(s) be the second derivative of 9/70*s**5 - 1/21*s**6 - 1/6*s**4 + 2/21*s**3 + 0*s**2 + 0 + 3*s + 1/147*s**7. What is l in t(l) = 0?
0, 1, 2
Let w = -12 - -17. Let n(o) be the second derivative of -4*o**2 - 17/6*o**4 - 2*o + 0 + 7/5*o**6 - 20/3*o**3 + 2*o**w. Determine k so that n(k) = 0.
-1, -2/3, -2/7, 1
What is j in 7/3*j**2 - 4/3*j**5 + 0 + 2/3*j - 8/3*j**4 + j**3 = 0?
-2, -1/2, 0, 1
Let u(a) = 9*a**2 - 3*a + 5. Let j(p) be the third derivative of -p**5/12 + p**4/12 - p**3/2 + p**2. Let d(b) = -5*j(b) - 3*u(b). Factor d(c).
-c*(2*c + 1)
Let j = -4523485/509 + 8887. Let c = j - -7643/2036. Determine u so that -3/4 + c*u + 3/4*u**2 - 15/4*u**3 = 0.
-1, 1/5, 1
Let t be -5 + (4 - -7) + -6. Determine h so that -5/2*h**3 - 2*h**2 - h**4 - 1/2*h + t = 0.
-1, -1/2, 0
Let y(m) be the third derivative of -m**5/20 - m**4 - 8*m**3 - 21*m**2. Factor y(f).
-3*(f + 4)**2
Let h(g) be the third derivative of g**7/1050 - g**6/300 + g**5/300 + g**2. Find n such that h(n) = 0.
0, 1
Let i be -2 - (-1)/(1/2). Let r be (-4 + (i - -2))/(-1). Determine o, given that -r*o**3 + 3*o**3 + 0*o - o = 0.
-1, 0, 1
Suppose -s = -j + 3*j - 19, -3*j = -2*s - 25. Let k be (-12)/j*-3 + -4. What is c in 13/5*c**3 + c**4 - 4/5*c + k + 4/5*c**2 = 0?
-2, -1, 0, 2/5
Factor 0 + 0*m - 4/7*m**2 + 2/7*m**3.
2*m**2*(m - 2)/7
Suppose -b + 18 = -4*m - 0*m, 3*m = -2*b - 8. Factor -q**2 + 5*q**b - q**2 + 23*q**3 - 20*q**3.
3*q**2*(q + 1)
Let p(n) be the second derivative of 2/3*n**2 + 1/21*n**7 + 1/3*n**3 + 0 + 3*n - 2/9*n**4 - 1/5*n**5 + 2/45*n**6. Find a such that p(a) = 0.
-1, -2/3, 1
Let a be (-2)/(1 - -21)*(5 - 7). Factor -a - 2/11*v**2 - 4/11*v.
-2*(v + 1)**2/11
Let l(t) be the third derivative of 0*t**3 + 3*t**2 + 0*t - 7/60*t**6 + 1/12*t**4 - 4/105*t**7 + 0 - 1/15*t**5. Factor l(f).
-2*f*(f + 1)**2*(4*f - 1)
Let l(v) = 5*v**3 + 95*v**2 - 35*v. Let y(x) = -x**3 - 16*x**2 + 6*x. Let s(n) = -6*l(n) - 35*y(n). Find h, given that s(h) = 0.
0, 2
Let y(k) be the first derivative of -k**5/90 - k**4/18 - 3*k**2 + 6. Let b(x) be the second derivative of y(x). Factor b(w).
-2*w*(w + 2)/3
Let c(q) be the second derivative of 0*q**3 + 0*q**2 - 1/12*q**4 + 0 + 1/10*q**5 - 1/30*q**6 - 3*q. Factor c(z).
-z**2*(z - 1)**2
Let x(i) be the third derivative of i**8/1596 - i**7/665 + i**6/1140 + 26*i**2. Factor x(k).
2*k**3*(k - 1)*(2*k - 1)/19
Factor 0 + 0*n**2 - 4/5*n**3 + 0*n.
-4*n**3/5
Suppose -b - w = -12 + 10, -3*b - 2 = -w. Factor -1/6*m**3 + 0*m + 0 + 1/6*m**4 + b*m**2.
m**3*(m - 1)/6
Let d = -18 - 3. Let a be (d/6)/((-8)/28). Determine c, given that 5*c - 35/2*c**3 - 3/4*c**2 + 1 + a*c**4 = 0.
-2/7, 1
Let j(w) = w**2 - w. Let q be j(4). Suppose -3*m = 3*t - q, 4*m + 2*t - 20 = -3*t. Factor 2/5*y**2 + 0*y - 4/5*y**3 + m + 2/5*y**4.
2*y**2*(y - 1)**2/5
Let i(n) = -20*n**4 - 68*n**3 - 68*n**2 + 12*n. Let q(u) = 8*u**4 + 27*u**3 + 27*u**2 - 5*u. Let p(c) = 5*i(c) + 12*q(c). Find s such that p(s) = 0.
-2, 0
Let q(x) = -x**2 + x + 4. Let l(r) = r**2 - 2*r - 5. Let d(o) = -o + 4. Let j be d(6). Let c(y) = j*l(y) - 3*q(y). What is t in c(t) = 0?
-2, 1
Suppose 1/2 + 0*l - 1/2*l**2 = 0. What is l?
-1, 1
Let c(a) be the first derivative of -a**8/1848 + a**6/220 - a**5/165 + 3*a**2 - 1. Let l(k) be the second derivative of c(k). Factor l(n).
-2*n**2*(n - 1)**2*(n + 2)/11
Let i(n) be the third derivative of n**8/336 - 27*n**2 + 1. Factor i(p).
p**5
Let a(t) be the third derivative of -t**8/3360 + t**7/504 - t**6/180 - t**5/60 - 4*t**2. Let x(p) be the third derivative of a(p). Factor x(y).
-2*(y - 1)*(3*y - 2)
Factor -14*o**2 + 6*o**3 - 3*o**4 - 8*o**2 - 6*o + 25*o**2.
-3*o*(o - 2)*(o - 1)*(o + 1)
Let q(m) be the first derivative of m**7/2100 - m**6/150 + m**5/25 - 2*m**4/15 - 5*m**3/3 - 5. Let a(w) be the third derivative of q(w). Factor a(r).
2*(r - 2)**3/5
Suppose -4*r + 18 = -2*w, -5*w = 3*r - w + 14. Suppose 0 = -3*t - 6, 0 = 2*q + t + 4*t - 4. Factor 0*n + q*n**2 - 2 + 5*n**r + 3*n + 7*n**3.
(n + 1)**2*(7*n - 2)
Let x(j) be the third derivative of j**8/112 - 3*j**7/70 + 3*j**6/40 - j**5/20 + 8*j**2. Let x(f) = 0. What is f?
0, 1
Factor -31*k**2 - 5*k + 24*k**2 + 17*k**2 - 5*k**5 + 10*k**3 - 5 - 5*k**4.
-5*(k - 1)**2*(k + 1)**3
Let p(g) be the second derivative of -2*g**7/105 + g**6/12 - 2*g**5/15 + g**4/12 - 5*g**2/2 + 8*g. Let i(y) be the first derivative of p(y). Factor i(h).
-2*h*(h - 1)**2*(2*h - 1)
Let f(h) be the first derivative of h**3/3 + h**2/2 + 55. Factor f(t).
t*(t + 1)
Let n(p) = -p**3 - 2*p**2 - 3*p. Let f(v) = -2*v**2 - v**2 - 7*v + 0*v**3 - v**2 - 2*v**3. Let c(m) = 2*f(m) - 5*n(m). Solve c(t) = 0.
-1, 0
Find u such that 1 - 22*u**2 + 3*u**2 + 18*u**2 = 0.
-1, 1
Let r(s) be the first derivative of 0*s - 1/8*s**6 + 3/16*s**4 + 0*s**3 - 3 + 0*s**2 + 0*s**5. Factor r(d).
-3*d**3*(d - 1)*(d + 1)/4
Suppose 0*x - 225 = -2*g + 5*x, -2*x + 486 = 4*g. Factor 2*r**3 - g*r + 120*r.
2*r**3
Let u be (-4)/(-10) - 52/(-20). Suppose -u*b - b + 8 = 0. Factor b - 8*q - 4*q**2 - 4 + 2*q.
-2*(q + 1)*(2*q + 1)
Let r(v) be the first derivative of 0*v + 5 + 0*v**2 - 1/6*v**4 + 4/9*v**3. Factor r(b).
-2*b**2*(b - 2)/3
Let n(r) be the third derivative of r**6/18 - 13*r**5/45 + 2*r**4/9 + 8*r**3/9 + 5*r**2. Solve n(t) = 0.
-2/5, 1, 2
Let h(o) = -o + 12. Let l be h(12). Let g(b) be the second derivative of 0 + 0*b**3 + 4*b + l*b**2 + 1/27*b**4 - 1/90*b**5. Factor g(q).
-2*q**2*(q - 2)/9
Let i(t) be the third derivative of -2*t**7/35 + t**6/6 + t**5/15 - 5*t**4/6 + 4*t**3/3 - 13*t**2. Suppose i(k) = 0. What is k?
-1, 2/3, 1
Let n be -2 + -4*2/(-4). Let k = 2 - n. Factor -2*m + 4*m**k - 1 - 4*m**2 + m**4 + 2*m**3.
(m - 1)*(m + 1)**3
Let l be 8/20*170/132. Let y = l + -2/11. Determine s so that 1/3*s**3 - y*s**2 - 1/3*s + 1/3 = 0.
-1, 1
Let g(x) be the first derivative of -1/4*x**4 - 1/2*x - 3 + 0*x**3 + 1/10*x**5 + 1/2*x**2. Determine d so that g(d) = 0.
-1, 1
Suppose 2 - 11 = -3*m. Let b(p) be the second derivative of 2*p + 1/7*p**2 + 1/14*p**4 - 1/7*p**m - 1/70*p**5 + 0. Factor b(j).
-2*(j - 1)**3/7
Suppose -3*c - 9 = 0, 3*p - c = -5*c. Factor -4 + 26*s - 25/2*s**3 + 125/2*s**p - 45*s**2.
(s + 1)*(5*s - 2)**3/2
Suppose -4*d + 15 = d. Let w = 1 + d. Factor -3*p**w + 4*p**5 + p**2 - 3*p**5 - 2*p**2 + 3*p**3.
p**2*(p - 1)**3
Let f(u) = -u**2 - 10*u - 10. Let q be f(-9). Let n be q/(-6)*-2*0. Find p, given that 2/3*p**4 + 4/3*p**3 + 0*p + 2/3*p**2 + n = 0.
-1, 0
Let q be 0 + 2 + (-1 - 1). Let y be 1/(-2 - 0) + (-35)/(-14). Factor 0*v - 2/3*v**3 - 1/3*v**5 + q*v**y + v**4 + 0.
-v**3*(v - 2)*(v - 1)/3
Let p be (15/(-45))/(2/(-18)). Let q(k) be the first derivative of -2/7*k + 6/35*k**5 - 3/7*k**2 - 4/21*k**p + 1/7*k**4 + 1 + 1/21*k**6. Factor q(s).
2*(s - 1)*(s + 1)**4/7
Suppose 0 = 2*s - 3*n - 10, 0*n = 5*s - 4*n - 18. Let d(k) = -4*k + 56. Let q be d(13). Factor u**s - 4*u**3 + 4*u**3 + u**2 + 2*u**q - 4*u**3.
2*u**2*(u - 1)**2
Let y = 60 - 60. Let t(z) be the third derivative of -3*z**2 - 1/21*z**3 + y + 1/210*z**5 + 0*z + 0*z**4. Factor t(m).
2*(m - 1)*(m + 1)/7
Let r = -5 + 7. Factor 2*v**r - 3*v**2 - v**2.
-2*v**2
Let a(i) be the first derivative of i**4/6 + 8*i**3/9 + 5*i**2/3 + 4*i/3 - 4. Factor a(m).
2*(m + 1)**2*(m + 2)/3
Let v = 10/1549 + 252437/7745. Let f = 33 - v. Let 0 + 0*j**2 - f*j**5 - 4/5*j**4 - 2/5*j**3 + 0*j = 0. Calculate j.
-1, 0
Determine i, given that 9*i + 4 + i - 6*i + i**2 = 0.
-2
Suppose 0 = -2*i - 0*g + 2*g - 4, 0 = -i + 3*g. Let w be (-2)/i + (-8)/(-12). Factor 2/3*s**2 + 2/3*s - w.
2*(s - 1)*(s + 2)/3
Suppose -2*a + 8 = -6*a. Let m be (1/(-3))/(a/30). Factor 6/7*z**m + 2*z + 44/7*z**3 + 2/7 + 26/7*z**4 + 36/7*z**2.
2*(z + 1)**4*(3*z + 1)/7
Find b such that -4 - 10*b - 4*b**2 + 19 - 3*b**2 + 2*b**2 = 0.
-3, 1
Factor -3/4*j**3 + 3/8*j**4 + 3/8*j**2 + 0*j + 0.
3*j**2*(j - 1)**2/8
Let h(q) be the second derivative of q**4/78 + q**3/13 + 2*q**2/13 - 9*q. Factor h(w).
2*(w + 1)*(w + 2)/13
Suppose -3*t = 4*w - 93, -3*t - 3*w + 36 = -54. Let c = t - 53/2. Factor -c*b + 1/4 + 1/4*b**2.
(b - 1)**2/4
Let p(k) = -12*k**4 - 16*k**3 + 8*k - 10. Let y(n) = -n**4 - 3*n**4 - n**4 + 1 + n**3 + 6*n**4. Let t(u) = -p(u) - 10*y(u). Determine l so that t(l) = 0.
-2, 0, 1
Let -2*c**2 - 6*c - 4*c**3 - 4 + 6*c**2 + 10*c**3 + 2*c**4 - 2*c**2 = 0. Calculate c.
-2, -1, 1
Let k(a) be the first derivative of 0*