s) = -9*s**3 - 25*s**2 + 25*s + 9. Let c(q) = -4*q**3 - 12*q**2 + 12*q + 4. Let r(t) = 13*c(t) - 6*z(t). Determine o, given that r(o) = 0.
1
Factor 2*r**3 - 2*r**2 + r**3 + 2*r**2 + 3*r**4 - 6*r**2.
3*r**2*(r - 1)*(r + 2)
Let v(p) be the first derivative of 2/45*p**5 + 3 - 2/27*p**3 + 1/27*p**6 + 0*p**2 + 0*p - 1/18*p**4. Solve v(b) = 0 for b.
-1, 0, 1
Let s(d) be the first derivative of 1/3*d**3 + 0*d + 0*d**2 - 1/4*d**4 + 1/6*d**6 - 1 - 1/5*d**5. Factor s(r).
r**2*(r - 1)**2*(r + 1)
Let k(u) be the second derivative of -u**4/102 - 2*u**3/51 + 8*u**2/17 - u. What is g in k(g) = 0?
-4, 2
Let b(f) = -2*f + 10. Let g(m) = -m**2 + m - 1. Suppose 2*n - 7*n - 10 = 0. Let k(v) = n*g(v) - b(v). Find h, given that k(h) = 0.
-2, 2
Let t(z) = -z**3 + 3*z**2 + 5*z + 1. Let h be t(4). Suppose -22 = -h*d - 4*p, 5*p - 10 - 15 = -5*d. Factor 2*a + 4*a**3 - 6*a**2 - 2*a**3 + 4*a**3 - d*a**4.
-2*a*(a - 1)**3
Let q(o) be the second derivative of o**6/240 - o**4/16 + o**3/6 + o**2 + 6*o. Let p(r) be the first derivative of q(r). Factor p(g).
(g - 1)**2*(g + 2)/2
Let p be 450/210 + 2/(-14). Find x, given that -8/5*x**p + 4/5*x + 8/5*x**4 - 4/5*x**3 + 0 = 0.
-1, 0, 1/2, 1
Let c(p) = 5*p**4 - 4*p**3 - 5*p**2 + p + 3. Let r(f) = f**4 - f**2 - f + 1. Let g(d) = 2*c(d) - 6*r(d). Suppose g(q) = 0. What is q?
-1, 0, 1, 2
Let w(a) = 4*a - 3. Let i(j) = 3*j - 3. Let r(p) = -3*i(p) + 2*w(p). Let y be r(3). Suppose 2/9*s**2 + 0 + y*s = 0. Calculate s.
0
Let m(v) be the third derivative of -v**6/105 - v**5/42 - v**4/84 + 2*v**2. Factor m(g).
-2*g*(g + 1)*(4*g + 1)/7
Let b(c) = -c + 2. Let r be b(7). Let m be (-2)/r*(2 + 3). Factor 4/7*y - 2/7*y**m - 2/7.
-2*(y - 1)**2/7
Let a be 0*((-3)/6 + 1). Let q(y) be the first derivative of 1/2*y**4 - 1 - 2/3*y**3 + 0*y**2 + a*y. Factor q(o).
2*o**2*(o - 1)
Let 0*p + 0 - 3/5*p**3 + 3/5*p**2 = 0. Calculate p.
0, 1
Factor -3 + 5*t**3 - 4*t**3 + 2*t**2 + 3.
t**2*(t + 2)
Let r be 6/(-20)*140/(-72). Let q = r - 1/12. Let -1/4 - 1/4*u**2 - q*u = 0. Calculate u.
-1
Let l(v) be the first derivative of v**5 - 5*v**4 + 5*v**3 + 10*v**2 - 20*v - 4. Factor l(x).
5*(x - 2)**2*(x - 1)*(x + 1)
Let n(i) be the third derivative of -i**6/60 - i**5/10 + i**4/12 + i**3 - 8*i**2. What is x in n(x) = 0?
-3, -1, 1
Suppose -4*k = -5*k + 5. Let m(h) be the second derivative of 0 + 0*h**3 - 1/30*h**k - h - 1/45*h**6 + 0*h**4 + 0*h**2. Solve m(q) = 0 for q.
-1, 0
Let 2 + 2/9*t**5 + 14/3*t + 20/9*t**2 - 4/3*t**3 - 2/3*t**4 = 0. What is t?
-1, 3
Factor 25/4 - 5/2*a + 1/4*a**2.
(a - 5)**2/4
Determine z, given that 0*z + 3/2*z**3 + 0 + 0*z**2 + 1/2*z**4 = 0.
-3, 0
Let f(q) = -25*q**3 + 64*q**2. Let p(k) = 5*k**3 - 13*k**2. Let y(m) = -2*f(m) - 11*p(m). Find l such that y(l) = 0.
0, 3
Let d(t) be the first derivative of -4/7*t - 9 + 3/7*t**2 - 2/21*t**3. Factor d(c).
-2*(c - 2)*(c - 1)/7
Suppose 755*p**2 + 4*p - 752*p**2 + 2*p + 3 = 0. What is p?
-1
Let y(a) be the second derivative of a**5/60 - 3*a**2 - 5*a. Let o(h) be the first derivative of y(h). Factor o(u).
u**2
Suppose -2*i + 4*i - 4 = 0. Suppose -i*n + z + 7 - 1 = 0, 3*n + z - 4 = 0. Factor 3*q**4 + 5*q**2 + 3*q**3 + q**5 - 3*q**2 - q**n.
q**2*(q + 1)**3
Let d = -3 + 6. Let y(c) be the second derivative of 0*c**d + 2*c + 1/12*c**4 + 0 - 1/2*c**2. What is q in y(q) = 0?
-1, 1
Let u = 37 - 34. Factor -1/4*m**u + 0*m - 1/2*m**2 + 0.
-m**2*(m + 2)/4
Let h(u) be the first derivative of -3*u**5/5 + 9*u**4/4 - 2*u**3 - 20. Factor h(l).
-3*l**2*(l - 2)*(l - 1)
Factor 150*x**4 + 125*x**5 - 43*x**3 - 60*x + 0 - 8 - 142*x**2 - 22*x**3.
(x - 1)*(x + 1)*(5*x + 2)**3
Let y(a) be the first derivative of 2*a**3/21 + 4. Factor y(k).
2*k**2/7
Let n(j) = j + 18. Let d be n(0). Let h be (d/12)/(3/4). Factor 0*q - 1/4*q**h + 1/4.
-(q - 1)*(q + 1)/4
Let a = -4 + 4. Let f(b) be the first derivative of -1/24*b**6 + 0*b**4 - 1/20*b**5 + 0*b**3 + a*b**2 - 1 + 0*b. Determine p so that f(p) = 0.
-1, 0
Let z(d) be the third derivative of d**6/540 - d**5/90 + d**4/36 - d**3/27 - 16*d**2. Determine l so that z(l) = 0.
1
Let m(q) = -4*q**2 - 2*q - 3. Let j be 5*(-1 - (-6)/15). Let z(c) = 7*c**2 + 3*c + 5. Let v(o) = j*z(o) - 5*m(o). Solve v(p) = 0 for p.
0, 1
Let m(p) be the second derivative of -1/7*p**2 + 2/35*p**5 - 3/14*p**4 + 0 + 3*p + 2/7*p**3. Suppose m(s) = 0. Calculate s.
1/4, 1
Suppose -5 = 2*q + 3*d, -5*d = 5*q + 6 - 1. Solve -2/11 + 4/11*p**q + 0*p**3 - 2/11*p**4 + 0*p = 0 for p.
-1, 1
Let u(c) be the first derivative of c**6/4 + 6*c**5/5 + 3*c**4/2 - 6. Factor u(w).
3*w**3*(w + 2)**2/2
Let g(d) be the second derivative of d**4/18 - 2*d**3/9 + d**2/3 + 16*d. Let g(x) = 0. Calculate x.
1
Let a(b) be the third derivative of b**9/60480 + b**8/8960 + b**7/3360 + b**6/2880 - b**4/6 + 4*b**2. Let n(i) be the second derivative of a(i). Solve n(f) = 0.
-1, 0
Let l = -3 - -7. Let 0 + 0*j - 2/5*j**l + 0*j**2 - 2/5*j**3 = 0. What is j?
-1, 0
Let 0 + 8/5*s + 8/5*s**3 - 34/5*s**2 = 0. What is s?
0, 1/4, 4
Let m be 14/(-36) - 4/(-10). Let g(k) be the third derivative of 0 + k**2 + 0*k + 0*k**3 + m*k**5 - 1/36*k**4. Factor g(d).
2*d*(d - 1)/3
Let i(t) be the first derivative of -t**7/1890 + t**6/1080 + t**5/540 - t**4/216 - 4*t**2 - 1. Let j(k) be the second derivative of i(k). Factor j(x).
-x*(x - 1)**2*(x + 1)/9
Let v(t) be the third derivative of -1/30*t**7 + 0*t - 5/18*t**4 + 2*t**2 + 1/18*t**6 + 0 + 2/9*t**3 + 17/180*t**5. What is z in v(z) = 0?
-1, 2/7, 2/3, 1
Let p(u) be the second derivative of u**5/230 - u**4/138 - u**3/69 + u**2/23 + 44*u. Factor p(f).
2*(f - 1)**2*(f + 1)/23
Let y(s) be the first derivative of -2/3*s**3 + 2/5*s**5 - 1/2*s**2 + 1/6*s**6 + 0*s - 1 + 0*s**4. Factor y(i).
i*(i - 1)*(i + 1)**3
Let 2/3 + 1/3*m**2 - m = 0. What is m?
1, 2
Suppose -2*s + 4*i = 5*i - 6, 5*s + 4*i - 18 = 0. Factor -2/3*x**s - 1/3*x**3 + 0 - 1/3*x.
-x*(x + 1)**2/3
Determine v, given that 0*v**3 - 2*v**3 + 106*v**2 - 92*v**2 = 0.
0, 7
Let r = -373 + 2613/7. Suppose -2/7*w**5 + 0*w**2 + r*w**3 + 0 + 0*w + 0*w**4 = 0. What is w?
-1, 0, 1
Let p(m) be the first derivative of -m**7/210 + m**6/120 + m**5/30 + 3*m**2 - 1. Let y(q) be the second derivative of p(q). Factor y(n).
-n**2*(n - 2)*(n + 1)
Let m(s) be the third derivative of 0 + 1/8*s**3 - 1/40*s**6 + 0*s - 5*s**2 + 3/40*s**5 + 1/280*s**7 - 1/8*s**4. Factor m(c).
3*(c - 1)**4/4
Let r = -5/4 + 3/2. Let x(u) be the first derivative of -1/3*u**3 - r*u**4 + 1 + 1/2*u**2 + u. What is g in x(g) = 0?
-1, 1
Let v(p) = 4*p**2 + 21*p - 21. Let s(r) = -r**2 - 5*r + 5. Let o(h) = 9*s(h) + 2*v(h). Let x be o(-3). What is g in -5*g + 4 - 2*g + x*g + g**2 = 0?
2
Let y(x) = -11*x - x**3 + 12 + 12 + 11*x**2 - 5 - 5. Let p be y(10). Find r such that -8/5*r + 2/5 - 8/5*r**3 + 12/5*r**2 + 2/5*r**p = 0.
1
Factor -6*u + u**3 + 11/2*u**2 - 1/2*u**4 - 18.
-(u - 3)**2*(u + 2)**2/2
Suppose 1 = -2*k - 5. Let a be (6 + k)*5/3. Factor -2/7*s**a + 2/7*s**4 + 0*s + 2/7*s**3 - 2/7*s**2 + 0.
-2*s**2*(s - 1)**2*(s + 1)/7
Let z(q) be the third derivative of -q**5/90 - 5*q**4/36 - 2*q**2 - 1. Factor z(j).
-2*j*(j + 5)/3
Let r be 6 + -7 - 151/(-91). Let h = 16/13 - r. Factor 0*p + h*p**2 - 2/7 - 2/7*p**4 + 0*p**3.
-2*(p - 1)**2*(p + 1)**2/7
Let d(l) be the third derivative of l**10/529200 - l**8/70560 - l**5/30 - 2*l**2. Let g(p) be the third derivative of d(p). Solve g(f) = 0 for f.
-1, 0, 1
Let r be 3/2 + (-1)/(-8)*-6. Factor 1/4*o + 1/2*o**4 + 1/4 - r*o**2 - 1/4*o**3.
(o - 1)**2*(o + 1)*(2*o + 1)/4
Suppose l = -3*l + 8. Suppose -4*k = -l*k. Solve k*m + 2/7*m**3 + 0 - 2/7*m**2 = 0 for m.
0, 1
Let x = 31307915/1143 - 27391. Let f = x - -20560/8001. Factor f*r**2 - 4/7*r - 2*r**3 + 0.
-2*r*(r - 1)*(7*r - 2)/7
Let c(k) be the third derivative of -k**7/140 - k**6/80 + k**5/40 + k**4/16 - 11*k**2. Factor c(r).
-3*r*(r - 1)*(r + 1)**2/2
Let 3*z + 28*z**2 + 3*z**3 + 3*z**3 - 14*z**3 + 13*z = 0. What is z?
-1/2, 0, 4
Let m = -10 - -13. Suppose m*u**2 + u**2 - 5*u**2 - u + 0*u = 0. What is u?
-1, 0
Let v = 2122/3 + -707. Factor 1/3*j**4 - v*j**2 + 0 - 1/3*j + 1/3*j**3.
j*(j - 1)*(j + 1)**2/3
What is r in 10/3 - 11/3*r + 1/3*r**2 = 0?
1, 10
Let l(d) be the third derivative of 0*d - 161/60*d**6 + 56/15*d**7 + 49/24*d**8 + 6*d**2 - 67/15*d**5 + 17/3*d**4 + 0 - 8/3*d**3. Suppose l(y) = 0. Calculate y.
-1, 2/7
Let d = -609/5 - -123. Le