 such that -3/4 - 5/4*a**2 + 1/4*a**3 + 7/4*a = 0.
1, 3
Let d(h) be the second derivative of h**7/84 - h**6/30 + h**4/12 - h**3/12 - h. Factor d(r).
r*(r - 1)**3*(r + 1)/2
Let h(y) be the first derivative of 6*y**3 - 18/5*y**5 - 4 + 9/2*y**6 + 0*y - 3/2*y**2 - 6*y**4. Find u such that h(u) = 0.
-1, 0, 1/3, 1
Let x = -8411/9 + 935. Determine v, given that -1/9*v + 1/9*v**3 + 0 - x*v**4 + 4/9*v**2 = 0.
-1, 0, 1/4, 1
Let u(f) be the second derivative of f**7/210 + f**6/40 + f**5/60 - f**3/2 - 2*f. Let s(a) be the second derivative of u(a). Factor s(v).
v*(v + 2)*(4*v + 1)
Let z be (-24)/36 + 14/18. Let l(k) be the first derivative of 4/3*k + 4/5*k**5 - 4 + 3*k**2 + 7/3*k**4 + z*k**6 + 32/9*k**3. Factor l(a).
2*(a + 1)**4*(a + 2)/3
Let f = 59/10 - 57/10. Find a, given that -1/5*a**2 + 0 - f*a = 0.
-1, 0
Suppose 0 = 4*j + 258 + 22. Let n be 1/2 + 7/j. Determine p so that 0 - n*p**3 + 6/5*p**2 - 4/5*p = 0.
0, 1, 2
Let a(k) = -5*k**4 + 2*k**3 + 6*k**2 + 4*k + 5. Let x(o) = -11*o**4 + 4*o**3 + 13*o**2 + 9*o + 11. Let q(s) = -13*a(s) + 6*x(s). Factor q(g).
-(g - 1)*(g + 1)**3
Let z = -10 - -14. Let p = z + -2. Solve 2*b**3 - 4*b**2 + p*b + 1 - 1 = 0 for b.
0, 1
Let f(x) be the first derivative of 3*x**4/16 - x**3/2 - 3*x**2/2 + 6*x - 7. Let f(b) = 0. What is b?
-2, 2
Factor 0 + 2/11*i**3 + 0*i - 2/11*i**2 + 2/11*i**4 - 2/11*i**5.
-2*i**2*(i - 1)**2*(i + 1)/11
Let v(b) be the second derivative of -b**5/80 - b**4/48 + b**3/12 - b. What is g in v(g) = 0?
-2, 0, 1
Let d(b) = -b**2 + 5*b - 2. Let a be d(3). Determine y, given that 12*y**4 + 12*y**3 + 3*y**2 - 5*y**a + 0*y - y - y = 0.
-1, 0, 2/7
Let p(k) be the third derivative of 0 - k**2 - 1/78*k**5 - 3/260*k**6 + 3/52*k**4 + 0*k - 2/39*k**3 + 1/195*k**7. Suppose p(n) = 0. Calculate n.
-1, 2/7, 1
Let m = 416 - 416. Factor -4/5*k**3 + 0*k**2 + 4/5*k + m.
-4*k*(k - 1)*(k + 1)/5
Suppose 0 = -5*x - 2 + 22. Let n(a) be the second derivative of -1/36*a**x - 1/18*a**3 - 2*a + 0 + 0*a**2. What is h in n(h) = 0?
-1, 0
Let u(h) = h**2 + 10*h - 9. Let d be u(-11). Let -3/4*n**4 - 9*n - 3 - 39/4*n**d - 9/2*n**3 = 0. Calculate n.
-2, -1
Let x = 2 - 2. Suppose -q + x*q = -2. Let -16*m**3 + 2*m**2 - m**2 + 7*m - q + 9*m**5 + m**2 = 0. Calculate m.
-1, 1/3, 2/3, 1
Let s(f) = 3*f**2 + 8*f - 2. Let z(m) = m**2 + 1. Let g(k) = s(k) + 2*z(k). Let q(j) = -j**2 - j. Let r(x) = g(x) + 6*q(x). Determine c so that r(c) = 0.
0, 2
Let r(c) = -48*c**2 - 27*c - 6. Let z(g) = -7*g**2 - 4*g - 1. Let x(m) = -4*r(m) + 27*z(m). Factor x(q).
3*(q - 1)*(q + 1)
Let 20*z**3 + 7*z + 0*z - 7*z + 8*z**2 = 0. Calculate z.
-2/5, 0
Let q = 2/89 + 168/445. Find t, given that -4/5*t - q*t**2 - 2/5 = 0.
-1
Let v = 12 - 24. Let c = v + 14. Determine a so that 2/9*a + 0 + 2/9*a**c = 0.
-1, 0
Let s(z) = -18*z + 234. Let p be s(13). Find n such that 2/7*n**2 + p*n - 2/7*n**3 + 0 = 0.
0, 1
Let g(o) be the third derivative of -o**6/60 - o**5/10 - o**4/4 - o**3/3 + 4*o**2. Suppose g(y) = 0. What is y?
-1
Let p = 0 + 2. Factor -12 + 9 + 0*k**3 - 9*k**p + 9*k + 3*k**3.
3*(k - 1)**3
Let p = -15/2 - -8. Determine w, given that p*w + 1 - 15/2*w**2 - 7/2*w**4 + 19/2*w**3 = 0.
-2/7, 1
Let y(j) be the first derivative of -5*j**4/4 + 20*j**3/3 - 25*j**2/2 + 10*j - 20. Find p, given that y(p) = 0.
1, 2
Suppose 21*p - 56 = -14. Determine h, given that 3/2*h**3 + 0*h + 1/2*h**p + 0 = 0.
-1/3, 0
Let t(o) = 13*o**3 + 18*o**2 - 7*o - 31. Let w(x) = 9*x**3 + 12*x**2 - 5*x - 21. Let y(s) = -5*t(s) + 7*w(s). Factor y(p).
-2*(p - 1)*(p + 2)**2
Factor 8/5*p - 12*p**2 + 96/5*p**3 + 64/5*p**4 + 0.
4*p*(p + 2)*(4*p - 1)**2/5
Let c(h) be the third derivative of h**7/735 - h**6/280 - h**5/60 + h**4/14 - 2*h**3/21 - 2*h**2 + 12*h. Suppose c(m) = 0. Calculate m.
-2, 1/2, 1, 2
Let n(y) be the first derivative of -16*y**5/5 - 7*y**4 + 8*y**3 + 14*y**2 - 8*y + 5. Suppose n(w) = 0. Calculate w.
-2, -1, 1/4, 1
Suppose -d - 4 = -0. Let s = d - -6. Find z, given that 11*z + 4 - z**2 - 9*z - z**s = 0.
-1, 2
Let q(d) = -2*d**3 + 34*d**2 + 35*d + 20. Let f be q(18). Factor 0 + 6/5*r**f - 2/5*r.
2*r*(3*r - 1)/5
Let c = -2398/5 + 14411/30. Let t = -4/15 + c. Determine g so that -g**2 - 3/4*g**3 + 1/4*g + t = 0.
-1, 2/3
Let d be (-559)/(-11) - 4/(-22). Solve -128*a**3 + 2 - 17*a - d*a**2 - 4*a - 3*a + 147*a**2 = 0 for a.
1/4
Let u be (-1)/8 - (-2 + 45/24). Let g(f) be the first derivative of 3 - 2/15*f**5 + 0*f**2 + 0*f**4 + u*f + 0*f**3. Factor g(d).
-2*d**4/3
Let d be 22/99 + (-25)/(-9). Solve 3*g - g**2 - 6*g**3 - 6*g - 11*g**2 + 12 + 9*g**d = 0 for g.
-1, 1, 4
Let v = 5 - 3. Suppose 0*o - 5*o**2 + 0*o + 3*o**2 + v*o**3 = 0. Calculate o.
0, 1
Let u(s) be the second derivative of s**7/840 - s**5/120 + s**3/24 - 3*s**2 + 2*s. Let o(h) be the first derivative of u(h). Solve o(t) = 0.
-1, 1
Let x(u) = 3*u**4 - 6*u**3 - 15*u**2 + 18*u + 12. Let m(l) = -3*l**4 + 6*l**3 + 16*l**2 - 19*l - 12. Let w(a) = 6*m(a) + 7*x(a). Solve w(z) = 0 for z.
-1, 2
Let h(x) be the second derivative of x**5/50 + 3*x**4/10 + 9*x**3/5 + 27*x**2/5 - x. Determine u, given that h(u) = 0.
-3
Let o(s) be the first derivative of s**6/3 - 4*s**5/5 + 4*s**3/3 - s**2 - 5. Factor o(j).
2*j*(j - 1)**3*(j + 1)
Factor 2/5*f**2 + 4/5 - 6/5*f.
2*(f - 2)*(f - 1)/5
Let x be (-19)/(-3) - ((-43)/6 + 7). Let -x*s**3 - 7/2*s**5 + 23/2*s**4 - 19/2*s**2 - 2 + 10*s = 0. What is s?
-1, 2/7, 1, 2
Suppose 3 + 3 = 3*s. Let i(p) = -p**2 + p + 3. Let d be i(0). Suppose -g**2 - 4*g**2 + g**d + 4*g**s = 0. Calculate g.
0, 1
Factor 4/3*l**2 + 16/3 - 20/3*l.
4*(l - 4)*(l - 1)/3
Let -4/3*j**5 + 5*j**4 - 16/3*j**3 + 2/3*j + j**2 + 0 = 0. What is j?
-1/4, 0, 1, 2
Let r(m) be the first derivative of 2*m**3/21 + 16*m**2/7 + 128*m/7 - 10. Suppose r(n) = 0. Calculate n.
-8
Suppose k - 5 = 0, 0 = -5*z - k + 17 + 3. Suppose -o = 1 - z. Factor -4*v + v**2 - o*v**2 + 3*v**2 + 2.
2*(v - 1)**2
Let k(s) be the second derivative of -s**8/5600 - s**7/1400 - s**6/1200 + s**4/6 + 2*s. Let q(i) be the third derivative of k(i). Factor q(w).
-3*w*(w + 1)*(2*w + 1)/5
Let w(m) be the second derivative of -11*m + 7/10*m**5 + 0*m**2 + 0 - 49/45*m**6 + 4/3*m**4 + 4/9*m**3. Factor w(l).
-2*l*(l - 1)*(7*l + 2)**2/3
Let s be ((-14)/4)/(-7)*0. Suppose 2*c + 4*u - 26 = s, 2*c - 2*u + 19 = 3*u. Factor -3/2*l**5 + 0*l - 5/2*l**4 - 1/2*l**c + 0 + 1/2*l**2.
-l**2*(l + 1)**2*(3*l - 1)/2
Let n = 14 + -6. Suppose 6*l**3 + 29*l + 2 - 2 - n*l - 6*l**4 + 24*l**2 - 3*l**5 + 6 = 0. Calculate l.
-1, 2
Let z(v) = -12*v + 8. Let q = -13 + 14. Let m(j) = -j**2 - j + 1. Let t(w) = q*z(w) - 4*m(w). Solve t(a) = 0 for a.
1
Let d(c) be the second derivative of -c**4/72 + 13*c**3/36 + 2*c + 1. Factor d(q).
-q*(q - 13)/6
Let z(h) be the first derivative of 1/10*h**5 + 0*h - 1/60*h**6 - 1/4*h**4 + 3 + 3/2*h**2 + 1/3*h**3. Let k(j) be the second derivative of z(j). Factor k(l).
-2*(l - 1)**3
Suppose -4*m + h = -5 - 13, 2*m + 5*h - 20 = 0. Factor 2*d**m - 3*d**4 - d**4 + 6*d**3 + 5*d**4 + 5*d**4 + 2*d**2.
2*d**2*(d + 1)**3
Let u(g) = -g + 2. Let s be u(-2). Let -x**s + 0*x**3 + 3*x**5 - 5*x**5 + x**3 = 0. What is x?
-1, 0, 1/2
Let u = 103 + -101. Let d(f) be the third derivative of 1/30*f**5 + 1/120*f**6 + 0*f**3 + 1/24*f**4 + 0*f - 3*f**u + 0. Factor d(h).
h*(h + 1)**2
Factor 9 - p**3 + 5*p**2 + 14*p - 5*p**2 - 29*p + 7*p**2.
-(p - 3)**2*(p - 1)
Let s be ((-2)/4)/(-14 + 2). Let l(w) be the second derivative of -1/12*w**3 + 0 + 0*w**2 - s*w**4 + 2*w. What is f in l(f) = 0?
-1, 0
Let g(p) be the first derivative of p**5/25 - 2*p**4/5 + 2*p**3/5 + 4*p**2 + 5*p + 23. Let g(q) = 0. Calculate q.
-1, 5
Let z(d) be the second derivative of -d**6/24 - d**5/8 - 5*d**4/48 - 35*d. Factor z(w).
-5*w**2*(w + 1)**2/4
Let a(y) be the first derivative of y**5/15 - 5. Let a(w) = 0. What is w?
0
Let k(w) be the third derivative of 2*w**7/7 + 13*w**6/30 + 2*w**5/15 + 46*w**2. Factor k(v).
4*v**2*(3*v + 2)*(5*v + 1)
Suppose 0 = 5*c - 0*h - h + 85, 2*c = -5*h - 7. Let l be (-24)/c - 3/2. Suppose -30/7*t**4 + l*t + 0 - 2*t**3 - 18/7*t**5 - 2/7*t**2 = 0. What is t?
-1, -1/3, 0
Let p(l) be the first derivative of -l**6/180 + l**4/12 + 2*l**3/9 - 3*l**2/2 + 1. Let a(i) be the second derivative of p(i). Solve a(j) = 0 for j.
-1, 2
Let p(i) = i**4 - 11*i**3 - 3*i**2 + 8*i - 4. Let s(l) = -12*l**4 + 120*l**3 + 32*l**2 - 88*l + 44. L