v**2 + 3. Let h be b(6). Suppose 5*f - h + 10 = m, 1 = m + f. Factor -8*s**3 + 2*s**3 + 5*s**2 + s**m - 2*s + 2*s**4.
2*s*(s - 1)**3
Let r be (-3 + -1)/(2 + -8). Let h be (-2 - -2)/(2 + -1). Factor -r + 1/3*q**3 - q + h*q**2.
(q - 2)*(q + 1)**2/3
Let w(g) be the second derivative of -g**4/72 + g**2/12 - g. Suppose w(k) = 0. What is k?
-1, 1
Let d be (1/(-2))/((-3)/2). Determine b so that -d*b**3 - 5/3*b + 4/3*b**2 + 2/3 = 0.
1, 2
Factor 1/4*o - 1/4*o**3 - 3/4 + 3/4*o**2.
-(o - 3)*(o - 1)*(o + 1)/4
Let j(u) be the second derivative of u**7/21 + u**6/5 - 2*u**4/3 - 17*u. Let j(c) = 0. What is c?
-2, 0, 1
Let h = -84 - -87. Let s(v) be the first derivative of 1/7*v**4 - 1/7*v**2 + 0*v**h + 0*v + 0*v**5 + 3 - 1/21*v**6. Determine p so that s(p) = 0.
-1, 0, 1
Let b(u) be the first derivative of -1/6*u**3 + 1/12*u**4 + 0*u - 1 + u**2 - 1/60*u**5. Let s(o) be the second derivative of b(o). Find g such that s(g) = 0.
1
Suppose -3*s + 3*q = 2 - 17, 0 = -2*s - q + 1. Suppose -3*p - 9 = -5*n, -p - 3 = 2*n + s*n. Find f, given that 1/2*f**2 + 5/4*f**3 + n + 0*f + 3/4*f**4 = 0.
-1, -2/3, 0
Let -1/4*x**3 - 7/4*x - 5/4*x**2 - 3/4 = 0. What is x?
-3, -1
Let h(c) be the third derivative of -5*c**2 + 0*c**5 + 2/21*c**3 + 0 - 1/420*c**6 + 0*c + 1/28*c**4. What is j in h(j) = 0?
-1, 2
Factor -1/6 - 2/3*s + 5/6*s**2.
(s - 1)*(5*s + 1)/6
Factor 3/4*d**2 + 5/4*d**4 + 0*d + 1/4*d**5 + 0 + 7/4*d**3.
d**2*(d + 1)**2*(d + 3)/4
Let o(i) be the second derivative of 1/110*i**5 + 0*i**2 + 0*i**4 - 1/33*i**3 + 4*i + 0. Solve o(p) = 0.
-1, 0, 1
Let u(d) be the second derivative of d**5/20 + 5*d**4/12 + d**3/2 - 9*d**2/2 + 13*d. Factor u(q).
(q - 1)*(q + 3)**2
Let d(x) be the third derivative of x**8/504 - x**6/90 + x**4/36 - 3*x**2. Find k, given that d(k) = 0.
-1, 0, 1
Suppose -8 = -2*n + 14. Let m = 11 - n. Determine t, given that 0 + m*t**2 - 2/9*t + 2/9*t**3 = 0.
-1, 0, 1
Let y = -14 + 11. Let a be 1 + y - (-288)/112. Factor a*t - 2/7 - 2/7*t**2.
-2*(t - 1)**2/7
Let v(s) = -s**3 + 2*s. Let w be v(-2). Let z(h) be the first derivative of 2/15*h**3 + 0*h**2 + 2 - 1/5*h**w - 6/25*h**5 + 0*h. Suppose z(r) = 0. What is r?
-1, 0, 1/3
Suppose -130*c**2 - 25*c**4 - 87*c**3 - 51*c**3 - 160 + 480*c + 13*c**3 - 40*c**3 = 0. Calculate c.
-4, 2/5, 1
Suppose 5*n = 2*b - 3*b - 5, -3*b = -n - 17. Let k be (1 + 20/(-16))*n. Determine v so that 0 + 0*v - k*v**3 + 1/2*v**2 = 0.
0, 1
Let z = 84 - 78. Let n(f) be the second derivative of -1/21*f**7 + 0*f**2 + 0*f**4 - 1/15*f**z + 0 - 2*f + 0*f**3 + 0*f**5. Factor n(u).
-2*u**4*(u + 1)
Let s be 37/(-20) + 2 - (-8)/32. Factor -6/5*m**3 + 0 - 2/5*m**5 + 6/5*m**4 + 0*m + s*m**2.
-2*m**2*(m - 1)**3/5
Let k(u) be the second derivative of 2*u**7/147 + 8*u**6/105 + 6*u**5/35 + 4*u**4/21 + 2*u**3/21 - 10*u. Find p such that k(p) = 0.
-1, 0
Let t(r) be the first derivative of 2*r**3/33 + 3. Factor t(m).
2*m**2/11
Let f(b) be the third derivative of b**7/105 + b**6/60 - 6*b**2. Suppose f(h) = 0. Calculate h.
-1, 0
Factor 9*l - 28*l - 2 - 8 - 5*l**2 + 4*l.
-5*(l + 1)*(l + 2)
Factor -4/9*s**2 - 16/9*s - 4/3.
-4*(s + 1)*(s + 3)/9
Let t = 4 - 1. Let b(c) be the third derivative of -1/21*c**t + 0*c + 2*c**2 + 0 - 1/42*c**4 - 1/210*c**5. Factor b(x).
-2*(x + 1)**2/7
Let t(d) = -d**2 + 9*d. Let q be t(9). Suppose 5*l - 16 = 3*k, q*l + 4*l + k = 6. Let -2 + 2 - m**l + m = 0. Calculate m.
0, 1
Suppose -4*r**3 - 4/13 - 28/13*r**4 - 22/13*r - 6/13*r**5 - 48/13*r**2 = 0. Calculate r.
-1, -2/3
Let g = -105/2 - -1687/32. Let q = g + 1/32. Factor 1/2*a**2 + q*a + 1/4*a**3 + 0.
a*(a + 1)**2/4
Let t(j) be the third derivative of j**5/20 + 3*j**4/8 + 11*j**2. Find p such that t(p) = 0.
-3, 0
Let f(c) be the second derivative of -c**6/15 + c**5/2 - 7*c**4/6 + c**3 + 2*c - 9. Factor f(t).
-2*t*(t - 3)*(t - 1)**2
Let t(l) be the first derivative of 2*l**6/27 + 8*l**5/15 + 13*l**4/9 + 16*l**3/9 + 8*l**2/9 + 15. Factor t(h).
4*h*(h + 1)**2*(h + 2)**2/9
Let k(y) = y - 7. Let v be k(9). Let u be (6/(-8)*v)/(-3). Factor -d + 1/2*d**2 + u.
(d - 1)**2/2
Let l(a) be the first derivative of -a**5/70 - a**4/21 - a**3/21 - 3*a + 3. Let g(k) be the first derivative of l(k). Factor g(u).
-2*u*(u + 1)**2/7
Let m(c) be the third derivative of -c**5/60 - c**4/12 - 16*c**2. Solve m(v) = 0.
-2, 0
Factor 3*y**2 - 6/5*y + 3/5*y**4 + 0 - 12/5*y**3.
3*y*(y - 2)*(y - 1)**2/5
Let k = 166/9 - 163/9. Factor -5/6*j**3 - 7/6*j - 1/6*j**4 - 3/2*j**2 - k.
-(j + 1)**3*(j + 2)/6
Let o = -299/3 - -100. Determine f so that -1/3*f + 1/3*f**3 + o - 1/3*f**2 = 0.
-1, 1
Let a be (-2)/((8/(-18))/2). Let k = -7 + 11. What is w in k*w**4 - 2*w**3 + 9 - a - 2*w**5 = 0?
0, 1
Let p(u) be the third derivative of 2*u**2 + 0*u**6 - 1/105*u**7 + 0*u**3 + 1/30*u**5 + 0*u + 0 + 0*u**4. Determine a, given that p(a) = 0.
-1, 0, 1
Let r = 37 + -35. Suppose 21/2*m**r - 1 + 1/2*m = 0. Calculate m.
-1/3, 2/7
Let g(t) be the first derivative of t**6/9 - 34*t**5/45 + 5*t**4/3 - 4*t**3/3 - t**2/9 + 2*t/3 + 9. Solve g(c) = 0 for c.
-1/3, 1, 3
Let w = 9 - 0. Let r = w - 9. Factor r - 2/3*m - 2/3*m**2 + 4/3*m**3.
2*m*(m - 1)*(2*m + 1)/3
Suppose -5*i + 3*t + 10 = -6, 4*t - 32 = -4*i. Suppose -3*a - i*d + 45 = 2*a, -2*a + d = -3. Suppose -1 - 2 - 4*s**3 + 2*s**4 + a*s + 1 = 0. Calculate s.
-1, 1
Factor -14/3*v - 4/3 + 8/3*v**2.
2*(v - 2)*(4*v + 1)/3
Let a(h) be the third derivative of 1/105*h**7 - 8*h**2 + 1/42*h**4 + 0*h - 1/70*h**5 - 1/140*h**6 - 1/392*h**8 + 0 + 0*h**3. Factor a(n).
-2*n*(n - 1)**3*(3*n + 2)/7
Let a(u) = 8*u**2 + 17*u + 17. Let j(y) = 25*y**2 + 50*y + 50. Let w(x) = -10*a(x) + 3*j(x). What is o in w(o) = 0?
-2
Let x(p) be the third derivative of -p**10/302400 - p**9/120960 - p**5/20 - p**2. Let z(b) be the third derivative of x(b). Factor z(v).
-v**3*(v + 1)/2
Let q(b) be the third derivative of b**7/350 - b**5/50 + b**3/10 - b**2. Find f such that q(f) = 0.
-1, 1
Let b(o) be the third derivative of o**6/240 - o**5/60 + 8*o**2. Find d such that b(d) = 0.
0, 2
Suppose 0 = 4*d - 79 - 17. Factor 92*c + 76*c**4 + d*c**4 + 32 - 24*c**2 + 20*c - 220*c**3.
4*(c - 2)*(c - 1)*(5*c + 2)**2
Let b(a) = 3*a**3 - 7*a**2 + 5*a + 5. Let s(c) = -2*c**3 + 4*c**2 - 3*c - 3. Let f(q) = -6*b(q) - 10*s(q). Factor f(d).
2*d**2*(d + 1)
Let w(p) be the second derivative of p**6/360 + p**5/120 - p**4/12 - p**3/3 - 3*p. Let j(t) be the second derivative of w(t). Find o such that j(o) = 0.
-2, 1
Let q(r) be the second derivative of -1/18*r**4 - 1/90*r**5 - r**2 + 0 + 1/60*r**6 + 0*r**3 - 2*r. Let b(x) be the first derivative of q(x). Factor b(g).
2*g*(g - 1)*(3*g + 2)/3
Let c be 1128/(-80) - (-4)/(-10). Let v = c - -15. Factor -v + 2*m + 2*m**3 - 3*m**2 - 1/2*m**4.
-(m - 1)**4/2
Let v(y) be the first derivative of y**3/2 + 3*y**2/4 - 3*y + 6. Factor v(u).
3*(u - 1)*(u + 2)/2
Factor -10*c + 939*c**2 + 588 - 74*c - 936*c**2.
3*(c - 14)**2
Let u(f) be the third derivative of -f**7/504 + 7*f**6/1080 - f**5/180 - f**3/3 + f**2. Let i(b) be the first derivative of u(b). Suppose i(p) = 0. What is p?
0, 2/5, 1
Let d(w) be the third derivative of -w**9/11340 - w**8/3780 + w**7/540 - w**6/270 + w**5/12 + 5*w**2. Let b(h) be the third derivative of d(h). Factor b(z).
-4*(z + 2)*(2*z - 1)**2/3
Let t(b) = 9*b**5 - 6*b**4 + 6*b**3 + 6. Let d(f) = 8*f**5 - 5*f**4 + 5*f**3 + 5. Let w(l) = 6*d(l) - 5*t(l). Suppose w(a) = 0. What is a?
0
Let n(f) be the third derivative of -f**9/332640 - f**8/110880 + f**7/13860 - f**5/60 + 3*f**2. Let p(o) be the third derivative of n(o). Factor p(t).
-2*t*(t - 1)*(t + 2)/11
Suppose 8*v = 3*v + 160. Let -6*p**2 + 11*p - 6 - 9*p**2 - v*p = 0. What is p?
-1, -2/5
Suppose -3*w = f - 5, -5*f + 2*f = 4*w - 5. Solve 4*h - w*h + h**3 - 5*h - 2 = 0.
-1, 2
Suppose 7 - 3 = -4*w - 2*o, -2*o = 4. Factor w - 3/5*p**3 + 3/5*p + 0*p**2.
-3*p*(p - 1)*(p + 1)/5
Let b(c) be the third derivative of 0*c + 1/40*c**5 - 1/16*c**4 + 4*c**2 - 1/2*c**3 + 0. What is h in b(h) = 0?
-1, 2
Suppose 3*h = 5*h + 2*c - 4, -2*h - 4*c + 12 = 0. Let o be (h/(-6) + 0)/1. Factor 0*g**2 + o*g**4 + 0*g + 0*g**3 + 1/3*g**5 + 0.
g**4*(g + 1)/3
Let j(u) be the third derivative of -u**6/120 + u**5/10 - u**4/2 - 5*u**3/6 + 6*u**2. Let l(q) be the first derivative of j(q). Factor l(y).
-3*(y - 2)**2
Let h(w) be the second derivative of -2*w**7/21 + 8*w**6/15 - 4*w**5/5