*w**2.
2*(w - 3)**2
Let b(g) be the second derivative of 5/12*g**4 - 10*g**2 - 10*g + 0 - 5/2*g**3. Solve b(z) = 0.
-1, 4
Let s(o) = o**3 + 12*o**2 - 2*o - 21. Let v be s(-12). Suppose 2*p = -2*a + 8, v*a + 5 = p + 9. Factor 0 - 3/2*y**p - 3*y.
-3*y*(y + 2)/2
Suppose -3*w = -5*o - 106 - 343, 2*o + 780 = 5*w. Let y = w - 1102/7. Factor 6/7*u - 2/7*u**2 - y.
-2*(u - 2)*(u - 1)/7
Let q(s) be the second derivative of 0 + 3/4*s**2 - 39*s + 1/6*s**3 - 1/24*s**4. Factor q(c).
-(c - 3)*(c + 1)/2
Let y be (-4)/(-14) + (-40)/(-7). Suppose p = 8 - y. Suppose 0*x**2 - 4*x**3 - 7*x**4 + 5*x**4 - p*x**2 = 0. Calculate x.
-1, 0
Suppose 79*o - 372 = 75*o. Let s = 95 - o. Factor -2/5*g**3 + 0 - 2/5*g - 4/5*g**s.
-2*g*(g + 1)**2/5
Let w(u) be the first derivative of 2*u**5/25 + 3*u**4/2 - 76*u**3/5 + 244*u**2/5 - 336*u/5 - 94. Find z, given that w(z) = 0.
-21, 2
Let u(c) be the third derivative of -c**8/168 - c**7/49 + c**6/84 + c**5/14 + c**4/42 - c**2 + 60*c. Suppose u(h) = 0. What is h?
-2, -1, -1/7, 0, 1
Let f(k) be the second derivative of k**5/90 - k**3/9 - 2*k**2/9 - 46*k. Factor f(n).
2*(n - 2)*(n + 1)**2/9
Let o = -2840 + 2844. Find d such that -11*d**o + 416*d - 1/2*d**5 - 145/2*d**3 - 76*d**2 - 256 = 0.
-8, 1
Let p(x) be the second derivative of -1/36*x**4 - 1/30*x**5 - 14*x + 0 + 0*x**3 - 1/90*x**6 + 0*x**2. Solve p(r) = 0 for r.
-1, 0
Let n = -339 + 258. Let f be (-24)/n*(-585)/(-60). Solve -f*g**2 + 8/3*g - 8/9 + 4/3*g**3 - 2/9*g**4 = 0.
1, 2
Let b = 143/16 - 113/16. Let m = b - -37/8. Solve 2 - 3*l**3 - 6*l + 1/2*l**4 + m*l**2 = 0 for l.
1, 2
Suppose 0 = -z - 3*z + 64. Let i = 18 - z. Factor 3*s**2 + i*s**2 - 6*s - 2 - 7*s**2 - 4*s**2 - 2*s**3.
-2*(s + 1)**3
Let o(y) be the second derivative of y**7/210 + 2*y**6/75 - y**4/6 - y**3/30 + 3*y**2/5 - 421*y. Let o(q) = 0. What is q?
-3, -2, -1, 1
Let j(a) be the first derivative of -a**5/6 - 55*a**4/6 - 1315*a**3/9 - 385*a**2 - 735*a/2 + 346. Factor j(m).
-5*(m + 1)**2*(m + 21)**2/6
Factor 2*r + 0 - 3/2*r**2 - 3/4*r**3 + 1/4*r**4.
r*(r - 4)*(r - 1)*(r + 2)/4
Let h(g) be the second derivative of g**5/40 + 19*g**4/8 + 70*g**3 + 196*g**2 + 135*g. Factor h(f).
(f + 1)*(f + 28)**2/2
Let t(l) be the second derivative of l**5/40 + 5*l**4/8 - 4*l**3/3 + 244*l. Factor t(f).
f*(f - 1)*(f + 16)/2
Let d = 31 + -28. Solve 15*l**4 + 53*l - 92*l - 10*l**d - 5*l**5 - 10*l**2 - 5 + 54*l = 0 for l.
-1, 1
Let j(h) be the third derivative of 17*h**2 - 1/360*h**5 - 1/12*h**3 + 1/36*h**4 + 0*h + 0. Find a such that j(a) = 0.
1, 3
Let w(k) be the second derivative of -k**6/30 + k**5/20 + k**4/12 - k**3/6 + 98*k. Find h such that w(h) = 0.
-1, 0, 1
Let f(p) be the third derivative of -5*p**8/336 - 4*p**7/21 - p**6/4 + 2*p**5/3 + 35*p**4/24 + 90*p**2. Determine j so that f(j) = 0.
-7, -1, 0, 1
Let o(x) be the third derivative of -x**6/60 + 37*x**5/30 - 71*x**4/12 + 35*x**3/3 - 533*x**2. Factor o(q).
-2*(q - 35)*(q - 1)**2
Let y be -2*1 + (-6 - -10). Let h be 2*7/y + -3. Factor 31 - 6*k**2 + 3*k**3 - 31 + 3*k**h.
3*k**2*(k - 1)*(k + 2)
Let b(k) = -5*k - 3. Let c be b(-2). Suppose -c*g = -2*g. Solve 1 + r**2 + 2*r + g*r**2 + 0*r**2 + 0*r**2 = 0.
-1
Let a(j) be the second derivative of j**5/180 - j**4/18 + j**3/6 - 5*j**2 + 23*j. Let d(z) be the first derivative of a(z). Factor d(w).
(w - 3)*(w - 1)/3
Suppose -3*s - 2*s -