1)/11
Let n(r) be the second derivative of r**7/441 - 4*r**6/315 - r**5/70 + 17*r**4/63 - 52*r**3/63 + 8*r**2/7 + 28*r. Determine l so that n(l) = 0.
-3, 1, 2
Let r(q) be the third derivative of q**8/168 + 11*q**7/105 + 23*q**6/30 + 3*q**5 + 27*q**4/4 + 9*q**3 + 12*q**2. Determine u so that r(u) = 0.
-3, -1
Let r(p) be the third derivative of 2*p**7/105 + p**6/10 + p**5/5 + p**4/6 - 7*p**2. Factor r(y).
4*y*(y + 1)**3
Let x(l) be the third derivative of -l**7/420 + l**6/80 - l**5/40 + l**4/48 + 2*l**2 + 5*l. Solve x(k) = 0 for k.
0, 1
Factor -676/7*t**3 - 16/7 - 468/7*t**2 + 192/7*t.
-4*(t + 1)*(13*t - 2)**2/7
Let i(b) be the first derivative of -5 + 3/4*b**4 + 1/3*b**3 - 1/6*b**6 - b**2 - 1/5*b**5 + 0*b. What is d in i(d) = 0?
-2, -1, 0, 1
Let r(k) be the second derivative of k**5/20 + k**4/4 - 2*k**2 - 4*k. Factor r(g).
(g - 1)*(g + 2)**2
Let a(q) be the first derivative of -q**3 + 3 + 2*q**2 + 1/6*q**4 + 3*q. Let f(p) be the first derivative of a(p). Factor f(o).
2*(o - 2)*(o - 1)
Let g(k) be the first derivative of -k**5/5 - k**4/4 + k**3/3 + k**2/2 + 20. Factor g(y).
-y*(y - 1)*(y + 1)**2
Let d(r) be the third derivative of -5*r**7/42 - r**6/3 - r**5/12 + 5*r**4/12 - 6*r**2. Factor d(n).
-5*n*(n + 1)**2*(5*n - 2)
Let z = 27 - 33. Let h be (-15)/(-12) + z/8. Factor -1/2*j**4 + 1/2*j**3 + 0 - 1/2*j + h*j**2.
-j*(j - 1)**2*(j + 1)/2
Factor 0 + 34/5*o**2 - 6*o**3 - 4/5*o.
-2*o*(o - 1)*(15*o - 2)/5
Let u(w) be the second derivative of -2/3*w**3 + 4/5*w**5 + 0*w**2 + 0 - w + 1/6*w**4 + 1/3*w**6. Factor u(b).
2*b*(b + 1)**2*(5*b - 2)
Let i(w) = -3*w**5 + w**4 - 2*w**2 + 2*w. Let q(x) = 3*x**5 + 3*x**2 - 3*x. Let b(s) = -3*i(s) - 2*q(s). Factor b(t).
3*t**4*(t - 1)
Let n(h) be the third derivative of h**5/30 - 5*h**4/6 + 25*h**3/3 + 7*h**2. Factor n(a).
2*(a - 5)**2
Let q(z) = -104*z - 413. Let j be q(-4). Factor 0*s + 4/13*s**j + 0 - 2/13*s**4 - 2/13*s**2.
-2*s**2*(s - 1)**2/13
Let c(w) be the third derivative of 0 + 0*w + 0*w**4 + 0*w**3 - 4*w**2 - 1/20*w**5. Factor c(t).
-3*t**2
Let i(n) be the first derivative of -n**4/2 + 24*n**3 - 432*n**2 + 3456*n - 29. Factor i(m).
-2*(m - 12)**3
Factor 9/2*o - 15/4 - 9/2*o**3 + 3*o**2 + 3/4*o**4.
3*(o - 5)*(o - 1)**2*(o + 1)/4
Let t(j) be the third derivative of 0 + 1/28*j**4 - 1/21*j**3 + 1/420*j**6 + 4*j**2 + 0*j - 1/70*j**5. Factor t(z).
2*(z - 1)**3/7
Let l(p) be the first derivative of -3*p**4/8 + p**3/12 - 1. Factor l(c).
-c**2*(6*c - 1)/4
Let t = 66 - 64. Let u be -2*(-2)/8*0. Solve -14/9*f**t + 4/9*f + 10/9*f**3 + u = 0.
0, 2/5, 1
Let h(y) be the third derivative of y**8/1176 - y**7/245 + y**6/140 - y**5/210 + 2*y**2. Let h(n) = 0. Calculate n.
0, 1
Let w(h) be the first derivative of -33/2*h**2 - 9*h**3 - 2 - 6*h. Let w(r) = 0. Calculate r.
-1, -2/9
Let h(s) = 40*s**3 - 35*s**2 - 15*s. Let y(p) = -20*p**3 + 17*p**2 + 7*p. Let v(j) = 2*h(j) + 5*y(j). Determine d, given that v(d) = 0.
-1/4, 0, 1
Let d be ((-6)/3)/(-3 + 2). Factor b**3 - 3*b**2 + b**2 + d*b**2 - b**4.
-b**3*(b - 1)
Let y = 5 + -3. Factor -2/5 - 1/5*g + 1/5*g**y.
(g - 2)*(g + 1)/5
Let p(d) be the third derivative of 1/240*d**5 + 0 - 2*d**2 - 1/24*d**4 + 0*d + 1/6*d**3. Solve p(g) = 0.
2
Suppose 6*h - 10 = 14. Let j(q) be the second derivative of -1/3*q**h - 2*q + 1/3*q**3 + 1/21*q**7 + q**2 + 1/15*q**6 - 1/5*q**5 + 0. Factor j(i).
2*(i - 1)**2*(i + 1)**3
Let y = -26/287 + -146423/2583. Let q = y + 57. Factor 0*j**2 + q - 4/9*j - 2/9*j**4 + 4/9*j**3.
-2*(j - 1)**3*(j + 1)/9
Let j(t) = t + 17. Let a be j(-11). Determine c so that 3*c**3 - 40*c**4 + 2 + 44*c**2 - 7 + 3*c**3 - a*c + 1 = 0.
-1, -1/4, 2/5, 1
Let s(h) be the first derivative of -2*h**3/33 + 4*h**2/11 - 6*h/11 - 2. Suppose s(d) = 0. Calculate d.
1, 3
Let o = 3 + -1. Let i(d) be the second derivative of -1/50*d**5 + o*d - 1/10*d**4 - 1/5*d**3 + 0 - 1/5*d**2. Factor i(b).
-2*(b + 1)**3/5
Suppose -20 = -4*j, m - j = 4*m - 11. Factor 1 + 5*z - 1 - 6*z + z**m.
z*(z - 1)
Let a(w) be the second derivative of -14*w**6/15 + 2*w**5/5 + 29*w. Factor a(q).
-4*q**3*(7*q - 2)
Suppose 5*o = 3 + 17. Find b, given that -3*b**2 + 2*b**4 - 7*b + b**o + 10*b - 3*b**3 = 0.
-1, 0, 1
Suppose 3*m = -5*a + 9, 2 = 4*a + m - 8. Suppose 3 = -a*p, 0*p - 1 = -t + p. Factor t*x**2 - 2 - 3*x**2 - 2*x**4 + 7*x**2.
-2*(x - 1)**2*(x + 1)**2
Let i be (-4)/18 - 58/(-18). Let i*z - 3*z**4 + 3*z**2 - z**3 + 2*z - 2*z**3 - 2*z = 0. What is z?
-1, 0, 1
Let v = 4 + -3. Suppose 2*p = 6, -v + 4 = -3*r + 4*p. Find i, given that 0*i**2 + 1 + 1/2*i**r - 3/2*i = 0.
-2, 1
Let k(o) = -o**5 - 5*o**4 + 8*o**3 - 2*o**2 + 2. Let y(q) = q**5 + 11*q**4 - 17*q**3 + 5*q**2 - 5. Let s(l) = -5*k(l) - 2*y(l). Suppose s(m) = 0. Calculate m.
-2, 0, 1
Let v(n) = -n**2 - 6*n + 1. Let r(d) = -7*d**2 - 37*d + 5. Let x(p) = -6*r(p) + 39*v(p). Solve x(k) = 0 for k.
1, 3
Let r = -4 - -8. Suppose -2 = -r*k + 3*k. Factor -k + 6*m**2 + 2*m**2 - 2*m**4 - 4*m**2 + 0.
-2*(m - 1)**2*(m + 1)**2
Factor -v**3 - 2*v**3 - 4*v**2 + 8*v - 2*v**3 - 3*v**3 + 4*v**4.
4*v*(v - 2)*(v - 1)*(v + 1)
Let o(p) = -p - 5. Let b be o(-4). Let j be b + 1 - (-2)/3. Factor 0*q**2 + 2/3*q**3 + 0 - j*q.
2*q*(q - 1)*(q + 1)/3
Let x = -9727/9 - -1081. Let 0*g**2 + 2/9*g**3 + 0 - x*g**4 + 0*g = 0. What is g?
0, 1
Suppose 0 = 2*d - 0*d - 5*w - 8, 5*d + 5*w = -50. Let q be ((-18)/(-24))/(d/(-4)). Factor 0*v - 1/2*v**2 - q*v**3 + 1/2*v**4 + 1/2*v**5 + 0.
v**2*(v - 1)*(v + 1)**2/2
Let a(c) = -c - 4. Let b be a(0). Let o be (-1)/b + (-33)/(-12). Determine x, given that 0 + 1/2*x + 1/2*x**o + x**2 = 0.
-1, 0
Let i(d) = 8*d**3 - 22*d**2 + 26*d. Let s(r) = r**2 + r + 1. Let t(b) = -2*b - 4. Let a be t(0). Let k(u) = a*s(u) + i(u). Factor k(p).
2*(p - 2)*(p - 1)*(4*p - 1)
Let s(x) be the second derivative of x**5/45 - x**4/18 - 8*x**3/27 - x**2/3 - 5*x. What is m in s(m) = 0?
-1, -1/2, 3
Suppose 0 = -4*o - 3*b - 19, -20 = 3*b + b. Let n = o - -3. Factor -2*t**n - 2/3 + 8/3*t.
-2*(t - 1)*(3*t - 1)/3
Suppose 8 = 4*s + 4*q - 12, -15 = -5*q. Let d(z) be the first derivative of -1/12*z**3 + 1/4*z - 1/16*z**4 + s + 1/8*z**2. Let d(l) = 0. Calculate l.
-1, 1
Let u(j) be the second derivative of -j**4/48 + j**3/12 - j**2/8 - 14*j. Factor u(m).
-(m - 1)**2/4
Let w(d) be the second derivative of -d**4/66 - 5*d**3/33 + 6*d**2/11 + 21*d. Factor w(h).
-2*(h - 1)*(h + 6)/11
Let t be (-45)/18*(-2 - 0). Suppose 0 = m - 4*i - 14, i - t*i - 18 = -3*m. Determine h, given that -2*h - h**m + 2 + 6*h**3 - 4*h**3 - h**2 = 0.
-1, 1
Factor -7*o**2 - 3*o**2 + o**2 + 9*o**3 + 3*o - 3*o**4.
-3*o*(o - 1)**3
Suppose 2*f + 2*f = 0. Let d(j) be the third derivative of 0*j - 1/480*j**6 - 1/96*j**4 + f*j**3 - 1/120*j**5 + j**2 + 0. Find a such that d(a) = 0.
-1, 0
Let g(u) be the third derivative of u**5/15 + 5*u**4/6 + 8*u**3/3 - 23*u**2. Factor g(o).
4*(o + 1)*(o + 4)
Let s(a) be the third derivative of 1/12*a**4 + 1/420*a**7 + 1/3*a**3 + 0 + 0*a - 4*a**2 - 1/40*a**5 - 1/120*a**6. Factor s(v).
(v - 2)**2*(v + 1)**2/2
Suppose 0 = 5*c - 3 - 12, 5*c - 15 = -3*k. Suppose k*j - 5*j = -15. Factor -2*f**5 + f**3 + 6*f + 2*f**2 - 6*f**2 - 5*f**j + 6*f**4 - 2.
-2*(f - 1)**4*(f + 1)
Let k(x) be the third derivative of x**6/24 - x**5/12 - 5*x**4/12 - x**2 - 6. Factor k(b).
5*b*(b - 2)*(b + 1)
Let i(n) be the third derivative of -n**5/120 - n**4/8 - 36*n**2. Suppose i(b) = 0. Calculate b.
-6, 0
Let g = 3 - 2. Suppose -q - 3*q - u = -13, 3*q = u + g. Factor -3 + 2*p**3 + 5 - 1 - q*p - p**4.
-(p - 1)**3*(p + 1)
Let n(s) be the third derivative of 0*s**3 + 3*s**2 - 1/210*s**5 + 1/42*s**4 - 1/420*s**6 + 0*s + 0. Solve n(o) = 0 for o.
-2, 0, 1
Let f = 2639/3 - 879. Suppose 0 + 0*p + 0*p**2 + f*p**3 = 0. Calculate p.
0
Let j = -80 - -84. Let u(q) be the third derivative of 0 + 0*q**j + 0*q + 1/30*q**5 - 1/3*q**3 - 3*q**2. Factor u(p).
2*(p - 1)*(p + 1)
Let d(o) = -o**5 + o**4 + o**3. Let x(t) = -12*t**5 + 3*t**4 + 3*t**4 + 3*t**4 + 2*t**2 + t + 11*t**3. Let g(v) = -22*d(v) + 2*x(v). Factor g(p).
-2*p*(p - 1)*(p + 1)**3
Let d(q) = -15*q**5 - 54*q**4 - 24*q**3 + 30*q**2 + 15*q. Let s(f) = -3*f**5 - 11*f**4 - 5*f**3 + 6*f**2 + 3*f. Let x(k) = -5*d(k) + 24*s(k). Factor x(j).
3*j*(j - 1)*(j + 1)**3
Let x(t) be the second derivative of -t**5/180 - t**4/36 + t**3/6 + 3*t**2 - 6*t. Let s(h) be the first derivative of x(h). Factor s(p).
-