erivative of -r**8/504 + 2*r**7/105 - r**6/15 + r**5/9 - r**4/12 + 8*r**2 - 2*r. Let a(o) = 0. What is o?
0, 1, 3
Let c(d) be the third derivative of 4/3*d**3 + 0 + 0*d + 1/6*d**4 - 1/15*d**5 + 3*d**2. Let c(x) = 0. Calculate x.
-1, 2
Let u(k) be the first derivative of -5*k**8/1512 + k**7/189 - k**6/405 - 2*k**3/3 - 6. Let j(x) be the third derivative of u(x). Solve j(r) = 0.
0, 2/5
Determine y so that -10*y + 5*y**5 - 19*y**4 + 13*y**4 - 9*y**4 + 15*y**2 + 5*y**3 = 0.
-1, 0, 1, 2
Let m(v) be the first derivative of -3*v**5/5 + 3*v**3 + 3*v**2 - 43. Factor m(u).
-3*u*(u - 2)*(u + 1)**2
Factor 2/9*j - 2/9*j**2 + 0.
-2*j*(j - 1)/9
Suppose -p - p = -8. Factor 2*n**2 + 3*n + p*n**2 - 3*n**2 + 4 - 4*n**2.
-(n - 4)*(n + 1)
Suppose 3*y**4 + 5*y**5 - 5*y**2 + 0*y**5 + 21*y**3 - 6*y**3 - 18*y**4 = 0. Calculate y.
0, 1
Factor -12*v**2 + 4*v + 0*v + 4*v + 4*v**3.
4*v*(v - 2)*(v - 1)
Let x(l) be the third derivative of l**7/70 - l**6/10 - 11*l**5/20 - 3*l**4/4 - 41*l**2. Solve x(f) = 0 for f.
-1, 0, 6
Let a(c) be the second derivative of -c**4/60 - c**3/3 - 27*c. Factor a(s).
-s*(s + 10)/5
Let v(g) = -6*g**5 + 6*g**4 + 6*g**3 + 8*g**2. Let z(k) = 5*k**5 - 5*k**4 - 5*k**3 - 7*k**2. Let q(d) = -6*v(d) - 7*z(d). Factor q(c).
c**2*(c - 1)**2*(c + 1)
Let x(m) be the first derivative of 2*m**5/15 + 13*m**4/21 + 6*m**3/7 + 4*m**2/21 - 8*m/21 + 7. Determine o, given that x(o) = 0.
-2, -1, 2/7
Factor 12/7*r**4 - 3/7*r**2 + 9/7*r**3 + 0*r + 0.
3*r**2*(r + 1)*(4*r - 1)/7
Suppose 3*a**3 + 382 - 48*a**2 + 192*a - 382 = 0. What is a?
0, 8
Let k(m) be the second derivative of -m**6/75 + 2*m**5/25 - m**4/6 + 2*m**3/15 - 5*m. Suppose k(y) = 0. Calculate y.
0, 1, 2
Let c(z) be the first derivative of -z**7/315 + z**6/180 - 3*z**2/2 - 1. Let w(a) be the second derivative of c(a). Factor w(d).
-2*d**3*(d - 1)/3
Suppose -3*k = 4*k + 112. Let b be -3*(1 + k/15). Factor b*p**3 - 2/5*p**2 + 1/5*p + 0.
p*(p - 1)**2/5
Let t(d) = 2*d - 3 + 5 - d**2 - 3. Let c(u) = u**2 - 2*u + 1. Let i(o) = 5*c(o) + 6*t(o). Solve i(s) = 0.
1
Let v(u) = 5*u - 47. Let i be v(10). Factor 0*c**i - 2/7*c + 4/7*c**4 + 2/7*c**5 + 0 - 4/7*c**2.
2*c*(c - 1)*(c + 1)**3/7
Suppose 30*c = 29*c + 2. What is v in 0 - 3/2*v**c + 1/2*v**3 + v = 0?
0, 1, 2
Let c(y) be the third derivative of -y**5/100 + y**4/24 - y**3/15 - 38*y**2. What is r in c(r) = 0?
2/3, 1
Let h = -81 + 83. Factor 4/7*q**3 + 0 - 8/7*q**h + 0*q.
4*q**2*(q - 2)/7
Let h(m) = -m**2 - 9*m + 12. Let x be h(-10). Let f(y) be the first derivative of 3 + 5/3*y**3 + x*y + 7/2*y**2. Factor f(w).
(w + 1)*(5*w + 2)
Let s(i) be the first derivative of -i**7/2940 + i**5/420 + i**3 + 3. Let h(f) be the third derivative of s(f). Determine c, given that h(c) = 0.
-1, 0, 1
Let c be (-1287)/3240 - (-6)/15. Let m(b) be the third derivative of 1/1260*b**7 + 0 - b**2 + c*b**5 - 1/360*b**6 + 0*b**4 + 0*b + 0*b**3. Solve m(a) = 0.
0, 1
Factor 0 + 1/5*n - 13/10*n**3 - 11/10*n**2.
-n*(n + 1)*(13*n - 2)/10
Suppose 5*k + 4*n = 6*n + 2, -4*k = 3*n - 20. Let q be (-11)/(-4)*2*2. Determine m so that 13*m - m**k - q*m - 4*m**2 = 0.
0, 2/5
Let z be -6*1*27/(-81). Factor 2/5*q**2 - 2/5*q + z*q**3 + 6/5*q**4 + 0.
2*q*(q + 1)**2*(3*q - 1)/5
Let v(x) = 8*x**3 - 40*x**2 + 92*x - 64. Let p(r) = -7*r**3 + 39*r**2 - 93*r + 64. Let l(f) = 4*p(f) + 3*v(f). Solve l(k) = 0.
1, 4
Let u(w) be the third derivative of -w**10/90720 + w**8/6720 - w**7/3780 + w**4/8 + 4*w**2. Let a(l) be the second derivative of u(l). Factor a(i).
-i**2*(i - 1)**2*(i + 2)/3
Suppose 0 - 1/2*y**3 - y + 3/2*y**2 = 0. Calculate y.
0, 1, 2
Let j = -75 - -79. Let s(a) be the second derivative of 1/42*a**j + 0 + 0*a**2 + 0*a**3 - 1/35*a**5 - 2*a + 1/105*a**6. Determine v, given that s(v) = 0.
0, 1
Let -4/5*q - 48/5*q**4 - 24/5*q**2 - 52/5*q**3 - 16/5*q**5 + 0 = 0. What is q?
-1, -1/2, 0
Factor 4/3 + 2/3*f**2 - 2*f.
2*(f - 2)*(f - 1)/3
Let 20*v**3 - 16*v**3 + 0*v**2 + 4 + 12*v + 12*v**2 = 0. Calculate v.
-1
Let m = -2/799 - -803/1598. Factor -l + m*l**2 + 1/2.
(l - 1)**2/2
Let g = -13 + 17. Factor -4*o**g + 6*o**5 + 6*o + 2*o - 8*o.
2*o**4*(3*o - 2)
Let q(h) be the third derivative of -h**6/24 - h**5/3 - 2*h**2. Factor q(v).
-5*v**2*(v + 4)
Let q(p) = -p**2 + 2*p + 4. Let g be q(3). Let c(y) be the first derivative of 1/9*y**2 + 1/18*y**4 + 0*y + g + 4/27*y**3. Suppose c(t) = 0. What is t?
-1, 0
Let a(g) = -6*g**5 - 12*g**4 + 3*g**2 + 15*g + 9. Let c(w) = 3*w**5 + 6*w**4 - 2*w**2 - 7*w - 4. Let t(n) = 4*a(n) + 9*c(n). Factor t(m).
3*m*(m - 1)*(m + 1)**3
Let m(t) be the first derivative of -5*t**6/6 + t**5 + 15*t**4/2 + 10*t**3/3 - 25*t**2/2 - 15*t + 27. Factor m(b).
-5*(b - 3)*(b - 1)*(b + 1)**3
Let w(t) = -4*t**2 + 17*t - 19. Let x(n) = 20*n**2 - 84*n + 96. Let q(r) = 16*w(r) + 3*x(r). Factor q(s).
-4*(s - 4)*(s - 1)
Let v = -3 - -5. Suppose 4*x = 9 - 1. Factor p**v - 5*p**2 + 4 + 4*p - x*p**2 + 7*p**2.
(p + 2)**2
Let y be ((-35)/175 + 1/5)/(-4). Factor y - 3/5*x**3 + 0*x**2 + 3/5*x.
-3*x*(x - 1)*(x + 1)/5
Let y = -2131/9 + 237. Let i(h) be the second derivative of -7/54*h**4 - 5/27*h**3 + 0 + y*h**2 - 2*h. Let i(a) = 0. What is a?
-1, 2/7
Let v(n) = -2*n**2 + 2*n - 13. Suppose 0 = 4*d + k + k - 46, 4*d - 64 = 4*k. Let l(t) = t**2 - t + 6. Let q(b) = d*l(b) + 6*v(b). Factor q(x).
x*(x - 1)
Let u(o) = -4*o**2 + 3. Let v be u(3). Let a = v - -67/2. Determine c so that -1/2*c**2 + 0 + a*c = 0.
0, 1
Let v = 63 + -313/5. Determine l, given that 2*l - 4/5 - v*l**3 - 6/5*l**2 + 2/5*l**4 = 0.
-2, 1
Let o(j) be the third derivative of j**8/2016 - j**6/120 - j**5/45 - j**4/48 - 25*j**2. Find p, given that o(p) = 0.
-1, 0, 3
Suppose -3*q - 7*q**3 - 2*q**2 - 3*q**4 - 7*q**2 - 2*q**3 = 0. What is q?
-1, 0
Let g = -11 + 16. Let y(t) be the first derivative of -2/3*t**3 - 1/2*t**4 + 1/2*t**2 + 1/6*t**6 + t + 3 + 1/5*t**g. Find h, given that y(h) = 0.
-1, 1
Let u be ((-3)/(9/30))/(-2). Suppose 17 = 5*l - u*o - 13, -3*o = 2*l + 3. Find d such that 4/3*d**l + 4/3*d**2 - 2/3*d - 2/3*d**4 - 2/3*d**5 - 2/3 = 0.
-1, 1
Let g = -796 - -798. Factor 0 + 14/5*i**g - 6/5*i.
2*i*(7*i - 3)/5
Factor 2/7*a**2 - 2/7 + 0*a.
2*(a - 1)*(a + 1)/7
Let v be -1 + (13/6 - (-2)/6). Suppose -v*z**2 - 3/2 + 3*z = 0. What is z?
1
Suppose 0 = c + 2*c + 159. Let z = c - -213/4. Factor -1/4*w - z*w**2 + 0.
-w*(w + 1)/4
Let x(k) be the second derivative of 2*k - 1/6*k**4 + 2*k**3 - 9*k**2 + 0. Determine r, given that x(r) = 0.
3
Let z(h) be the second derivative of 3*h**5/20 + h**4/4 - 4*h. Factor z(f).
3*f**2*(f + 1)
Let n(r) be the second derivative of r**5/50 + r**4/30 - r**3/3 + 3*r**2/5 - 11*r. Factor n(d).
2*(d - 1)**2*(d + 3)/5
Let t = 55 + -53. Factor 0*x - 1/4*x**5 + 0 + 0*x**t + 0*x**4 + 1/4*x**3.
-x**3*(x - 1)*(x + 1)/4
Suppose 0 = -h + 4*h - 6. Determine c, given that 4*c**h + c + 0*c - c - 8 - 4*c = 0.
-1, 2
Let k(d) = -d**2 - d - 1. Let r be 2*3/(-6)*1. Let h(i) = -8*i**2 - 12*i - 10. Let o(v) = r*h(v) + 6*k(v). Find g such that o(g) = 0.
-2, -1
Solve 8/15*d - 2/15*d**2 - 2/5 = 0.
1, 3
Let s be 0*(-3)/(-9) - 3. Let o = s + 4. Factor y - y - y**2 + o.
-(y - 1)*(y + 1)
Let d(m) be the first derivative of -m**5/60 + m**4/12 - m**3/6 + m**2/6 + 3*m + 2. Let a(q) be the first derivative of d(q). Factor a(k).
-(k - 1)**3/3
Let -3*s + 8*s**2 + 13*s**2 + 0*s**2 = 0. What is s?
0, 1/7
Let h(w) = -w**3 + 0*w**3 + 1 + 3*w - 3*w. Let i(n) = 580*n**3 - 160*n**2 - 28*n + 4. Let r(j) = 4*h(j) + i(j). Let r(p) = 0. Calculate p.
-2/9, 1/4
Let p(l) = -6*l**4 - 6*l**3 - 9*l**2 + 3*l. Let s(u) = -u**4 + u**3 - u**2 + u. Let b(t) = p(t) - 3*s(t). Factor b(w).
-3*w**2*(w + 1)*(w + 2)
Suppose 3 + 30*d**4 + 70*d**2 - 3*d - 13 + 95*d**3 - 2*d + 0*d = 0. Calculate d.
-2, -1, -1/2, 1/3
Let p(d) be the second derivative of -2/27*d**3 + 7*d + 0 + 0*d**2 - 1/54*d**4. Factor p(b).
-2*b*(b + 2)/9
Let r(k) be the second derivative of 0 - 1/2*k**2 + 3*k + 1/12*k**3 + 1/24*k**4. Factor r(n).
(n - 1)*(n + 2)/2
Let r(o) be the second derivative of o**6/60 + o**5/30 + 3*o**2 + 6*o. Let f(u) be the first derivative of r(u). Factor f(g).
2*g**2*(g + 1)
Let q(b) be the second derivative of -b**6/420 + b**5/420 + b**4/42 - b**3/6 + 3*b. Let n(a) be the second derivative of q(a). Factor n(z).
-2*(z - 1)*(3*z + 2)/7
Let f(m) be the third derivative of 0 + 11/42*m**7 + 0*m + 25/336*m**8 + 19/