o(q) be the second derivative of -q**5/20 + q**4/6 + q**3/2 + 72*q. Solve o(r) = 0.
-1, 0, 3
Let t = -1970 + 1972. Factor -3/2*s**t - 3/4*s + 3/2 + 3/4*s**3.
3*(s - 2)*(s - 1)*(s + 1)/4
Let j(o) = o**2 - 26*o - 2. Let x(t) = -4*t**2 + 78*t + 7. Let v(u) = -17*j(u) - 6*x(u). Factor v(w).
(w - 4)*(7*w + 2)
Let d(c) be the second derivative of 0 - 12*c + 0*c**4 - 3*c**2 + 3/2*c**3 - 3/20*c**5. Factor d(u).
-3*(u - 1)**2*(u + 2)
Let t(d) be the third derivative of -1/52*d**4 + 35*d**2 - 1/390*d**5 + 4/39*d**3 + 0*d + 0. Factor t(a).
-2*(a - 1)*(a + 4)/13
Let b(v) = -4*v**2 + 29*v - 64. Let c be (3/(-2))/((-2)/4). Let p(f) = 8*f**2 - 59*f + 128. Let n(w) = c*p(w) + 5*b(w). Factor n(i).
4*(i - 4)**2
Let h(x) = 2*x**2 + 22*x - 5. Let f be h(-11). Let n be f + 2/((-12)/(-30)). Factor n + 5/4*u**3 - 5/4*u**2 - 5/2*u.
5*u*(u - 2)*(u + 1)/4
Let q(k) = -16*k**2 + 12*k - 1. Let n(r) = 16*r**2 - 11*r + 1. Suppose 2*x = -5*a + 15, -3*a - 4*x + 3 = -2*a. Let h(y) = a*q(y) + 4*n(y). Factor h(v).
(4*v - 1)**2
Let p(y) be the second derivative of 5*y**4/8 + 5*y**3/6 - 5*y**2/4 - 12*y + 6. Determine d, given that p(d) = 0.
-1, 1/3
Let s(m) be the second derivative of m**10/60480 - m**9/6048 + m**8/4480 + m**7/560 - 4*m**4/3 + 2*m. Let z(b) be the third derivative of s(b). Factor z(l).
l**2*(l - 3)**2*(l + 1)/2
Let g(a) = 14*a**2 + 5*a - 36. Let z(s) = 3*s**2 - 2. Let c(d) = g(d) - 3*z(d). Suppose c(o) = 0. Calculate o.
-3, 2
Let l(a) be the second derivative of a**5/25 + 77*a**4/60 + 91*a**3/30 + 9*a**2/5 - 2*a - 15. Suppose l(y) = 0. Calculate y.
-18, -1, -1/4
Let g = 753/7 + -4511/42. Let r(x) be the first derivative of 10 - g*x**3 + 0*x - 1/12*x**6 - 3/8*x**4 - 3/10*x**5 + 0*x**2. Find f such that r(f) = 0.
-1, 0
Let u(l) be the first derivative of 3*l**4/4 + 17*l**3/3 + 5*l**2 + 78. Factor u(y).
y*(y + 5)*(3*y + 2)
Let j(q) be the second derivative of q**7/3780 + q**6/1080 - q**5/90 + 4*q**4/3 + 15*q. Let u(x) be the third derivative of j(x). Factor u(z).
2*(z - 1)*(z + 2)/3
Let i(o) = -55*o**2 - 760*o - 705. Let s(f) = 5*f**2 + 69*f + 64. Let k(l) = -4*i(l) - 45*s(l). Let k(t) = 0. What is t?
-12, -1
Let o = 19434/5 - 3886. Factor -4/5*a**2 - 2/5 + 6/5*a**4 - o*a**3 + 6/5*a - 2/5*a**5.
-2*(a - 1)**4*(a + 1)/5
Let g = -155 - -155. Let i(t) be the third derivative of 1/35*t**7 + 0*t**3 + 0 + 0*t**5 + g*t - t**2 + 0*t**4 + 1/60*t**6. Let i(n) = 0. Calculate n.
-1/3, 0
Suppose -4676*x + 7744 + 95*x**3 - x**5 - 10*x**4 + 20147*x**2 - 19687*x**2 + 276*x = 0. Calculate x.
-11, 4
Solve 2*c**3 - 5*c**3 + 735*c - 6*c**2 - 2319*c - 730 - 129*c**2 - 722 = 0 for c.
-22, -1
Let x(p) be the second derivative of -p**5/190 - 23*p**4/38 + 142*p**3/57 + 28*p + 2. Solve x(t) = 0.
-71, 0, 2
Let a(h) be the second derivative of -h**5/160 + 107*h**4/96 - 2915*h**3/48 + 2809*h**2/16 + h + 95. Factor a(k).
-(k - 53)**2*(k - 1)/8
Let h be 2/(-14) + (-213)/(-21). Suppose -h = -2*x + 4*w, w = -3*w - 8. What is b in -14*b**2 - 12*b**2 + 28*b**2 + x - 6*b + 3 = 0?
1, 2
Let -24/5*z + 9/5*z**3 - 16/5 + 31/5*z**2 = 0. Calculate z.
-4, -4/9, 1
Let u = -54 - -71. Factor u*l**5 - 28*l**5 + 3*l**3 - l**2 - 4*l**3 + 12*l**5 + l**4.
l**2*(l - 1)*(l + 1)**2
Suppose -404*c + h - 35 = -411*c, 3*h = -3*c + 33. Factor -15/2*y - c - 3*y**2 + 1/2*y**3.
(y - 8)*(y + 1)**2/2
Let k(j) = -12*j**4 + 2*j**3 - 2*j**2 - 8*j. Let v(l) = 34*l**4 - 6*l**3 + 4*l**2 + 24*l. Let y(u) = -14*k(u) - 5*v(u). Factor y(h).
-2*h*(h - 2)*(h - 1)*(h + 2)
Let r be 96/3120*45/3. Factor -r*c**3 - 6/13*c**2 - 2/13*c**4 + 0 - 2/13*c.
-2*c*(c + 1)**3/13
Let t(c) be the third derivative of 5/6*c**4 + 0*c + 5/2*c**3 + 0 + 1/12*c**5 + 9*c**2. Let t(q) = 0. What is q?
-3, -1
Let c be 12/(-12)*(5 - 7). Let q(k) be the third derivative of 1/9*k**3 - 1/45*k**5 + 0*k + 2*k**c + 0 - 1/36*k**4. What is y in q(y) = 0?
-1, 1/2
Suppose -26792/3*o**2 - 19652/3 - 42772/3*o - 3880/3*o**3 - 212/3*o**4 - 4/3*o**5 = 0. Calculate o.
-17, -1
Let o = -39087/7 + 5586. Factor 3/7 + o*w**2 - 18/7*w.
3*(w - 1)*(5*w - 1)/7
Let k be (-508)/10 - 17/85. Let v be k/(-34) - (-1)/2. Let 13*h - 148 + 5*h + 3*h**v + 175 = 0. What is h?
-3
Let -20*m**3 + 0 - 2/3*m**4 - 784/3*m - 168*m**2 = 0. Calculate m.
-14, -2, 0
Let s(x) be the third derivative of -x**8/20160 - x**7/5040 + 31*x**5/60 + 12*x**2. Let i(d) be the third derivative of s(d). Factor i(y).
-y*(y + 1)
Let u(a) be the second derivative of -a**4/16 - 15*a**3/8 + 51*a**2/4 - 99*a. Solve u(q) = 0 for q.
-17, 2
Suppose 6 = 6*u - 3*u. Suppose -5*h + 10*h - 30 = 0. Factor -6*t**4 + 2*t - 4*t**2 + 4*t**3 - h*t**u + 10*t**3.
-2*t*(t - 1)**2*(3*t - 1)
Let v be (-2)/14*((-3)/24 + (-1775)/1704). What is c in -v*c**3 - 5/6*c**2 - 1/2 - 7/6*c = 0?
-3, -1
Suppose 12*j = 13*j + 5. Let r(x) = x**3 + 5*x**2 + 2*x + 14. Let p be r(j). Factor 2/9 + 4/9*m**3 + 0*m**2 - 2/9*m**p - 4/9*m.
-2*(m - 1)**3*(m + 1)/9
Factor -1/8*f**2 - 7/4*f - 49/8.
-(f + 7)**2/8
Let -345/4*n**2 - 6*n**5 - 225/4*n + 45*n**4 - 15/2*n**3 - 21/2 = 0. Calculate n.
-1/2, 2, 7
Let k = 4 - 4. Suppose k = 6*y - 11*y + 20. Determine v so that 0*v**3 - 6*v**4 + v**3 + 7*v**y = 0.
-1, 0
Factor -5845/3*h**2 - 5/6*h**5 - 155/6*h**4 - 955/3*h**3 - 42875/6 - 35525/6*h.
-5*(h + 5)**2*(h + 7)**3/6
Suppose -7*o - i = -12*o + 5, -5*o = -4*i + 10. Factor -20*v + 7*v**o + 11*v**2 - 20 + v**2 - 24*v**2.
-5*(v + 2)**2
Let v = -44187 - -44190. Factor -2/9*f + 8/9*f**2 - 8/9 + 2/9*f**v.
2*(f - 1)*(f + 1)*(f + 4)/9
Let f(g) be the first derivative of -5*g**6/8 - 13*g**5/4 - 95*g**4/16 - 55*g**3/12 - 5*g**2/4 - 62. Suppose f(z) = 0. Calculate z.
-2, -1, -1/3, 0
Let w(r) be the second derivative of -2/3*r**3 - 2/21*r**7 + 19*r - 4/15*r**6 - 4*r**2 + 2/5*r**5 + 4/3*r**4 + 0. What is j in w(j) = 0?
-2, -1, 1
Let r(t) be the first derivative of -2*t**3/45 + 14*t**2/5 - 294*t/5 + 17. Factor r(v).
-2*(v - 21)**2/15
Let l(g) be the first derivative of g**3/9 - 2*g**2 + 32*g/3 - 139. Factor l(r).
(r - 8)*(r - 4)/3
Factor 0 + 108/7*p + 110/7*p**2 + 2/7*p**3.
2*p*(p + 1)*(p + 54)/7
Let f(r) be the first derivative of r**4/4 - 7*r - 26. Let w(q) be the first derivative of f(q). Factor w(d).
3*d**2
Factor 34 - g - 19 + 2*g**3 - 15*g**2 - 2*g + 0*g**3 + g**3.
3*(g - 5)*(g - 1)*(g + 1)
Let y(c) be the second derivative of c**5/5 - 14*c**4/3 + 16*c**3 + 91*c - 2. What is v in y(v) = 0?
0, 2, 12
Let p(g) be the first derivative of 32/5*g**5 + 5/3*g**6 + 8 + 0*g + 12/5*g**3 + 0*g**2 + 69/10*g**4. Determine w, given that p(w) = 0.
-2, -3/5, 0
Let p(h) be the second derivative of h**6/6 + 5*h**5/4 + 25*h**4/12 - 25*h**3/6 - 15*h**2 + 313*h. Find z such that p(z) = 0.
-3, -2, -1, 1
Let c(h) = 2*h**2 + 8*h + 4. Let f(k) = -k + 4. Let r(l) = -2*c(l) + 28*f(l). Factor r(z).
-4*(z - 2)*(z + 13)
Suppose -34*q - 18 = -86. Suppose 2/7*n**q + 50/7 + 20/7*n = 0. Calculate n.
-5
Let k(q) = -q + 2. Let c be k(-2). Factor 13*o**4 + 5*o + 14*o**2 - 3*o**c + 6*o**2 + 25*o**3.
5*o*(o + 1)**2*(2*o + 1)
Let b(g) be the second derivative of -g**4/24 - 17*g**3/12 + 9*g**2/2 + 2*g - 280. Factor b(a).
-(a - 1)*(a + 18)/2
Suppose 5*l - 5 = -25. Let b be (7 - (-2 - -3)) + l. Let -19*t - t**2 - 6 + 10*t - 2*t**b = 0. What is t?
-2, -1
Let s(p) = -4*p + 36. Let f be s(8). Suppose -2*o + 4*n + 4 = -0*o, -2*o = -n - f. Factor -2/5*d**o + 8/5 + 6/5*d.
-2*(d - 4)*(d + 1)/5
Let a be -3*(-6)/(-63)*(14/(-4) - -3). What is c in 0 + 4/7*c**3 - a*c**4 + 2/7*c - 5/7*c**2 = 0?
0, 1, 2
Suppose -5*m = -10*m - 145. Let z = -27 - m. Suppose c**4 + 3 + 14*c**2 - c - 2 - 16*c**4 - z*c**3 - 6*c + 9*c**5 = 0. What is c?
-1, 1/3, 1
Factor 4*t**2 + 28038 + 15441 + 824*t - 1043.
4*(t + 103)**2
Let y(c) = -3*c**2 - 2*c + 1. Let i(l) = -2*l**2 - l + 1. Suppose 3*f - k = -5*k + 26, 0 = f - 3*k. Let g(p) = f*y(p) - 10*i(p). Let g(m) = 0. Calculate m.
-1, 2
Let p be 1/(-5) + 18/90. Suppose -6*q - 4*q = p. Find m such that 0 + 1/7*m**2 + q*m = 0.
0
Let d(c) be the third derivative of -c**7/2016 - c**6/36 - 2*c**5/3 + 11*c**4/12 - 28*c**2. Let b(v) be the second derivative of d(v). Factor b(g).
-5*(g + 8)**2/4
Suppose 5*p + 42 = 3*p. Let m = -19 - p. Let -2*w**3 - 4 + 7 + m*w - w**2 - 3 + w**4 = 0. Calculate w.
-1, 0, 1, 2
Let o(x) be the second derivative of 5*x**7/168 - 5*x**6/12 + 3*x**5/2 - 55*x**4/24 + 35*x**3/24 - 139*x. Factor o(m).
5*m*