 Calculate n.
-1, -2/7
Let v(d) be the third derivative of -d**7/280 - d**6/30 - d**5/10 + 2*d**3/3 + 5*d**2. Let l(i) be the first derivative of v(i). Suppose l(n) = 0. Calculate n.
-2, 0
Let b(h) be the second derivative of -h**8/11200 + h**7/4200 + h**6/1200 - h**5/200 - 11*h**4/12 - 2*h. Let l(m) be the third derivative of b(m). Factor l(g).
-3*(g - 1)**2*(g + 1)/5
Let p be -3 + 1 + 3 - 2/3. Let r(k) be the first derivative of -p*k**3 - 1 + 1/2*k**2 + 0*k. Factor r(m).
-m*(m - 1)
Let f = -1/11 + 19/88. Let p(v) be the third derivative of 1/3*v**3 + 0*v + 0 + 1/60*v**5 + 4*v**2 - f*v**4. Factor p(g).
(g - 2)*(g - 1)
Let r = -7819664/735 + 10639. Let k(y) be the third derivative of 0*y**3 + 0*y**4 + 0 + r*y**7 + 0*y**6 - 1/210*y**5 + 0*y - y**2. Factor k(a).
2*a**2*(a - 1)*(a + 1)/7
Let n be (21 - 1) + (-9 - -11). Let x be ((-12)/14)/(n/(-77)). What is b in -3/2*b**2 + x - 3/2*b = 0?
-2, 1
Let v(z) = -12*z**4 + 12*z**3 + 36*z**2 - 5*z - 31. Let d(i) = 4*i**4 - 4*i**3 - 12*i**2 + 2*i + 10. Let a(p) = -7*d(p) - 2*v(p). Determine o so that a(o) = 0.
-1, 1, 2
Let m(o) be the third derivative of -o**7/840 + o**6/1440 + o**3/3 - 2*o**2. Let f(h) be the first derivative of m(h). Suppose f(c) = 0. What is c?
0, 1/4
Let o be -3 - (-2 - -1) - -2. Suppose -2*t + 4 = -0*t. Solve -1 + o*d**2 - d**2 - t*d + 4*d = 0.
1
Suppose -3*h + 4*c = 14, 0 = -4*h + 6*h - 3*c + 11. Solve -2/9*t**h + 2/9 + 0*t = 0.
-1, 1
Let j(n) be the first derivative of -n**4/20 - n**3/5 + 4*n/5 + 10. Suppose j(l) = 0. What is l?
-2, 1
Let o be 2 - 0*1/2. Suppose 6 = -0*l + 3*l. Determine d, given that -o*d**3 - d**4 - 1 + 0*d**3 + 2*d**l + 2*d**5 + d - d**5 = 0.
-1, 1
Let f(c) be the third derivative of -c**7/630 - c**6/180 - c**4/12 + 3*c**2. Let j(k) be the second derivative of f(k). Factor j(u).
-4*u*(u + 1)
Let q(r) be the third derivative of r**6/240 - 11*r**2. Factor q(j).
j**3/2
Let a(n) be the second derivative of -10*n**4/3 - 6*n**3 + 2*n**2 + 28*n. Factor a(z).
-4*(z + 1)*(10*z - 1)
Let w(j) be the first derivative of -j**6/6 - j**5/20 + j**4/4 + j**3/12 - 8. Suppose w(c) = 0. What is c?
-1, -1/4, 0, 1
Suppose 0 = 3*h, 0 = 3*g + 4*h - h. Factor -1/3*w**2 - 2/3*w + g.
-w*(w + 2)/3
Let q(i) be the first derivative of 2*i**3/21 - 6*i**2/7 + 18*i/7 - 3. Solve q(l) = 0.
3
Suppose -20 = -5*q, -4*q + 13 = 3*l - 3*q. Let n(c) be the first derivative of 0*c + 1/10*c**5 - 3/8*c**4 + 1/2*c**3 + l - 1/4*c**2. Solve n(a) = 0 for a.
0, 1
Let o(r) = r**2 - 5*r - 2. Let v be o(6). Let 3*k**v - 2*k**4 + 0*k**3 - 2*k**3 + 4*k**3 + k**2 = 0. Calculate k.
-1, 0
Let r(l) = 6*l**3 - 6*l - 6. Let j(d) = 5*d**3 + d**2 - 5*d - 5. Let m(w) = 3*j(w) - 2*r(w). Solve m(q) = 0.
-1, 1
Let w(q) be the first derivative of -2*q**6/27 + 16*q**5/15 - 16*q**4/3 + 256*q**3/27 - 36. Let w(a) = 0. Calculate a.
0, 4
Let p = 101/21 + -15/7. Find k such that 4*k**2 - p*k + 2/3 + 2/3*k**4 - 8/3*k**3 = 0.
1
Let v = -64/7 + 319/28. Let b be 0 - 0 - (-5 - -1). Factor -21/4*x**b + 0 + 4*x**3 + v*x**5 + 0*x - x**2.
x**2*(x - 1)*(3*x - 2)**2/4
Let p(g) be the second derivative of g**5/10 - g**4/6 + g**2/2 - 2*g. Let r be p(1). Solve -2*a**2 - r + a**2 + 3*a - a = 0 for a.
1
Suppose -27 + 54 = 9*k. What is j in -4/3*j**k - 8/3*j**2 + 0 - 4/3*j = 0?
-1, 0
Let l(v) be the first derivative of v**4/2 - 10*v**3/3 + 12. Factor l(c).
2*c**2*(c - 5)
Let v(u) be the third derivative of u**7/13860 - u**6/3960 + u**4/8 + u**2. Let g(i) be the second derivative of v(i). Find b such that g(b) = 0.
0, 1
Determine w, given that 90 + 13*w**2 - 105*w - 5*w**3 + 26*w**2 + 4*w**2 - 3*w**2 = 0.
2, 3
Let a(u) = 0*u - 4 + 6*u**3 - 3*u - 4*u**2 - 2. Let q(h) = 8 + 3*h**3 + 2*h**3 + h**2 - 7 - 6*h**3. Let j(w) = -2*a(w) - 14*q(w). Factor j(y).
2*(y - 1)**3
Let g(z) = -5*z - 1. Let w be g(-5). Let b be (-16)/54*w/(-32). Determine y, given that 0*y - 2*y**5 + 0 - 2/3*y**4 - b*y**2 + 10/9*y**3 = 0.
-1, 0, 1/3
Let r(y) = 3*y - 3. Let d be r(2). Factor -2*l**2 - 3*l**2 + l**2 + l + d*l**3.
l*(l - 1)*(3*l - 1)
Let f(n) be the first derivative of 0*n**2 + 1/5*n - 4 - 1/15*n**3. Solve f(d) = 0 for d.
-1, 1
Suppose q - 6 = -q. Factor -2*g + 0 + q*g**2 + 5*g - 6 + 0*g.
3*(g - 1)*(g + 2)
Let h(p) be the third derivative of p**9/30240 + p**8/3360 - p**6/90 - p**5/30 + p**2. Let u(i) be the third derivative of h(i). Suppose u(x) = 0. Calculate x.
-2, 1
Let d(x) be the first derivative of x**3/3 + 13*x**2/2 + x + 8. Let c(a) = -6*a. Let y(s) = -10*c(s) - 4*d(s). Factor y(o).
-4*(o - 1)**2
Let n(k) = k**5 + k**3 - k + 1. Suppose m - 2 = -1. Let o(c) = c**5 + 3*c**4 - 2*c**2 + c + 1. Let i(x) = m*o(x) - 2*n(x). Factor i(s).
-(s - 1)**4*(s + 1)
Let h(n) be the first derivative of 4*n**2 - 12*n + 5 + 20/3*n**3. Find q, given that h(q) = 0.
-1, 3/5
Let x be (19/(-9) - -2)/(4/(-84)). Factor -3*b**3 + x*b**4 + 0 + 2/3*b**2 + 0*b.
b**2*(b - 1)*(7*b - 2)/3
Let s = 0 + 2. Let a be (-5)/(-15) + -2*22/(-12). Let 3*n**2 - 5*n**2 + s + 4*n**2 + a*n = 0. Calculate n.
-1
Let v(a) be the first derivative of -a**7/210 - a**6/60 + a**4/12 + a**3/6 - a**2 + 4. Let c(o) be the second derivative of v(o). Factor c(x).
-(x - 1)*(x + 1)**3
Let o(b) be the third derivative of -b**7/8820 + b**6/1260 + b**4/4 - b**2. Let l(g) be the second derivative of o(g). Find r, given that l(r) = 0.
0, 2
Factor 80 - 164 + 84 - 4*z**3.
-4*z**3
Let u = -1045/2236 - -11/43. Let b = 1/26 - u. Factor b*y + 0 - 1/4*y**4 - 1/4*y**3 + 1/4*y**2.
-y*(y - 1)*(y + 1)**2/4
Suppose -15 = 4*b + 3*r, 5*b - 3*r = r + 20. Factor b + 0*v + 2/9*v**4 - 2/9*v**2 + 0*v**3.
2*v**2*(v - 1)*(v + 1)/9
Let j(b) be the second derivative of 3/20*b**5 + 0 + 1/6*b**4 + 0*b**2 + 4*b + 0*b**3. Solve j(i) = 0.
-2/3, 0
Suppose 0*y = y - 3, -4*l = 5*y - 19. Suppose 5*z - 6 = -l. Factor -d + 4 + z - 5 - d**2 + 2*d**3.
d*(d - 1)*(2*d + 1)
Suppose -5*i - 38 = -5*c + 52, 3*c + 4*i = 40. Determine z so that -3*z**3 + 2*z + c*z**2 - 6*z**2 + 11*z**3 = 0.
-1, -1/4, 0
Let x(i) be the third derivative of -i**6/660 - i**5/330 - 7*i**2. Solve x(c) = 0 for c.
-1, 0
Let w(z) = -z. Let c(r) = r**3 + 5*r**2 - 7*r + 4. Let m be c(-6). Let n(q) = -q**3 - 5*q. Let v(i) = m*w(i) - 2*n(i). Suppose v(k) = 0. Calculate k.
0
Let g = -65 - -327/5. Find y such that 2/5*y**2 + 2/5*y**5 + 0 - g*y**4 - 2/5*y**3 + 0*y = 0.
-1, 0, 1
Factor -1/10*p**4 + 7/10*p**2 - 3/2*p + 3/10*p**3 - 9/5.
-(p - 3)**2*(p + 1)*(p + 2)/10
Let k = 420 + -1679/4. Find b such that -1/4*b**4 - 1/4*b + 0 + 1/4*b**2 + k*b**3 = 0.
-1, 0, 1
Let s(g) be the second derivative of 0*g**2 + 0*g**3 + 4*g - 1/6*g**4 + 1/10*g**5 + 0. Factor s(m).
2*m**2*(m - 1)
Let o be (-2)/(-11) + 870/(-792). Let p = 103/60 + o. Solve -2/5*g**2 - p*g + 0 = 0 for g.
-2, 0
Let p(t) be the first derivative of t**4/36 - t**3/9 - t - 2. Let x(y) be the first derivative of p(y). Factor x(d).
d*(d - 2)/3
Let -2/11*y**3 + 0 - 20/11*y**2 - 18/11*y = 0. Calculate y.
-9, -1, 0
Suppose 9*j - 8 = 5*j. Suppose 5*z + 17 = -3*h + j, 4*h - 2*z - 6 = 0. Factor 0*i + 1/2*i**3 + 0 + i**4 + 1/2*i**5 + h*i**2.
i**3*(i + 1)**2/2
Let o(j) = -3*j**2 + 15*j + 3. Let z(w) = 3*w**2 - 14*w - 4. Let d(f) = 4*o(f) + 3*z(f). Determine k, given that d(k) = 0.
0, 6
Let d(i) be the third derivative of i**5/30 - i**4 - 13*i**3/3 - 3*i**2 + 6*i. Let d(q) = 0. What is q?
-1, 13
Let v(r) = -r**3 + 5*r**2 + 2*r - 4. Let b be v(4). Let t be 5/b - 26/(-8). Factor -23/2*m**4 - 27/2*m**3 - t*m**5 + 0 - 13/2*m**2 - m.
-m*(m + 1)**3*(7*m + 2)/2
Let m(g) be the third derivative of 2*g**7/525 + g**6/50 + 2*g**2. Find r such that m(r) = 0.
-3, 0
Suppose 2*v + 3*v - 15 = 0. Factor -3*g**2 - 4*g**v + 3*g**2 + 2*g**3.
-2*g**3
Suppose 0 = -5*y - 3*h + 9, h - 13 = -y - 4*y. Let -w**3 - 2*w + 0*w**3 + y*w**2 - w + 1 = 0. What is w?
1
Factor 3*f**2 - 1/3 + 5/3*f**3 + f.
(f + 1)**2*(5*f - 1)/3
Factor 0 + 2/11*f - 4/11*f**2 + 2/11*f**3.
2*f*(f - 1)**2/11
Let n(d) be the third derivative of d**8/168 + 4*d**7/105 + d**6/10 + 2*d**5/15 + d**4/12 - 5*d**2. Solve n(g) = 0.
-1, 0
Let h = 59 + -30. Let a be -6 - -3 - h/(-7). Factor a - 8/7*t + 2/7*t**2.
2*(t - 2)**2/7
Suppose 2 = 2*i - 5*d + 18, -d = -4. Solve -2*b**3 + 2*b - 2*b**2 + 0*b**i + 2 - 2*b + 2*b = 0 for b.
-1, 1
Let q = 7 + -5. Let n be 42/8 - (-1)/(-4). Factor q*b + 2*b**5 + 0*b**n + 0*b - 4*b**3.
2*b*(b - 1)*