rst derivative of 0*r - k - 2/9*r**3 - 1/3*r**2. Factor l(a).
-2*a*(a + 1)/3
Let l(p) be the third derivative of -p**6/40 + p**4/8 + 29*p**2. Suppose l(w) = 0. Calculate w.
-1, 0, 1
Suppose -2*o - 58 = -5*z, 4*o - 52 = -2*z - 2*z. Let u(v) = v + 1. Let d(c) = 7*c**2 - 2*c - 4. Let g(p) = z*u(p) + 3*d(p). Factor g(y).
3*y*(7*y + 2)
Let h(p) be the first derivative of -p**4/4 - 5*p**3/3 + 7*p**2/2 - 4*p + 1. Let y(d) = 2*d**3 + 4*d**2 - 6*d + 4. Let k(r) = 4*h(r) + 3*y(r). Factor k(f).
2*(f - 2)*(f - 1)**2
Let j(s) be the first derivative of s**6/3 - s**5/5 - 4*s**4/3 + 2*s**3/3 + 3*s**2 + 4*s - 4. Let r(x) be the first derivative of j(x). Factor r(d).
2*(d - 1)**2*(d + 1)*(5*d + 3)
Let i(d) = 301*d**3 - 455*d**2 + 185*d - 24. Let s(v) = -151*v**3 + 227*v**2 - 92*v + 12. Let o(l) = -4*i(l) - 7*s(l). Suppose o(b) = 0. What is b?
2/7, 1
Suppose 12*l = -10*l. Let q(f) be the first derivative of 0*f + 0*f**3 + 1/3*f**6 + 4/5*f**5 + l*f**2 + 4 + 1/2*f**4. Factor q(r).
2*r**3*(r + 1)**2
Suppose -13*s + 140 = -133. Let 84/5*i - 177/5*i**2 - 12/5 + s*i**3 = 0. What is i?
2/7, 2/5, 1
Let k(z) = -z**3 + 6*z**2 + z - 3. Let i be k(6). Suppose 0 = -2*y - 2*o, 2*y + 4*o + 3 = -1. Solve 4*b - 2*b**i + 12*b**y + 23 - 7 - 28*b = 0 for b.
2
Suppose 3*o - 9 = -0*o. Suppose -z + o = -2. Let -w**4 + 5*w + 2*w**2 - z*w**3 - 4*w - 1 + 2*w**3 + w**3 + w**5 = 0. What is w?
-1, 1
Let n(v) = -v + 1. Let o be n(-1). Solve 5*i**2 - i - 6*i**2 + 2*i**o = 0.
0, 1
Let t(x) be the third derivative of 1/336*x**8 - 1/30*x**5 + 0*x - 1/24*x**4 + 0 + 2*x**2 + 1/105*x**7 + 0*x**6 + 0*x**3. Let t(i) = 0. Calculate i.
-1, 0, 1
What is o in 4 + 4*o - 2*o**2 - 4*o - 2*o = 0?
-2, 1
Let m(r) = 9*r + 229. Let s be m(-25). Factor 3/5*j**s + 3/5*j**2 + 0 + 0*j - 6/5*j**3.
3*j**2*(j - 1)**2/5
Let p(w) = 5*w - 6. Let r be p(2). Factor 0*a - 2/5 - 2/5*a**r + 0*a**3 + 4/5*a**2.
-2*(a - 1)**2*(a + 1)**2/5
Let d = -2 + 4. Let f(y) be the second derivative of -4/9*y**d + 4/27*y**3 - 1/54*y**4 + 2*y + 0. Let f(c) = 0. Calculate c.
2
Let l(x) be the third derivative of -x**6/1440 + x**5/480 - 4*x**3/3 + 10*x**2. Let n(p) be the first derivative of l(p). Find m, given that n(m) = 0.
0, 1
Let k(q) = 7*q**4 - 3*q**3 - 19*q**2 + 3*q. Let v(o) = 76*o**4 - 32*o**3 - 208*o**2 + 32*o. Let f(h) = 32*k(h) - 3*v(h). Factor f(j).
-4*j**2*(j - 2)*(j + 2)
Let l(t) be the second derivative of -t**5/150 + t**3/15 - 3*t**2/2 + 3*t. Let u(i) be the first derivative of l(i). Suppose u(o) = 0. What is o?
-1, 1
Let j(i) = 2*i**3 + i**2 - 2*i + 2. Let l be j(1). Let t(d) be the second derivative of 0 - 1/6*d**2 - 2*d - 1/6*d**l + 1/9*d**4. What is p in t(p) = 0?
-1/4, 1
Let n(k) be the third derivative of 0*k + 1/8*k**4 + 2*k**2 - 1/3*k**3 + 0 - 1/60*k**5. Factor n(p).
-(p - 2)*(p - 1)
Suppose 0 + 6 = 2*n. Suppose 0 = -8*s + n*s. Factor s*v**2 + 1/3*v**3 + 0*v - 1/3*v**5 + 0*v**4 + 0.
-v**3*(v - 1)*(v + 1)/3
Let u(r) = -r**2 + 5*r + 3. Let d be u(5). Solve 4*q**2 - 3*q**2 + 11*q**2 + 15*q + 0*q**3 + 3*q**d + 6 = 0.
-2, -1
Let c(m) = m + 10. Let i be c(-6). Suppose -35*r**3 - 14*r + 2 + 69/2*r**2 + 25/2*r**i = 0. What is r?
2/5, 1
Let j(f) be the third derivative of -1/120*f**6 + 0*f**3 + 1/180*f**5 + f**2 + 0 + 0*f**4 + 0*f. Factor j(t).
-t**2*(3*t - 1)/3
Suppose -g + 4*g = 3*p, 3*p + 3 = 4*g. Let v be 288/126 + 1*-2. Factor -v*j**2 - 8/7*j**g - 6/7*j**4 + 0*j + 0.
-2*j**2*(j + 1)*(3*j + 1)/7
Suppose a - 2*r = -1, -r + 26 + 15 = 4*a. Let s = 12 - a. Factor 1/3*c - 1/3*c**s + 1/3 - 1/3*c**2.
-(c - 1)*(c + 1)**2/3
Let z = 16 - 13. Let f(d) be the second derivative of 1/20*d**5 + 0 + 0*d**2 + 0*d**z + 1/12*d**4 + d. Let f(w) = 0. Calculate w.
-1, 0
Let v = 48/7 + -473/70. Let m(j) be the second derivative of 0*j**6 + 0*j**2 - 1/6*j**3 - 1/42*j**7 + 0*j**4 - 2*j + v*j**5 + 0. Factor m(o).
-o*(o - 1)**2*(o + 1)**2
Factor 0 + 0*o - 2/3*o**4 - 4/3*o**3 + 0*o**2 + 2*o**5.
2*o**3*(o - 1)*(3*o + 2)/3
Let o be (-3)/(-6) + 3/6. Let r(l) = -l**3 - l**2. Let j(a) = 2*a**4 - 9*a**3 - 3*a**2 + 2*a. Let u(z) = o*j(z) - 4*r(z). Determine q so that u(q) = 0.
-1/2, 0, 1, 2
Let z(u) be the third derivative of u**5/450 - u**4/90 + 5*u**2. Factor z(v).
2*v*(v - 2)/15
Let y(v) be the first derivative of -v**6/18 - v**5/5 - v**4/4 - v**3/9 - 7. Factor y(k).
-k**2*(k + 1)**3/3
Suppose -5*y - 4*s + 25 = -12, -3*y + 2*s + 9 = 0. Suppose 4*q + o + 2*o = 9, 0 = y*q + 5*o - 15. Factor -b**3 - 2*b + q*b**5 + 2*b - 2*b**4 - b**5.
-b**3*(b + 1)**2
Let p(v) be the second derivative of -2*v + 1/40*v**5 - 1/4*v**2 - 1/12*v**3 + 0 + 1/24*v**4. Determine x, given that p(x) = 0.
-1, 1
Let b(s) be the first derivative of -s**5/110 + s**4/22 - 4*s**2/11 - 2*s + 2. Let q(r) be the first derivative of b(r). Factor q(x).
-2*(x - 2)**2*(x + 1)/11
Let q(x) be the first derivative of -3*x**4/20 - 2*x**3/5 - 3*x**2/10 - 7. Determine o, given that q(o) = 0.
-1, 0
Let m(w) be the second derivative of 0*w**2 + 1/12*w**4 + 1/12*w**7 + 0 + 0*w**3 + 3/40*w**5 - 1/5*w**6 + 4*w. Determine j so that m(j) = 0.
-2/7, 0, 1
Let t(v) be the first derivative of 9/4*v**4 - 4*v + 8*v**2 + 2 - 7*v**3. Factor t(b).
(b - 1)*(3*b - 2)**2
Let f(j) be the third derivative of 0*j - 2*j**2 - 3/8*j**4 + 0 + j**3 + 1/20*j**5. Factor f(s).
3*(s - 2)*(s - 1)
What is c in -18/7*c + 6/7*c**2 + 12/7 = 0?
1, 2
Let m be 5*((-2)/(-150))/(1/6). What is n in -2/5*n + 0 - m*n**2 = 0?
-1, 0
Factor 9/2*k**2 + 3/2*k**3 + 0 + 3*k.
3*k*(k + 1)*(k + 2)/2
Let g = -78346/39 - -2009. Let h = 7/13 + g. What is c in 5*c**2 - 11/3*c + h = 0?
1/3, 2/5
Let d be 2/(-5) + 228/45. Let s be 3 + -7 + -4 + 8. Factor -16/3*q**3 + s - 4/3*q - 2*q**4 - d*q**2.
-2*q*(q + 1)**2*(3*q + 2)/3
Let p(m) = -10*m**4 - 225*m**3 - 1405*m**2 - 2200*m - 1000. Let r(d) = 15*d**4 + 338*d**3 + 2107*d**2 + 3300*d + 1500. Let u(c) = 8*p(c) + 5*r(c). Factor u(v).
-5*(v + 1)**2*(v + 10)**2
Let b = -3 - -5. What is i in 4*i**3 + i + 4*i**2 + i**5 - 7*i + b + i**5 + 0 - 6*i**4 = 0?
-1, 1
Solve -5*q**2 - 161*q**4 + 316*q**4 - 3*q + 2 + 3*q**3 + 4*q**2 - 156*q**4 = 0.
-1, 1, 2
Factor 8*u**4 + 15*u**2 - 20*u**3 + 8*u - 20*u - 4*u**4 + 13*u**2.
4*u*(u - 3)*(u - 1)**2
Let f(y) = 4*y - 30. Let j be f(8). Let q(w) be the first derivative of 8*w + 2/3*w**3 + 4*w**2 - j. Factor q(m).
2*(m + 2)**2
Find i, given that -1/5 - 1/5*i + 1/5*i**3 + 1/5*i**2 = 0.
-1, 1
Let m(v) be the second derivative of -7*v**7/15 - 28*v**6/75 - 2*v**5/25 - 6*v - 5. Suppose m(a) = 0. What is a?
-2/7, 0
Let c(n) be the first derivative of -n**3/3 - n**2 - n - 2. Factor c(y).
-(y + 1)**2
Let l = 5 - -4. Suppose 0*y + l = 2*h + 3*y, 4*y - 12 = 2*h. Suppose -2/9*s**4 + 4/9*s**3 - 2/9*s**2 + h + 0*s = 0. What is s?
0, 1
Let n = -23 + 23. Factor 2*c**2 - c + n*c + c**3 - 2 - c**4 + c**2.
-(c - 2)*(c - 1)*(c + 1)**2
Suppose 0 = -4*n + 6*n. Suppose n*a - 10 = -5*a. Solve -a*h**2 + h**2 - 2*h + 4*h = 0 for h.
0, 2
Let a(q) = -q**2 - 20*q - 75. Let p be a(-5). Let p*i + 4/7*i**4 + 0*i**2 - 2/7*i**5 - 2/7*i**3 + 0 = 0. Calculate i.
0, 1
Let c(k) be the second derivative of 2/9*k**3 - k - 1/180*k**5 + 2*k**2 + 0*k**4 + 0. Let x(f) be the first derivative of c(f). Suppose x(b) = 0. What is b?
-2, 2
Let n(x) be the first derivative of 4*x**3/3 + 4*x**2 - 22. Determine r, given that n(r) = 0.
-2, 0
Suppose 5*l - 3*z + 2*z - 76 = 0, 4*z + 19 = l. Determine s so that -l*s + 12*s**2 - 8*s**2 + 3*s + 8 = 0.
1, 2
Let p(j) = -5*j**4 - 4*j**3 + 7*j**2 + 6*j. Let b(h) = 6*h - h**2 - 5*h - h**3 + 2*h**2 - h**4. Let f(l) = -6*b(l) + p(l). What is z in f(z) = 0?
-1, 0
Let p = 59/660 + -1/44. Let v(x) be the third derivative of p*x**6 - 1/6*x**3 - 1/12*x**4 + 1/30*x**5 + 1/168*x**8 - x**2 + 1/30*x**7 + 0*x + 0. Factor v(z).
(z + 1)**4*(2*z - 1)
Let c(v) be the first derivative of 3*v + 2 + 9/4*v**2 + 1/2*v**3. Factor c(n).
3*(n + 1)*(n + 2)/2
Let f(k) be the third derivative of -2/3*k**3 + k**2 + 0 - 7/12*k**4 + 2/15*k**5 + 0*k. Factor f(y).
2*(y - 2)*(4*y + 1)
Suppose -4 + 1 = -j. Factor 0*x**3 + x**5 - x**4 + j*x**4 + x**3.
x**3*(x + 1)**2
Let y(k) be the first derivative of k**8/1008 - k**7/315 + k**6/360 - k**2/2 + 3. Let o(q) be the second derivative of y(q). Suppose o(d) = 0. What is d?
0, 1
Let a = 7 + 3. Let q be 3*4/6*1. Factor 8 + t**q + t**2 - a.
2*(t - 1)*(t + 1)
Let v be 4/((-48)/(-50)) - 4.