 384*p - 21. Factor -3/4*m**2 + 3/4*m**4 + 3/2*m**p - 3/2*m + 0.
3*m*(m - 1)*(m + 1)*(m + 2)/4
Let s(b) be the first derivative of 3*b**4/16 + b**3/2 + 3*b**2/8 - 2. What is l in s(l) = 0?
-1, 0
Let y(a) be the first derivative of 1/24*a**6 + 0*a**2 - 3/20*a**5 + 3/16*a**4 - 2 + 0*a - 1/12*a**3. Determine l, given that y(l) = 0.
0, 1
Let h(w) = 5*w**2 - 1. Let t be h(-1). Determine n so that n + 7*n**3 + 0*n**2 - 2*n + n**2 + t*n**4 + n**2 = 0.
-1, 0, 1/4
Let x(n) be the second derivative of -5*n**7/126 + n**5/4 - 5*n**4/18 - 5*n. Solve x(s) = 0.
-2, 0, 1
Let j(q) be the second derivative of -q**8/40320 - q**7/7560 - q**6/4320 + q**4/12 - 3*q. Let k(h) be the third derivative of j(h). Factor k(c).
-c*(c + 1)**2/6
Suppose 2*l + 25 = 5*j - 3*l, 5*l = -4*j - 7. Factor t**4 + 2*t**2 + t**j - 2*t**2 - 2*t**3 + 0*t**3.
t**2*(t - 1)**2
Let o be ((-116)/(-10))/((-12)/3) - -3. Let z(y) be the third derivative of 0 - o*y**5 - 1/3*y**3 + 3*y**2 + 1/3*y**4 + 0*y. Factor z(u).
-2*(u - 1)*(3*u - 1)
Solve -2/7*h + 4/7*h**4 + 6/7*h**2 - 2/7 + 10/7*h**3 = 0 for h.
-1, 1/2
Suppose 20 = -8*q + 4*q. Let k(t) = t + 7. Let l be k(q). Factor 0*j**3 - 2*j**3 + 6*j**4 + j**5 - 5*j**4 + j**3 - j**l.
j**2*(j - 1)*(j + 1)**2
Let c(p) = -p**2 + 1. Let d(u) = -2*u**3 + 8*u**2 + 4*u - 6. Let q(x) = -12*c(x) - 2*d(x). Factor q(v).
4*v*(v - 2)*(v + 1)
Suppose -f - 3*s - 1 - 11 = 0, -3*f + 4*s = -16. Let j(c) be the first derivative of 0*c + 1/12*c**3 + f*c**2 - 2 + 1/16*c**4. Factor j(b).
b**2*(b + 1)/4
Suppose -3*s - 2 + 11 = 0. Let t(m) be the second derivative of 1/24*m**s + 0*m**2 + 1/48*m**4 + 0 - 2*m. Let t(d) = 0. Calculate d.
-1, 0
Let w(y) be the third derivative of 0*y - 1/40*y**6 - 27/8*y**4 + 27/2*y**3 + 0 + 8*y**2 + 9/20*y**5. Factor w(z).
-3*(z - 3)**3
Let h = -6 + 12. Let l be (h/10)/(7/35). Factor i**2 + 1/3*i + 2/3*i**l + 0.
i*(i + 1)*(2*i + 1)/3
Suppose 5 - 30 = -5*f. Let x = f + -3. Solve 0 + d**3 - 1/4*d**4 - 5/4*d**x + 1/2*d = 0.
0, 1, 2
Let d(t) be the second derivative of -t**7/28 - t**6/10 + t**4/4 + t**3/4 - 5*t. Factor d(n).
-3*n*(n - 1)*(n + 1)**3/2
Let b(v) = v**5 - 2*v**4 - 3*v**3 + 2*v + 2. Let x(s) = s**5 - 5*s**4 - 6*s**3 + 5*s + 5. Let m(r) = -5*b(r) + 2*x(r). Solve m(h) = 0.
-1, 0, 1
Let r(d) = -2*d**2 - 5*d. Let c(y) = -9*y + 11*y + 2*y**2 - y**2. Let a(v) = 14*c(v) + 6*r(v). Let a(h) = 0. Calculate h.
0, 1
Let p(k) = -10*k**2 - 7*k**3 + 10*k - 10 + 3 + 6*k**3. Let l be p(-11). Factor 2/5*b**2 - 2/5*b**3 - 2/5*b**l + 2/5*b + 0.
-2*b*(b - 1)*(b + 1)**2/5
Suppose -61 = 4*f - 73. Let o(y) be the third derivative of -3*y**2 + 1/144*y**4 + 0*y + 0*y**5 + 0 + 0*y**f - 1/720*y**6. Suppose o(p) = 0. Calculate p.
-1, 0, 1
Let k(d) = 6*d**2 + 15*d + 21. Let m(o) = 7*o**2 + 14*o + 20. Let h(g) = -4*k(g) + 3*m(g). Factor h(n).
-3*(n + 2)*(n + 4)
Let j = -269/5 - -1339/25. Let f = j + 37/50. Factor f*p**2 - 1 - 1/2*p.
(p - 2)*(p + 1)/2
Let g(b) be the second derivative of -9*b + 0*b**3 + 0*b**2 + 1/10*b**5 + 0 + 1/6*b**4. Let g(h) = 0. Calculate h.
-1, 0
Find v such that -1/3*v**3 + 2/3*v + 0 - 1/3*v**2 = 0.
-2, 0, 1
Let 3/2 - 5/4*c**3 - 3*c**2 + 11/4*c = 0. Calculate c.
-3, -2/5, 1
Let w be 3 + (-12)/(-4) + -4. Let l(d) be the third derivative of -2/135*d**5 + 0*d + 4*d**w + 2/27*d**3 + 0 - 7/108*d**4. Factor l(n).
-2*(n + 2)*(4*n - 1)/9
Let d(v) = 3*v**2 - 1. Let a(t) = 16*t**2 - 5. Suppose 0 = 2*f + 5*c - 17, -12 = -f + 4*c - 3*c. Let m(q) = f*d(q) - 2*a(q). What is y in m(y) = 0?
-1, 1
Suppose 7*i + 665 = 2*i. Let p be 3/(-4) + i/(-140). Suppose -1/5*q**4 - 1/5*q - 1/5*q**5 + 2/5*q**2 - p + 2/5*q**3 = 0. What is q?
-1, 1
Let u(s) = s**2 - 8. Let g(z) = -3 + 1 + 1 + 2. Let b(v) = 14*g(v) + 2*u(v). Factor b(j).
2*(j - 1)*(j + 1)
Let b(g) = 2*g**2 + 1. Let x be b(1). Factor 5*z**4 - 2*z**3 - x*z**4 - z - 2*z**2 + 3*z.
2*z*(z - 1)**2*(z + 1)
Let a be 18/(-90) + 2/10. Solve 2/3*z**5 - 2/3*z**3 + 0*z**4 + a*z**2 + 0*z + 0 = 0.
-1, 0, 1
Let o(q) be the third derivative of q**7/3360 + q**6/720 + q**5/480 - 5*q**3/3 - 7*q**2. Let t(a) be the first derivative of o(a). Factor t(z).
z*(z + 1)**2/4
Factor -2/3*l + 0 - 8/9*l**2.
-2*l*(4*l + 3)/9
Let c(l) be the first derivative of 2*l**3/9 - 2*l/3 + 4. Factor c(k).
2*(k - 1)*(k + 1)/3
Suppose -2*j = 2*a - 2, 4*a = -3*j + 1 + 6. Suppose 6*c**a + 3*c**4 + 0*c**4 - 9*c**3 - 3*c**5 + 3*c**2 = 0. Calculate c.
0, 1
Factor -60*x**3 - 5*x + 20*x**4 + 65*x**2 - 6*x + x - 20*x**2.
5*x*(x - 2)*(2*x - 1)**2
Let o = 278 + -4168/15. Let s(y) be the third derivative of 1/150*y**5 - y**2 + 0 + o*y**3 - 1/20*y**4 + 0*y. Factor s(b).
2*(b - 2)*(b - 1)/5
Let m(r) be the first derivative of r**4/15 + 2*r**3/15 - 4*r**2/5 - 3*r + 1. Let z(g) be the first derivative of m(g). Factor z(n).
4*(n - 1)*(n + 2)/5
Let m be (3 - (-1 + 2)) + -1. Let w be (m/9)/(2/6). Suppose -p**3 + 0 + 0*p + w*p**2 = 0. Calculate p.
0, 1/3
Let a(d) be the first derivative of -d**3/2 + 9*d**2/4 - 3*d + 3. Factor a(r).
-3*(r - 2)*(r - 1)/2
Let n = -16 - -21. Factor 5*s**3 - n*s**3 - 6*s**4 + 8*s**2 + 10*s**3 - 8*s.
-2*s*(s - 2)*(s + 1)*(3*s - 2)
Let t be 2*9*(-3)/(-18). Let r(y) be the third derivative of 5/2*y**4 + 2*y**t + 0 + 3*y**2 + 0*y + 1/10*y**6 + 17/20*y**5. Factor r(k).
3*(k + 2)**2*(4*k + 1)
Let y(f) be the first derivative of 3*f**5/20 - 3*f**4/4 + 3*f**3/2 - 3*f**2/2 + 3*f + 4. Let b(m) be the first derivative of y(m). Factor b(i).
3*(i - 1)**3
Factor -1/11*a**3 + 9/11 - 5/11*a**2 - 3/11*a.
-(a - 1)*(a + 3)**2/11
Let l = 2/39 - -3/26. Suppose -1/2*k**2 - l*k**3 + 0 - 1/3*k = 0. Calculate k.
-2, -1, 0
Let y(g) be the second derivative of g**7/840 + g**6/40 + 9*g**5/40 + g**4/2 + 4*g. Let q(d) be the third derivative of y(d). Factor q(n).
3*(n + 3)**2
Factor -6/5*c**2 + 6/5*c - 2/5 + 2/5*c**3.
2*(c - 1)**3/5
Let t = -9 - -11. Suppose t*z = -0*z. Factor -1/4*v**2 + 1/4*v**3 + z - 1/2*v.
v*(v - 2)*(v + 1)/4
Let t(u) be the third derivative of -u**6/60 - u**5/10 - u**4/4 - u**3/3 - 33*u**2. Find p such that t(p) = 0.
-1
Suppose -g - 2*r + 8 = 0, -3*g - 3*r + 13 = -g. Factor -3 - 1/3*s**g + 2*s.
-(s - 3)**2/3
Let y(l) = -l + 19. Let n be y(13). Let i(j) = -j**3 + 7*j**2 - 6*j. Let f be i(n). Factor 2/7*r**4 + f*r**2 + 0*r + 2/7*r**3 + 0.
2*r**3*(r + 1)/7
Let z be 2 + -3 + 18/14. Let a = 371 + -369. Factor -z + 2/7*d**3 + 2/7*d**a - 2/7*d.
2*(d - 1)*(d + 1)**2/7
Let k(f) = 4*f**2 - f. Let d be 0/(-1) - 1*-1. Let i be k(d). Let i - 6 + c**3 - 4*c**2 - 5*c - 2*c**3 + 1 = 0. What is c?
-2, -1
Let m = -54 - -33. Let v be 1/14 + m/(-49). Determine c, given that 1/2*c**3 - v*c**4 - 1/2*c + 1/2*c**2 + 0 = 0.
-1, 0, 1
Factor -2*a**2 + 3*a**2 - a - a**4 + a**3 + 0*a**2.
-a*(a - 1)**2*(a + 1)
Let u(k) be the first derivative of 1/3*k**3 + 3/2*k**2 + 2 - 3*k. Let n(c) = 3*c**2 + 7*c - 7. Let l(r) = 3*n(r) - 7*u(r). Factor l(q).
2*q**2
Let m(q) be the first derivative of 3*q**3/5 + 3*q**2 + 9*q/5 + 17. Solve m(u) = 0 for u.
-3, -1/3
Let z(w) be the third derivative of -w**6/480 + w**5/240 + w**4/96 - w**3/24 - 7*w**2. Factor z(n).
-(n - 1)**2*(n + 1)/4
Factor 0 + 2*j**2 + j**4 + 1/2*j + 5/2*j**3.
j*(j + 1)**2*(2*j + 1)/2
Let o = -7 - -22. Suppose 3*l - o + 3 = 0. Factor -3*h**l + 1/2*h**5 + 6*h**3 + 0 + 0*h - 4*h**2.
h**2*(h - 2)**3/2
Factor 4/9*c**3 + 0 + 2/9*c**2 + 0*c.
2*c**2*(2*c + 1)/9
Let 1117 + 3*m - 1117 - m**2 = 0. What is m?
0, 3
Let s be 34/8 + (-1)/4. Suppose -20 = -k + 4*o - s, o + 13 = k. Find t, given that 18*t**2 + 10*t**3 + 4*t + k*t**3 - 8*t**3 = 0.
-1, -2/7, 0
Let k(p) be the second derivative of -1/8*p**5 + 0 - 2*p - 11/4*p**4 - 11/3*p**3 + 5/12*p**6 - 2*p**2. Let k(a) = 0. Calculate a.
-1, -2/5, 2
Let u(s) = s**2 - 26*s - 27. Let v be u(27). Factor 0*d**4 - 3/5*d**5 + 0*d**2 - 3/5*d + 6/5*d**3 + v.
-3*d*(d - 1)**2*(d + 1)**2/5
Suppose 2*p + 5 = 5*i, -12*p + 8*p + 4*i - 4 = 0. Let -2/3*j**3 - 4/3*j**4 + 0 - 2/3*j**5 + 0*j**2 + p*j = 0. Calculate j.
-1, 0
Let z be (16 + -17)*14/(-8). Let h = 243/4 - 60. Factor -z*f + 1/2 + 2*f**2 - h*f**3.
-(f - 1)**2*(3*f - 2)/4
Let n(m) be the first derivative of -2*m**5/25 + 3*m**4/5 - 26*m**3/15 + 12*m**2/5 - 8*m/5 + 17. Determine r so that n(r) = 0.
1, 2
Suppose -x = 2*x - 12. Solve -21/4*o - 3*o**x - 39/4*o**3 - 3/4 - 45/4*o**2 = 0 for o.
-1, -1/4
Let t(o) be the first derivative of -o**6/200 - o**5/100 -