 + b). Factor 9/4*j**5 + 15/4*j**y + 7/4*j**3 + 1/4*j**2 + 0 + 0*j.
j**2*(j + 1)*(3*j + 1)**2/4
Suppose -25*b = -8*b. Let f(a) be the third derivative of a**2 + 0*a**3 + 1/1176*a**8 + b*a + 0*a**5 + 0*a**7 - 1/210*a**6 + 0 + 1/84*a**4. Factor f(h).
2*h*(h - 1)**2*(h + 1)**2/7
Let g(p) be the first derivative of 2*p**7/105 + p**6/30 - 2*p**5/15 - 3*p**2/2 + 2. Let q(f) be the second derivative of g(f). Determine t so that q(t) = 0.
-2, 0, 1
Factor 440*c**3 + 118*c - 210*c**4 - 630*c**4 + 480*c**2 + 245*c**5 - 38*c.
5*c*(c - 2)**2*(7*c + 2)**2
Let h = -25 - -22. Let r(p) = -12*p**2 - 10*p + 22. Let x(t) = 4*t**2 + 3*t - 7. Let v(z) = h*r(z) - 10*x(z). Factor v(w).
-4*(w - 1)*(w + 1)
Suppose -6*q + 5*q + 3 = 0. Suppose 2*l + 2*g - 20 = -g, -l = 4*g - 20. Factor z - q*z + l*z**2 - 2*z**2 - 4*z**2.
-2*z*(z + 1)
What is q in 0 + 2/5*q - 3/5*q**2 = 0?
0, 2/3
Let u(w) be the third derivative of -3*w**2 + 0*w**3 + 0 + 0*w + 1/84*w**4 + 1/105*w**5 + 1/420*w**6. Factor u(f).
2*f*(f + 1)**2/7
Let d(f) = -f - 3. Let v = -21 - -16. Let x be d(v). Let 2/3 - 2/3*c**x + 0*c = 0. What is c?
-1, 1
Suppose 2 = 4*d - 2*m, 0 = -d - m + 3*m + 2. Let z(f) be the second derivative of 1/75*f**6 + 0*f**2 + 1/50*f**5 + d + f + 0*f**3 + 0*f**4. Factor z(k).
2*k**3*(k + 1)/5
Factor -126*c + 14*c - 4*c**3 - 108 - 36*c**2 + 4*c.
-4*(c + 3)**3
Let s(c) be the second derivative of c**4/6 + c**3/6 - 3*c**2/2 - 9*c. Let k(x) = -x + 1. Let g(a) = -3*k(a) - s(a). Factor g(w).
-2*w*(w - 1)
Let n(o) be the first derivative of 1/2*o**4 + 0*o + o**2 + 4 + 4/3*o**3. Factor n(q).
2*q*(q + 1)**2
Let t(r) be the second derivative of -r**6/300 + r**5/75 - r**4/60 - r**2/2 - r. Let z(c) be the first derivative of t(c). Factor z(n).
-2*n*(n - 1)**2/5
Let w(l) be the first derivative of -l**3/3 + 2*l**2 - 3*l - 19. What is s in w(s) = 0?
1, 3
Factor 0 - 3/2*l**3 + 3/2*l**2 + 3*l.
-3*l*(l - 2)*(l + 1)/2
Factor -1/3*y - 1/6*y**2 + 4/3.
-(y - 2)*(y + 4)/6
Let l(k) = k + 12. Let u be l(-9). Factor 1 + 7*g + u + 2*g**2 - g.
2*(g + 1)*(g + 2)
Let y(f) be the first derivative of -4*f**3/3 - f**2/3 + 27. Find c such that y(c) = 0.
-1/6, 0
Find f such that 6/7*f**3 + 0*f - 6/7*f**4 + 2/7*f**5 + 0 - 2/7*f**2 = 0.
0, 1
Let b(j) be the second derivative of j**5/100 + j**4/15 - j**3/10 - 9*j**2/5 - 15*j. Determine a so that b(a) = 0.
-3, 2
Let m(d) be the first derivative of d**7/70 - 3*d**6/40 + 3*d**5/20 - d**4/8 + d**2 - 10. Let n(t) be the second derivative of m(t). Solve n(y) = 0.
0, 1
Suppose 8*v = 7*v + 4. Let r(z) = z - 1. Let t be r(v). Factor 0*y**2 - 6/7*y**4 + 0 - 2/7*y**t - 4/7*y**5 + 0*y.
-2*y**3*(y + 1)*(2*y + 1)/7
Determine k so that -1/4*k**3 + 0*k**2 + 0 + 1/4*k = 0.
-1, 0, 1
Let j be 1/(-1 + (-12)/(-8)) + -2. Let n = 149/335 + -3/67. Factor 0*h**3 + n*h**4 + j*h**2 + 0 + 0*h.
2*h**4/5
Solve 2/3*y**2 + 2/3 + 4/3*y = 0 for y.
-1
Let j(g) = -g**2 + 25. Let v be j(-5). Let r = -70 + 143/2. Factor 1/2*n**2 + 0 - 1/2*n**5 + v*n + 3/2*n**4 - r*n**3.
-n**2*(n - 1)**3/2
Let g = -23 - -40. Suppose 0 = -3*a - 5 + g. What is j in 1/2*j**3 - 1/2*j + 1/2*j**2 + 0 - 1/2*j**a = 0?
-1, 0, 1
What is f in 15/4*f - 3/4*f**3 + 3/4*f**2 + 9/4 = 0?
-1, 3
Let u be (6/10)/(1/5). Let v(o) be the third derivative of 0*o**4 + 1/180*o**5 + 0 + 0*o**u - 3*o**2 + 0*o. Factor v(l).
l**2/3
Factor 3/2*w - 3/2*w**3 - 3/2*w**2 + 3/2.
-3*(w - 1)*(w + 1)**2/2
Let g(q) = -q**4 - 2*q**3 + 5*q**2 + 2*q - 2. Let d(b) = b**4 - b**3 + b**2 + b - 1. Let z(y) = -2*d(y) + g(y). Factor z(x).
-3*x**2*(x - 1)*(x + 1)
Let v = 7100/7 + -1014. Factor 0 - v*l**2 - 6/7*l**4 + 0*l + 6/7*l**3 + 2/7*l**5.
2*l**2*(l - 1)**3/7
Suppose 3*d - 32 - 49 = 0. Let s be 12/d*6 - 2. Factor 4/3*q**3 - 2/3 + s*q**4 - 4/3*q + 0*q**2.
2*(q - 1)*(q + 1)**3/3
Let i(a) = -17*a**2 + 16*a - 17. Let p(v) be the second derivative of v**4/3 - 2*v**3/3 + 2*v**2 - 4*v. Let x(r) = -2*i(r) - 9*p(r). Factor x(u).
-2*(u - 1)**2
Let n(c) = -2*c**4 - 11*c**3 - 11*c**2 - 2*c. Let x(p) = -p**4 - 6*p**3 - 6*p**2 - p. Let m(l) = 6*n(l) - 10*x(l). Solve m(q) = 0.
-1, 0
Let x be (-20)/6*(-12)/8 + -3. Factor 0*h - 1/4 + 1/4*h**x.
(h - 1)*(h + 1)/4
Let k = 30961/120 - 258. Let i(h) be the third derivative of 0*h - 1/48*h**4 + k*h**5 + 0*h**3 + 0 - h**2. What is y in i(y) = 0?
0, 1
Let c(x) be the second derivative of -2*x**7/21 + 2*x**6/15 + 2*x**5/5 - 2*x**4/3 - 2*x**3/3 + 2*x**2 + 2*x. Factor c(d).
-4*(d - 1)**3*(d + 1)**2
Let y(t) = -3*t**3 - t**2 + t + 1. Let f(c) = 16*c**3 + 5*c**2 - 5*c - 5. Let g(j) = 2*f(j) + 11*y(j). Solve g(u) = 0.
-1, 1
What is h in 222*h - 6591/2*h**4 + 1287*h**2 + 3549/2*h**3 + 12 = 0?
-2/13, 1
Let z(d) = d**3 - 6*d**2 - 7*d. Let a(c) = 3*c - 14. Let o be a(7). Let h be z(o). Factor 0*j**2 + 0*j + h + 2/3*j**5 + 2/3*j**4 + 0*j**3.
2*j**4*(j + 1)/3
Let o(k) be the third derivative of k**9/45360 + k**8/20160 - k**7/7560 - k**6/2160 - k**4/8 - k**2. Let c(j) be the second derivative of o(j). Factor c(d).
d*(d - 1)*(d + 1)**2/3
Let q be 516/60 - (-2)/5. Suppose -9*b**3 - 3*b**5 - b**2 + 9*b + 7*b**2 + 3*b**3 - q*b**4 + 3 = 0. What is b?
-1, 1
Let x(c) = -2*c**3 + 3*c**2 + c - 2. Let w be x(2). Let m be 6/w*(-17)/51. Factor t**4 - t**2 - 1/2*t + 0 + m*t**5 + 0*t**3.
t*(t - 1)*(t + 1)**3/2
Let x(u) = u + 3. Let w be x(0). Factor 4*l**3 - l + w*l**3 - l - 5*l**3.
2*l*(l - 1)*(l + 1)
Suppose 5*i - 11 - 9 = 0. Suppose 2 = 2*z - i. Factor 0 + 1/2*d**2 - 1/2*d**z + d.
-d*(d - 2)*(d + 1)/2
Let c(q) be the second derivative of q**5/180 - q**4/36 + q**3/18 - q**2 + 3*q. Let m(g) be the first derivative of c(g). Suppose m(a) = 0. Calculate a.
1
Find c such that -6/7*c**4 - 2/7*c**2 + 34/7*c**3 - 10/7*c**5 - 24/7*c + 8/7 = 0.
-2, -1, 2/5, 1
Factor -2/5*s**4 - 6/5*s**2 + 0*s + 8/5*s**3 + 0.
-2*s**2*(s - 3)*(s - 1)/5
Let n(l) = -l**3 + 4*l**2 + 7*l - 7. Let b be n(5). Let h(u) be the first derivative of u**2 + 1/3*u**b + 0*u - 1. Factor h(q).
q*(q + 2)
Suppose 0 + 7/5*y**2 - 2*y - 1/5*y**3 = 0. What is y?
0, 2, 5
Let j = -423 + 427. Determine a so that -4/5*a**3 + 0 - 4/5*a**2 - 1/5*a**j + 0*a = 0.
-2, 0
Let x be 3 + 3 + (1 - -2 - 3). Let v(y) be the second derivative of -1/5*y**5 - 1/45*y**x + y - 4/3*y**3 - 4/3*y**2 + 0 - 13/18*y**4. Let v(k) = 0. Calculate k.
-2, -1
Let t = -8 + 12. Suppose 9 = 4*r - 3*n, -n + 1 = 3*r + t. Suppose 2/7*u**4 - 2/7*u**2 + r - 2/7*u + 2/7*u**3 = 0. Calculate u.
-1, 0, 1
Let k = 3 - 2. Let q = 1 - k. Factor 2/3 - 2/3*p**2 + q*p.
-2*(p - 1)*(p + 1)/3
Solve 0*j - 2/3*j**3 + 0 + 2/3*j**2 = 0 for j.
0, 1
Let p(q) be the third derivative of -q**7/840 + q**6/360 + q**5/60 + 2*q**3/3 + 6*q**2. Let a(c) be the first derivative of p(c). Factor a(h).
-h*(h - 2)*(h + 1)
Suppose -4*r = -0*r + 40. Let c = r - -12. What is u in -4*u**2 - 20/3*u**4 - 2/3*u + 0 - c*u**5 - 8*u**3 = 0?
-1, -1/3, 0
Let w = 114 + -453/4. Determine q, given that -1/2*q - w*q**2 + 0*q**3 + 1/4*q**4 + 0 = 0.
-1, 0, 2
Let c(u) be the second derivative of -u**5/180 - 5*u**2/2 - 6*u. Let o(i) be the first derivative of c(i). Find h such that o(h) = 0.
0
Let y(u) be the second derivative of u**4/30 + 2*u**3/3 + 5*u**2 + 41*u. Find r, given that y(r) = 0.
-5
Let i(v) be the first derivative of 1/180*v**5 + 0*v + 2 + 1/36*v**4 + 1/18*v**3 + v**2. Let s(l) be the second derivative of i(l). Let s(r) = 0. Calculate r.
-1
What is l in 1/6*l**2 - 5/3*l + 25/6 = 0?
5
Suppose 2*t**2 + 25*t**4 - 10*t**2 - 16*t + 11*t**4 - 8*t**2 + 36*t**3 = 0. What is t?
-1, -2/3, 0, 2/3
Let s(i) be the first derivative of 66/5*i**5 + 5/2*i**6 + 69/4*i**4 - 24*i - 1 - 42*i**2 - 14*i**3. Solve s(d) = 0 for d.
-2, -1, -2/5, 1
Let j(u) be the third derivative of -u**6/480 + u**5/80 - 6*u**2. Factor j(i).
-i**2*(i - 3)/4
Let t(q) = -q**2 + 12*q + 13. Let x(b) = 6*b**2 - 84*b - 90. Let r(h) = -27*t(h) - 4*x(h). What is p in r(p) = 0?
-3, -1
Let w = 25 - 23. Let t(h) be the third derivative of h**w + 0*h**3 + 1/240*h**5 + 1/96*h**4 + 0 - 1/240*h**6 + 0*h. Factor t(p).
-p*(p - 1)*(2*p + 1)/4
Suppose 4 = -14*y + 32. Factor 1/2*s**2 + 3/2 + y*s.
(s + 1)*(s + 3)/2
Factor 6 - 6 - 5*w**2 + w + 19*w - 20.
-5*(w - 2)**2
Let u(q) be the first derivative of 2 + 0*q - 1/4*q**2 - 1/6*q**3. Factor u(w).
-w*(w + 1)/2
Factor -3*u - 1/4*u**2 - 9.
-(u + 6)**2/4
Let t(c) be the third derivative of -3*c**7/70 + c**6/20 + c**5/5