.
2*o**3*(o - 1)*(o + 1)
Let g(l) be the second derivative of -l**6/2160 + l**5/360 - 5*l**3/2 - 4*l. Let h(q) be the second derivative of g(q). Solve h(x) = 0 for x.
0, 2
Let r(m) be the second derivative of m**4/96 - m**3/3 - 6*m - 7. Solve r(q) = 0 for q.
0, 16
Let i(m) = m + 21. Let k be i(-7). Find d such that 78*d**3 + k*d**5 - 5*d**2 + 24*d**4 - 72*d**3 + d**2 = 0.
-1, 0, 2/7
Suppose 11*f - 82 = -82. Let u(d) be the third derivative of -4*d**2 + 1/32*d**4 + 0*d**3 - 1/96*d**6 - 1/120*d**5 + f + 0*d. Factor u(c).
-c*(c + 1)*(5*c - 3)/4
Let s(k) be the first derivative of k**6/12 + 7*k**5/5 + 73*k**4/8 + 86*k**3/3 + 44*k**2 + 32*k + 218. What is x in s(x) = 0?
-4, -1
Let d(i) be the second derivative of i**5/10 - 4*i**3/3 - 110*i - 2. Factor d(k).
2*k*(k - 2)*(k + 2)
Suppose 0 = -3*a - 0*a. Let u(r) be the first derivative of 2*r**3 + 4 + 4 - 4*r + a + r**2. Factor u(i).
2*(i + 1)*(3*i - 2)
Let s = -1/949 + -4734/10439. Let o = s - -21/22. Let 2*d**3 + 3*d**2 + 1/2 + 2*d + o*d**4 = 0. Calculate d.
-1
Solve 64 + 16*z - 29*z**3 - 44*z**2 - 13/2*z**4 - 1/2*z**5 = 0.
-4, -2, 1
Factor -5*o + 7 - o**2 + 5*o - 15*o + 10*o**2 + 0*o**3 - o**3.
-(o - 7)*(o - 1)**2
Suppose 4*s + 0*x = 3*x - 10, 5 = 5*s + 5*x. Let z(u) = -3*u**3 - 12*u**2 + 12*u - 3. Let f(p) = p**4 + p**2 + p - 1. Let v(m) = s*z(m) - 3*f(m). Factor v(a).
-3*(a - 1)**3*(a + 2)
Let h(u) = 3*u**2 - 4*u - 27. Let l be h(-6). Let c = l + -105. Determine m, given that -5/6*m**3 + c + 1/6*m**4 - 1/6*m**2 + 1/2*m**5 + 1/3*m = 0.
-1, 0, 2/3, 1
Let f(p) be the first derivative of 4*p**3/15 - 44*p**2 + 42. Factor f(i).
4*i*(i - 110)/5
Let f(g) be the third derivative of -g**6/1620 + g**5/135 + 10*g**3/3 - 13*g**2. Let m(h) be the first derivative of f(h). Let m(s) = 0. Calculate s.
0, 4
Let a(q) be the second derivative of q**6/30 + q**5 + 21*q**4/2 + 98*q**3/3 - q**2/2 + 44*q. Let m(u) be the first derivative of a(u). Factor m(x).
4*(x + 1)*(x + 7)**2
Let h = -8/1231 - -1287/8617. Determine c, given that -1/7*c**2 + h + 0*c = 0.
-1, 1
Factor 18 + 27/4*i**2 - 51/2*i + 3/4*i**3.
3*(i - 2)*(i - 1)*(i + 12)/4
Let d(x) be the first derivative of x**6/60 - 5*x**4/24 + x**2 + 18*x + 41. Let a(u) be the first derivative of d(u). Determine q, given that a(q) = 0.
-2, -1, 1, 2
Suppose 4*l - 242 = 10. Let y be (2 - 16/6) + 258/l. What is n in -y*n + 12/7*n**2 - 2/7*n**3 + 16/7 = 0?
2
Factor -6*r**2 + 0 + 0*r + 3/2*r**3.
3*r**2*(r - 4)/2
Factor -5832/5*g - 216/5*g**2 - 2/5*g**3 + 0.
-2*g*(g + 54)**2/5
Suppose 15 = k + 2*k. Suppose -k*p + 5*n - 10 = 0, 4*p + 4*n - 22 = p. Let -3*m**2 - 2*m**3 - m**3 + p*m**3 - 3*m + 7*m**3 = 0. What is m?
-1/2, 0, 1
Suppose -2*u - 5*b = 175, -2*u = -7*u - 5*b - 445. Let w be ((-4)/(-6))/(460/u + 6). Factor 3/2*p**3 - w*p**4 + 0*p**2 - 3/2*p + 3/4.
-3*(p - 1)**3*(p + 1)/4
Let s(o) be the third derivative of o**7/168 - o**5/48 - 2*o**2 - 39*o. Factor s(g).
5*g**2*(g - 1)*(g + 1)/4
Let a(l) be the second derivative of 2*l**6/15 + l**5 - 11*l**4/3 - 22*l**3 - 36*l**2 - 83*l. Factor a(y).
4*(y - 3)*(y + 1)**2*(y + 6)
Solve 4/5*w**4 - 24/5*w - 32/5*w**3 + 52/5*w**2 + 0 = 0 for w.
0, 1, 6
Let q be ((-2275)/(-77))/5 + -5*1 + 0. Factor -2/11*i**2 + q + 8/11*i.
-2*(i - 5)*(i + 1)/11
Let i = 1 - -1. Let m be 4/2 - -3 - i. Factor 0 - 8*o**4 - 2*o**3 + 0 - 2*o**m - 4*o**5.
-4*o**3*(o + 1)**2
Let j(p) be the first derivative of 0*p + 0*p**2 + 1/8*p**4 - 15 - 1/6*p**3. Find w, given that j(w) = 0.
0, 1
Let v(x) be the second derivative of -x**4/16 + x**3/4 - 3*x**2/8 + 196*x. Solve v(t) = 0 for t.
1
Let 0 - 8/11*n**4 + 2/11*n**5 + 0*n - 2/11*n**3 + 8/11*n**2 = 0. What is n?
-1, 0, 1, 4
Let o(n) be the first derivative of 3*n**5/20 - 3*n**4/4 - n**3/4 + 3*n**2/2 + 125. Factor o(d).
3*d*(d - 4)*(d - 1)*(d + 1)/4
Let r be ((-984)/(-4510))/(-3*3/(-30)). Determine f, given that 0 + r*f + 2/11*f**2 = 0.
-4, 0
Find p such that 64/21*p + 2/21*p**2 - 136/21 = 0.
-34, 2
Let w(a) be the second derivative of -a**6/6 - 5*a**5/2 - 35*a**4/3 - 20*a**3 - 12*a - 6. Factor w(o).
-5*o*(o + 2)**2*(o + 6)
Let f(o) = -7*o**2 + 15*o - 3. Let h = 2 + -7. Let d(u) = u**2 - u - 1. Let y(v) = h*d(v) - f(v). Factor y(s).
2*(s - 4)*(s - 1)
Factor -47/2*t**2 - 14*t - 7/2*t**3 + 6.
-(t + 1)*(t + 6)*(7*t - 2)/2
Let q(k) = 71*k + 73. Let h be q(-1). Factor 0*t**3 - 2*t**4 + 0*t + 8/3*t**h + 0 - 2/3*t**5.
-2*t**2*(t - 1)*(t + 2)**2/3
Factor 8 + 14 + 21*w**2 + 48*w - 1 + 15 + 3*w**3.
3*(w + 2)**2*(w + 3)
Solve 1570*v - 21694 - 32*v**2 - 101551 + 91*v**2 - 30*v**2 - 34*v**2 = 0.
157
Let c(y) = y**2 + 4*y + 3. Let r be c(-4). Factor -2*h**4 - 15*h**r + 0*h**3 + 10*h**2 + 6*h**2 - 103*h**5 + 108*h**5 - 4*h.
h*(h - 1)**2*(h + 2)*(5*h - 2)
Factor -156/7 - 4/7*n**3 + 156/7*n**2 + 4/7*n.
-4*(n - 39)*(n - 1)*(n + 1)/7
Let m(n) = -5*n**2 - 3*n. Let b(p) be the second derivative of p**4/2 + p**3/2 + 14*p. Let d(r) = 2*b(r) + 3*m(r). Let d(y) = 0. Calculate y.
-1, 0
Let t(o) be the second derivative of -o**7/42 + o**6 - 56*o**5/5 - 5*o**4/2 + 75*o**3/2 - 4*o - 1. Factor t(m).
-m*(m - 15)**2*(m - 1)*(m + 1)
Let b(z) = -z - 2*z + 5*z**2 + 3 - z - 4. Let q(d) = -45*d**2 + 35*d + 10. Let s(t) = 35*b(t) + 4*q(t). Suppose s(l) = 0. What is l?
-1, 1
Let c(m) = 2*m**2 - 2*m + 2. Let g(q) = 3*q**2 + 922*q - 43237. Let p(n) = 4*c(n) - g(n). Factor p(i).
5*(i - 93)**2
Suppose -209 = -5*u + 4*k - 183, u = -3*k - 10. Factor -3/7 - 5/7*r**u + 1/7*r**3 + r.
(r - 3)*(r - 1)**2/7
Let u = -463 + 465. Let y(p) be the first derivative of -3*p**2 - 2*p**3 - 1/2*p**4 + 1 - u*p. Let y(b) = 0. Calculate b.
-1
Let u(i) be the third derivative of 0 + 13*i**2 + 1/12*i**4 + 1/3*i**3 + 0*i - 1/60*i**6 - 1/30*i**5. Factor u(g).
-2*(g - 1)*(g + 1)**2
Let n be (-1)/(3/(-30)*5). Let a(s) be the first derivative of 3*s - n*s**2 - 10 + 1/3*s**3. Determine t, given that a(t) = 0.
1, 3
Let u be (-8)/((-40)/(-9))*(-20)/90. What is t in 16/5*t + u*t**3 - 8/5 - 2*t**2 = 0?
1, 2
Let y = 2167/16 - 135. Let q(h) be the first derivative of 5/12*h**3 + 0*h - 4 - 1/4*h**2 + y*h**4. Factor q(v).
v*(v + 1)*(7*v - 2)/4
Let c(b) = -b**2 + b + 2. Let g be c(0). Determine y, given that 7*y**4 + 5*y**5 + g*y**3 + 29 - 29 = 0.
-1, -2/5, 0
Let j be (-7)/(-4) - 5/(-20). Suppose 20*b - 4*b**2 + 7*b**j + 0*b**3 + 17*b**2 + 5*b**3 = 0. Calculate b.
-2, 0
Let y(p) be the third derivative of 1/735*p**7 - 1/210*p**6 + 0*p**3 + 0*p + 0 + 30*p**2 - 1/210*p**5 + 1/42*p**4. Let y(m) = 0. Calculate m.
-1, 0, 1, 2
Let x = -4138/9 + 460. Determine j so that 0 + 0*j + x*j**5 + 2/9*j**2 - 2/9*j**4 - 2/9*j**3 = 0.
-1, 0, 1
Let h(w) be the first derivative of 57 - 5/6*w**6 + 5/2*w**4 - 5*w + 10/3*w**3 - 5/2*w**2 - w**5. Factor h(s).
-5*(s - 1)**2*(s + 1)**3
Let w(c) = -2*c**4 - 4*c**3 + 2*c**2 + 4*c - 3. Let x = -11 + 4. Let g(t) = 4*t**4 + 8*t**3 - 4*t**2 - 8*t + 7. Let r(i) = x*w(i) - 3*g(i). Factor r(h).
2*h*(h - 1)*(h + 1)*(h + 2)
Let q = 13231 - 13228. Factor 0 + 0*k + 2/9*k**2 + 0*k**q - 2/9*k**4.
-2*k**2*(k - 1)*(k + 1)/9
Factor 6*m - 12/7*m**3 + 9/7 + 3*m**2.
-3*(m - 3)*(m + 1)*(4*m + 1)/7
Let q = 338/1375 - 8/125. Factor -q*n**5 - 2/11*n**2 + 2/11*n**4 + 2/11*n**3 + 0*n + 0.
-2*n**2*(n - 1)**2*(n + 1)/11
Let o(i) be the second derivative of i**7/42 + 23*i**6/60 + 77*i**5/40 + 43*i**4/24 - 95*i**3/12 - 25*i**2/2 - 5*i + 13. Find t such that o(t) = 0.
-5, -2, -1/2, 1
Suppose 4*j = j - 78. Let m = -26 - j. Factor m*h - 2/3*h**4 + 0 - 4/3*h**2 + 2*h**3.
-2*h**2*(h - 2)*(h - 1)/3
Let g(m) be the second derivative of -19/78*m**4 + 8*m - 5 + 7/39*m**3 + 4/195*m**6 + 3/13*m**2 + 1/26*m**5. Let g(u) = 0. What is u?
-3, -1/4, 1
Let o(v) be the third derivative of -v**7/42 + v**6/24 + v**5/2 - 5*v**4/6 - 20*v**3/3 + v**2 + 89*v. Factor o(d).
-5*(d - 2)**2*(d + 1)*(d + 2)
Let s = 88 + -84. Determine d, given that -1687*d**2 + 37*d**3 + 5*d**s + 1732*d**2 - 7*d**3 - 20*d - 60 = 0.
-3, -2, 1
Let i(v) = 2*v**3 + 2*v**2 + 2*v. Let n(d) = 17*d**3 + 22*d**2 + d + 8. Let s(t) = 24*i(t) - 3*n(t). Determine o, given that s(o) = 0.
-8, 1
Let b(c) be the third derivative of -c**5/390 - c**4/12 - 22*c**3/39 + 60*c**2. Factor b(p).
-2*(p + 2)*(p + 11)/13
Let f(i) = -i**2 - i. Let r be (-1 + (1 - 1))*2. Let z(o) = 3*o**2 + o**2 - 49*o**3 + 3*o + 0*o**2 + 50*o**3. Let t(b) = r*z(b) - 4*f(b). Factor t(x).
-2*x*(x + 1