). Let c be (27/(-24))/(3/(-4)). Factor -z*d - 3/2*d**2 - c.
-3*(d + 1)**2/2
Let p(g) be the first derivative of -g**4 + 128*g**3/9 + 22*g**2/3 + 406. Suppose p(i) = 0. Calculate i.
-1/3, 0, 11
Let r be (-229)/(-110) + 4/(-22). Let l = r - 3/2. Suppose l*q + 0*q**2 + 0 - 2/5*q**3 = 0. Calculate q.
-1, 0, 1
Let v(o) be the first derivative of -4*o**5/35 + 5*o**4/7 - 8*o**3/7 - 8*o**2/7 + 32*o/7 - 119. What is s in v(s) = 0?
-1, 2
Let x(k) be the third derivative of 2*k**7/105 - k**6/5 + 13*k**5/15 - 2*k**4 + 8*k**3/3 + 7*k**2 - 13. Factor x(w).
4*(w - 2)**2*(w - 1)**2
Let p(s) be the third derivative of -s**7/42 + 7*s**6/24 - 3*s**5/4 - 35*s**4/24 + 25*s**3/3 - 71*s**2 - s. Let p(n) = 0. What is n?
-1, 1, 2, 5
Factor -34/11 + 2/11*r**2 - 32/11*r.
2*(r - 17)*(r + 1)/11
Let q(c) be the third derivative of c**5/330 + 13*c**4/132 + 4*c**3/11 - 350*c**2. Factor q(w).
2*(w + 1)*(w + 12)/11
Let r(s) be the first derivative of s**8/5880 + s**7/2940 - s**6/630 + 2*s**3/3 - 2*s**2 + 17. Let t(w) be the third derivative of r(w). Solve t(v) = 0.
-2, 0, 1
Let v be 11*4/(1 + 3). Let t = -11 + v. Factor -3/2*u**4 - 1/2*u**2 - 1/2*u**5 + t + 0*u - 3/2*u**3.
-u**2*(u + 1)**3/2
Let x be (-3 - (0 - 1)) + 2 - -2. Factor x*p - 18*p**2 + 575*p**3 + 2*p + 8*p**4 - 569*p**3.
2*p*(p - 1)*(p + 2)*(4*p - 1)
Let x(l) be the first derivative of -l**5/510 - 11*l**4/204 + 29*l**2/2 - 28. Let g(n) be the second derivative of x(n). Let g(m) = 0. Calculate m.
-11, 0
Determine z so that -82*z**2 + 60*z - 86*z**2 + 64 + 164*z**2 = 0.
-1, 16
Let d = -34 + 37. Let -5*q**3 - 3*q**5 + 5*q**3 + 9*q + 0*q**4 - 3 - 6*q**d + 9*q**4 - 6*q**2 = 0. What is q?
-1, 1
Let z = -169/2 + 509/6. Factor 4/3*d + 5/3 - z*d**2.
-(d - 5)*(d + 1)/3
Let h(z) be the third derivative of -1/10*z**4 - 1/150*z**5 + 0*z**3 + z**2 + 0*z + 0. What is d in h(d) = 0?
-6, 0
Solve -15*l**3 + 15 - 75 - 192*l - 27*l**2 - 84*l**2 = 0.
-5, -2, -2/5
Let g(c) = c**2 + c. Let k(u) = -2*u**4 + 16*u**3 - 31*u**2 + u. Let o be (-8)/(-5) - (-4)/10. Let s(m) = o*k(m) - 2*g(m). Factor s(j).
-4*j**2*(j - 4)**2
Suppose -301*g = -314*g + 52. Let t(k) be the third derivative of 1/6*k**3 + 0*k + 1/16*k**g + 0 - 4*k**2 + 1/120*k**5. Factor t(j).
(j + 1)*(j + 2)/2
Let n be (-7155)/530 + 1*14. Factor n*a**2 + 49/2 - 7*a.
(a - 7)**2/2
Factor z + z**5 + 4*z**2 - 5*z**2 + 2*z**4 + 7*z - 101*z**3 + 96*z**3 - z**4 - 4.
(z - 1)**3*(z + 2)**2
Let o(x) be the second derivative of x**7/21 + 8*x**6/45 - x**5/10 - 2*x**4/3 + 4*x**3/9 - 83*x. Determine l so that o(l) = 0.
-2, 0, 1/3, 1
Let p(o) be the third derivative of 1/108*o**4 + 0*o**3 + 0 + 0*o - 1/54*o**5 + 5*o**2. Factor p(i).
-2*i*(5*i - 1)/9
Let k(c) be the third derivative of c**5/240 + 3*c**4/32 + 5*c**3/6 + 35*c**2. Solve k(w) = 0 for w.
-5, -4
Let w(f) be the second derivative of f**6/15 + 14*f**5/5 + 40*f**4 + 400*f**3/3 - 2000*f**2 - 93*f. Factor w(n).
2*(n - 2)*(n + 10)**3
Let d(v) be the third derivative of 5*v**7/42 + 67*v**6/6 + 1179*v**5/4 - 1215*v**4/4 + 280*v**2. Determine j so that d(j) = 0.
-27, 0, 2/5
Let g(u) = -4*u + 9. Let m be g(1). Let a(v) be the second derivative of 2*v + 1/24*v**3 + 0 + 0*v**2 + 0*v**4 - 1/80*v**m. Factor a(q).
-q*(q - 1)*(q + 1)/4
Let f = -32 + 37. Find z such that 17*z**2 - 10*z**4 - 3*z - f*z**2 + z**4 - 3*z**4 + 3*z**3 = 0.
-1, 0, 1/4, 1
Let y(a) be the first derivative of a**8/1680 - a**7/210 + 2*a**5/15 - 2*a**4/3 + 19*a**3/3 - 9. Let j(k) be the third derivative of y(k). Factor j(t).
(t - 2)**3*(t + 2)
Let s(o) be the first derivative of o**5/10 + o**4/2 - o**3/3 - 3*o**2 + 2*o + 5. Let x(p) be the first derivative of s(p). Factor x(r).
2*(r - 1)*(r + 1)*(r + 3)
Let f(w) be the third derivative of -w**6/40 + 879*w**5/80 - 12045*w**4/8 - 3025*w**3/2 - 502*w**2. Factor f(x).
-3*(x - 110)**2*(4*x + 1)/4
Determine f so that 0 + 4/3*f**2 - 4/3*f**4 - 8/3*f**3 + 2*f + 2/3*f**5 = 0.
-1, 0, 1, 3
Let b(o) be the second derivative of -o**4/3 + 22*o**3/3 - 20*o**2 + 11*o. Find i, given that b(i) = 0.
1, 10
Let p(i) = -i + 1. Let b = 8 - 4. Let t(h) = 0*h - 7 + 0*h + 3*h + 2*h - h**2. Let y(f) = b*t(f) + 28*p(f). Factor y(u).
-4*u*(u + 2)
Factor -3*w**2 - 8*w**2 - 2*w**2 - 120 + 8*w**2 + 50*w.
-5*(w - 6)*(w - 4)
Suppose -m = -s - 9 + 54, 3*s = m + 145. Let u = s - 32. Factor u - 12*g - 18*g**2 + 11*g**2 + 9*g**2.
2*(g - 3)**2
Let h = 0 - -3. Suppose 2*k + 4*v = -0*k + 10, -3*v - 33 = -h*k. What is q in -12*q**4 + k*q**4 - 4*q**4 + 13*q**3 - 14*q**4 - 2*q**2 = 0?
0, 2/7, 1/3
Factor 0*d + 80/13*d**3 + 0 + 2/13*d**5 + 2*d**4 + 72/13*d**2.
2*d**2*(d + 2)**2*(d + 9)/13
Let c = 201 - 69. Let l = 397/3 - c. Suppose 1/3*t**2 + 0 + l*t = 0. What is t?
-1, 0
Suppose 0 = 2*t, t + 3*t = s - 3. Suppose s*g - 2 = h, 0*g - 3*g + 14 = 2*h. Suppose -4*x**g + 8*x - 16/3 + 2/3*x**3 = 0. What is x?
2
Let l(m) be the second derivative of -1/108*m**4 + 0*m**2 - 3*m - 1/18*m**3 + 0. Factor l(r).
-r*(r + 3)/9
Let -5/4*s**3 + 35/4*s - 15/2*s**2 + 0 = 0. What is s?
-7, 0, 1
Let y(g) = -g**3 - 2*g**2 + 7*g + 12. Let r be y(-2). Let l be (-3)/r - 16/12. Factor -l + 1/3*a - 1/6*a**2.
-(a - 1)**2/6
Let f = -9 - 15. Let m = 28 + f. Determine j, given that 3/2*j**2 - 9/2*j**m + 0 - 3*j + 6*j**3 = 0.
-2/3, 0, 1
Let l(v) = -v**3 - 18*v**2 - 17*v + 3. Let p be l(-17). Factor 0 - 2*b + 0*b + 3 - 6*b**2 + p*b**5 - 6*b**3 + 5*b + 3*b**4.
3*(b - 1)**2*(b + 1)**3
Let u(a) be the first derivative of -5*a**4/4 - 35*a**3 - 300*a**2 - 500*a - 362. Determine h so that u(h) = 0.
-10, -1
Factor 3/2*w + 3/2*w**2 + 0.
3*w*(w + 1)/2
Suppose 98 = 4*r - 226. Let d = -242/3 + r. Suppose 1/6 + 1/6*q**2 + d*q = 0. Calculate q.
-1
Solve 10*v**4 - 55*v**4 + 76*v - 165*v**3 + 12*v**5 + 24 + 50*v + 111*v**2 + 117*v**3 = 0 for v.
-1, -1/4, 2, 4
Let n(o) be the third derivative of -o**5/10 + 15*o**4/16 - 9*o**3/4 + 4*o**2 + 3*o. Suppose n(i) = 0. Calculate i.
3/4, 3
Let y be 3 - (5/4 + 5/(-20)). Factor 51*l + l**4 - 3*l**y + 3*l**3 + 0*l**4 + 6*l**2 - 50*l.
l*(l + 1)**3
Let m(z) be the first derivative of 2*z**3/3 - 4*z**2 + 6*z - 72. Factor m(i).
2*(i - 3)*(i - 1)
Let x(q) = -q**4 + 63*q**3 - 952*q**2 - 1032*q - 8. Let b(r) = r**2 - r - 1. Let z(h) = 24*b(h) - 3*x(h). Determine k, given that z(k) = 0.
-1, 0, 32
Let w(u) be the first derivative of -4*u**5/5 + 5*u**4 + 16*u**3/3 - 88*u**2 + 192*u + 12. Factor w(t).
-4*(t - 4)*(t - 2)**2*(t + 3)
Factor 2/7*y**5 + 4/7*y**3 + 0 + 0*y + 0*y**2 + 6/7*y**4.
2*y**3*(y + 1)*(y + 2)/7
Let t be (-8 - -1)/7*-2. Let -4/9 - 2/9*a**t + 2/3*a = 0. What is a?
1, 2
Let n(t) be the second derivative of -t**4/3 - 340*t**3 - 130050*t**2 - 22*t - 12. What is j in n(j) = 0?
-255
Let y = 8167/3644 - -8/911. Factor -y*o**2 + 3/4*o**4 - 3/4*o + 3/2 + 3/4*o**3.
3*(o - 1)**2*(o + 1)*(o + 2)/4
Let o(y) be the first derivative of -y**6/51 + y**4/17 - y**2/17 - 34. Factor o(b).
-2*b*(b - 1)**2*(b + 1)**2/17
Let z(x) be the first derivative of -7*x**6/2880 - x**5/96 - x**4/64 - 41*x**3/3 - 49. Let h(r) be the third derivative of z(r). Find o, given that h(o) = 0.
-1, -3/7
Let d = 1051/201 + -328/67. Factor -1/3*c**2 + d - c**3 + c.
-(c - 1)*(c + 1)*(3*c + 1)/3
Let a(z) be the second derivative of z**7/16380 - z**6/1560 + 2*z**4 - 45*z. Let h(d) be the third derivative of a(d). Factor h(f).
2*f*(f - 3)/13
Let a(c) be the first derivative of -c**9/9072 - c**8/720 - c**7/315 + 2*c**6/135 - 5*c**3/3 - 10. Let m(p) be the third derivative of a(p). Factor m(t).
-t**2*(t - 1)*(t + 4)**2/3
Let x(z) be the third derivative of -1/100*z**5 + 0*z + 2*z**2 - 1/20*z**4 + 0 + 0*z**3. Suppose x(s) = 0. What is s?
-2, 0
Let j(a) be the first derivative of -2/7*a**2 + 2/7*a**4 + 2/21*a**3 - 5 - 6/35*a**5 + 0*a. Suppose j(g) = 0. What is g?
-2/3, 0, 1
Let g be (-11)/22 + 136/144. Factor -g*o**4 - 14/9*o + 4/9 + 2/9*o**5 + 16/9*o**2 - 4/9*o**3.
2*(o - 1)**4*(o + 2)/9
Let q = -225 - -676/3. Let c(a) be the second derivative of a**2 + q*a**3 - 1/10*a**5 + 0 - 1/6*a**4 + 3*a. Find i, given that c(i) = 0.
-1, 1
Let h = -237 + 238. Let o be ((1 + (-1)/h)/(-2))/(-3). What is x in 2/13*x**2 + o*x + 0 = 0?
0
Let r(s) be the first derivative of 0*s + 4/15*s**3 - s**2 + 1/15*s**4 - 3 + 1/150*s**5. Let q(n) be the second derivative of r(n). Let q(l) = 0. Calculate l.
-2
Suppose -4*h + 20 = 4. Suppose 0*a + h = 2*a. What