q(a).
-2*a**2*(5*a + 1)/11
Let z(k) be the second derivative of k**7/147 - 2*k**5/35 + k**4/21 + k**3/7 - 2*k**2/7 - 7*k. Find q, given that z(q) = 0.
-2, -1, 1
Let p = 70545/2 + -2327113/66. Let g = p - 94/11. Suppose -g*f + 4/3 - 4/3*f**3 + 14/3*f**2 = 0. Calculate f.
1/2, 1, 2
Suppose 9 = 3*k, -3 = 5*y + 3*k - 27. Let h(q) be the third derivative of 1/27*q**4 + 1/270*q**5 + 4/27*q**y - 4*q**2 + 0*q + 0. Let h(d) = 0. Calculate d.
-2
Let z be (9/12)/(8/(512/21)). Suppose 0 - 24/7*w**4 - 4/7*w**5 - 48/7*w**2 - 52/7*w**3 - z*w = 0. Calculate w.
-2, -1, 0
Let j(b) be the third derivative of -b**7/525 + b**6/150 + b**5/50 - b**4/15 - 4*b**3/15 - 15*b**2. Factor j(w).
-2*(w - 2)**2*(w + 1)**2/5
Let s = -86 - -86. Let p(x) be the first derivative of 2 + s*x + 2/9*x**3 + 0*x**2 - 1/6*x**4. Factor p(j).
-2*j**2*(j - 1)/3
Let y(g) be the first derivative of g**3/3 - 7*g**2 + 4*g - 4. Let s be y(14). Determine o, given that 0 - 4/7*o**s - 6/7*o**5 + 4/7*o**2 + 0*o + 6/7*o**3 = 0.
-1, -2/3, 0, 1
Let n(d) be the third derivative of d**6/360 - d**5/40 + d**4/12 + d**3/2 - 2*d**2. Let z(m) be the first derivative of n(m). Factor z(w).
(w - 2)*(w - 1)
Find t such that 97*t**5 + 2*t + 8*t**4 - 8*t**2 - 101*t**5 + 2*t = 0.
-1, 0, 1
Factor -3*u**3 - 5*u + 5*u - 9*u**4.
-3*u**3*(3*u + 1)
Let j be (1546/(-7)*1)/2. Let a = j + 111. Factor -2*l**2 + 18/7*l - a.
-2*(l - 1)*(7*l - 2)/7
Factor 32*h + 0 - 44*h**2 - 4 - 23*h**2 + 40*h**3 - h**2.
4*(h - 1)*(2*h - 1)*(5*h - 1)
Factor o - 4*o**2 - 3*o - 2*o**3 + 0*o.
-2*o*(o + 1)**2
Suppose 29 = 5*y + 14. Let z(b) be the second derivative of 0*b**4 + 0*b**2 + 0 + 0*b**3 - 1/135*b**6 + y*b - 1/90*b**5. Factor z(m).
-2*m**3*(m + 1)/9
Let z(x) = -3*x**4 - x**3 - 3*x**2 + x + 1. Let q(f) = -2 + 1 + 33*f**4 - 30*f**4 + 2*f**2. Suppose 6*t + 20 = 2*t. Let b(n) = t*q(n) - 4*z(n). Factor b(u).
-(u - 1)**2*(u + 1)*(3*u - 1)
Let i(n) be the third derivative of n**6/40 - n**5/10 + n**4/8 - 2*n**2. Solve i(c) = 0 for c.
0, 1
Suppose 56*j**2 - 24*j**2 - 4*j - 30*j**2 - 6 = 0. Calculate j.
-1, 3
Solve f**5 + 1/4 - 2*f**3 + 1/4*f**4 - 1/2*f**2 + f = 0.
-1, -1/4, 1
Let g(m) = -4*m + 3. Let n be g(0). Suppose 6 - n = l. Factor -4/5*r - 2*r**2 + 0 - 8/5*r**l - 2/5*r**4.
-2*r*(r + 1)**2*(r + 2)/5
Factor 0 - 2/5*v**2 - 4/5*v + 4/5*v**3 + 2/5*v**4.
2*v*(v - 1)*(v + 1)*(v + 2)/5
Let b(f) be the second derivative of f**6/50 + 9*f**5/50 - 2*f**4/5 - 3*f**3/5 + 21*f**2/10 - 8*f + 1. Suppose b(p) = 0. What is p?
-7, -1, 1
Factor 0 - 1/2*r - 1/4*r**3 + 3/4*r**2.
-r*(r - 2)*(r - 1)/4
Suppose 0*x + 5*x + 3*q = 22, 4 = -4*x + 3*q. Suppose -2/9*i**x + 2/9*i**4 + 0 + 0*i + 2/9*i**3 - 2/9*i**5 = 0. What is i?
-1, 0, 1
Let o(g) be the second derivative of -g**6/10 + 3*g**5/20 + 3*g**4/4 - g**3/2 - 3*g**2 - 4*g. Let o(j) = 0. What is j?
-1, 1, 2
Let g = -5 + 1. Let d(o) = -3*o**2 + o - 6. Let h(w) = -2*w + 7*w**2 + 10 - 2 + 5. Let l(u) = g*h(u) - 9*d(u). Factor l(y).
-(y - 1)*(y + 2)
Let z = 721 + -5035/7. What is q in z*q - 2/7*q**2 - 18/7 = 0?
3
Let l(b) be the first derivative of -5*b**4/16 - 5*b**3/6 - 2. Suppose l(d) = 0. Calculate d.
-2, 0
Let r be (4/(-14))/((-1)/((-42)/(-30))). Factor -8/5*h**3 + 0*h**4 + 6/5*h + 4/5 - 4/5*h**2 + r*h**5.
2*(h - 2)*(h - 1)*(h + 1)**3/5
Solve o + 3*o + 2*o**4 + 8*o**2 - o**5 - 10*o**4 - 3*o**5 = 0.
-1, 0, 1
Let p be 0 + -3 - (-4 - -1). Suppose p = -g - 3*n + 9, 2*n = 3 + 3. Factor -2 + g*r - 2*r - 4*r - 4*r**2.
-2*(r + 1)*(2*r + 1)
Let j = 4 + -2. Factor -2*y**j - 2*y + y**2 - 1 - 2 + 2.
-(y + 1)**2
Factor -18*l - 5*l**2 + 8*l + 30 - 35.
-5*(l + 1)**2
Let s(m) = 3*m**4 + 2*m**3 - 2*m - 1. Let u(h) = -h**4 - 2*h**4 + 2*h**4. Let g(y) = -s(y) - 2*u(y). What is l in g(l) = 0?
-1, 1
Factor 0 + 1/6*m**3 + 1/6*m**2 + 0*m.
m**2*(m + 1)/6
Let d = -18 + 20. Let j(v) be the third derivative of 0*v + 1/240*v**5 + 1/24*v**3 + 0 - 2*v**d + 1/48*v**4. Determine b so that j(b) = 0.
-1
Let u(x) be the first derivative of 2*x**6/3 - 12*x**5/5 + 2*x**4 + 8. Suppose u(j) = 0. What is j?
0, 1, 2
Let z(g) be the second derivative of -2*g**2 - g - 1/6*g**4 + g**3 + 0. Factor z(w).
-2*(w - 2)*(w - 1)
Factor 0 + 9/5*y - 3/5*y**2.
-3*y*(y - 3)/5
Let l(o) = -o**3 - 5*o**2 - 6*o - 3. Let x be l(-4). Let r(t) be the second derivative of 0*t**3 + 1/36*t**4 + t + 0 + 1/60*t**x + 0*t**2. Factor r(q).
q**2*(q + 1)/3
Let f(h) be the third derivative of h**6/120 - h**5/15 - h**4/24 + 2*h**3/3 - 16*h**2. Determine w, given that f(w) = 0.
-1, 1, 4
Let -1/10*q**2 + 0 + 0*q = 0. What is q?
0
Suppose 0 = 2*k - k + 4*o - 19, 13 = 3*k + o. Let q be (-1)/(1/(-2)) + -2. Solve 2/9*s**k + 0*s + 2/9*s**4 + q*s**2 + 0 = 0.
-1, 0
Let c(q) be the first derivative of q**4/40 - q**3/30 + 63. Factor c(b).
b**2*(b - 1)/10
Let o = -118/21 - -368/63. Find k such that 2/9*k**2 - 4/9*k + o = 0.
1
Let l(p) be the third derivative of -p**5/30 - p**4/12 + 10*p**2. Determine a, given that l(a) = 0.
-1, 0
Let p(g) = g**4 + g**2. Let v(s) = 14*s**3 + 8*s**2 - 110*s - 100. Let t(j) = 4*p(j) - 2*v(j). Factor t(n).
4*(n - 5)**2*(n + 1)*(n + 2)
Let d(l) be the first derivative of 3 - 1/3*l**3 - 1/12*l**6 + 1/10*l**5 - 1/4*l**2 + 1/2*l + 1/4*l**4. Determine b, given that d(b) = 0.
-1, 1
Suppose -5*u - 16*u + 105 = 0. Factor -1/6*s**2 + 0 + 1/6*s**4 - 1/6*s**3 + 1/6*s**u + 0*s.
s**2*(s - 1)*(s + 1)**2/6
Let z(v) be the first derivative of -2*v**5/25 - 2*v**4/5 - 2*v**3/5 + 7. Factor z(r).
-2*r**2*(r + 1)*(r + 3)/5
Factor 6*y**2 + 1 - 5 - 3*y**2 - y**3.
-(y - 2)**2*(y + 1)
Factor 45*m**4 + 39*m**4 - 82*m**4 + 2*m**3 - 10*m**2 + 6*m.
2*m*(m - 1)**2*(m + 3)
Let q(v) = -v**3 + 3*v**2 + v. Let j be q(3). Let m = j - 0. Factor 0*k**4 - m*k**4 - k**3 - k**2 - k**5 - 2*k**3.
-k**2*(k + 1)**3
Let q(o) be the first derivative of -3*o**4/20 - 3*o**3/5 - 3*o**2/5 - 7. Factor q(s).
-3*s*(s + 1)*(s + 2)/5
Let i(s) be the third derivative of -s**6/30 + 2*s**5/15 - 3*s**2. Find l such that i(l) = 0.
0, 2
Let z(t) be the first derivative of -9*t**6/2 - 18*t**5/5 + 6*t**4 + 6*t**3 + 3*t**2/2 + 2. Solve z(k) = 0.
-1, -1/3, 0, 1
Let m(d) be the first derivative of -2*d**5/35 + 13. Suppose m(t) = 0. Calculate t.
0
Let w = -16 - -28. Factor 13*h - 3*h**3 + 4*h**3 + 2*h**2 - w*h.
h*(h + 1)**2
Let q(c) be the first derivative of -c**3/12 + 5*c**2/4 - 50. Let q(d) = 0. Calculate d.
0, 10
Let 4*d**5 + 2*d**4 + 12*d - 20*d - 2*d**2 - 6*d**3 + 10*d = 0. Calculate d.
-1, 0, 1/2, 1
Factor 2 + 4*m**2 + 2*m**5 - 7*m**2 + 4*m**3 - 6*m**4 + 7*m**2 - 6*m.
2*(m - 1)**4*(m + 1)
Let z(r) = -r**2 + r + 1. Suppose 2*x + 12 = 6*x. Let d(q) = 12 + 6*q + 8*q - 12*q**2 - q**x - q**3 - 2*q. Let m(h) = -d(h) + 10*z(h). Factor m(b).
2*(b - 1)*(b + 1)**2
Suppose 2*y = -4*z, z - 5*y = -y + 18. Factor 2/7*n**4 + 0*n + 0*n**3 + 2/7 - 4/7*n**z.
2*(n - 1)**2*(n + 1)**2/7
Let n(t) = -2*t**2 - 12*t + 3. Let v be n(-6). Let d(b) be the first derivative of -2 - 2/27*b**v + 0*b + 0*b**2. Factor d(l).
-2*l**2/9
Let r(v) be the third derivative of -v**5/135 - v**4/12 - 4*v**3/27 - 8*v**2. Solve r(l) = 0 for l.
-4, -1/2
Let x = -3502/9 - -388. Let w = x - -16/9. Solve 0*v + w*v**2 - 2/3 = 0 for v.
-1, 1
Let r(u) be the first derivative of -u**5/20 + u**4/16 - 10. Factor r(a).
-a**3*(a - 1)/4
Suppose -14 = 4*a - 5*k, 0*k = -k + 2. Let t(m) = -m**2 + m. Let j(d) = 8*d**2 - 5*d. Let p(b) = a*j(b) - 5*t(b). Find x, given that p(x) = 0.
0
Let m(a) be the first derivative of -3*a**6/4 + 3*a**4/4 + 4*a**3/9 + a**2/12 - 8. Solve m(y) = 0 for y.
-1/3, 0, 1
Let o(n) = -n + 2. Let c be o(1). Let q = c - -1. Solve -q*h**4 + 4*h**3 - 4*h + 0*h**3 + 0*h**3 + 2 = 0.
-1, 1
Let d(b) be the second derivative of -4*b - 1/240*b**5 - 3/8*b**3 + 0 + 1/16*b**4 - 3/2*b**2. Let z(n) be the first derivative of d(n). Factor z(m).
-(m - 3)**2/4
Let n(k) be the third derivative of 2*k**7/105 + 2*k**6/15 - 11*k**5/15 + k**4 - 2*k**2 - 8. Determine x, given that n(x) = 0.
-6, 0, 1
Let n(a) be the third derivative of a**9/120960 - a**8/20160 + a**7/10080 - a**5/15 + 3*a**2. Let o(i) be the third derivative of n(i). Factor o(t).
t*(t - 1)**2/2
Factor 0 - 12/7*u**4 - 2/7*u**5 - 26/7*u**3 - 8/7*u - 24/7*u**2.
-2*u*(u + 1)**2*(u + 2)**2/7
Suppose -2*r = r - 36. Let w = -8 + r. Solve f**4 - f**3 - 2*f**w + 0 + 0 = 0.
-1, 0
Let f(b) be the second derivative of -1/48*b**4 + 2*