or 0 - 40/3*k - 4/3*k**2.
-4*k*(k + 10)/3
Suppose -o + 7 = 2*l, -5*l = -o - 4*o + 20. Let y = 5 - o. Factor 2/9*t**2 - 2/9*t + y.
2*t*(t - 1)/9
Let f(b) be the second derivative of -b**7/1680 + b**6/720 + b**5/120 - b**3/2 - 5*b. Let d(k) be the second derivative of f(k). Find w, given that d(w) = 0.
-1, 0, 2
Let r(h) be the third derivative of 0 + 1/420*h**6 + 0*h**4 + 6*h**2 + 0*h + 0*h**3 + 1/210*h**5. Factor r(i).
2*i**2*(i + 1)/7
Let w(d) be the first derivative of -1/90*d**5 - 1 + 1/72*d**4 - d**2 + 0*d + 1/18*d**3. Let m(p) be the second derivative of w(p). Factor m(k).
-(k - 1)*(2*k + 1)/3
Factor -o**4 + 22*o + 7*o**2 - 9*o**2 - 28*o**3 - 22*o**2 - 7 + 38*o**3.
-(o - 7)*(o - 1)**3
Let x be ((-2)/3)/((-8)/60). Let -6*s**4 - 8*s + 13*s**2 + 23*s**3 - x*s**4 - 15*s**5 + 2*s**2 + 0 - 4 = 0. What is s?
-1, -2/5, 2/3, 1
What is b in -9/7*b**3 - 3/7*b**4 + 15/7*b**2 - 6/7*b + 0 + 3/7*b**5 = 0?
-2, 0, 1
Let j(n) = -8*n**4 - n**3 - 3*n**2 - 8*n - 7. Let m(d) = -d**4 - d - 1. Let h(o) = 4*j(o) - 36*m(o). Factor h(z).
4*(z - 2)*(z - 1)*(z + 1)**2
Let o(d) be the first derivative of d**3/7 - 9*d**2/14 - 12*d/7 + 2. Factor o(w).
3*(w - 4)*(w + 1)/7
Let u(d) be the first derivative of 1/4*d**2 - 4 - 1/6*d - 1/6*d**3 + 1/24*d**4. Factor u(r).
(r - 1)**3/6
Let z(c) be the third derivative of 3/50*c**5 + 4*c**2 + 1/10*c**4 + 1/15*c**3 + 1/75*c**6 + 0*c + 0. Factor z(k).
2*(k + 1)**2*(4*k + 1)/5
Let g(l) be the first derivative of 3*l**5/25 - 3*l**4/20 - l**3/5 + 3*l**2/10 - 7. Factor g(r).
3*r*(r - 1)**2*(r + 1)/5
What is y in 4/3*y - 2 - 2/9*y**2 = 0?
3
Let h(y) be the first derivative of y**3 + 9*y**2 + 24*y - 1. Determine z so that h(z) = 0.
-4, -2
Let p(j) be the third derivative of -j**8/126 + 17*j**7/315 - j**6/9 + 2*j**5/45 - j**2. Let p(r) = 0. Calculate r.
0, 1/4, 2
Let s(q) be the first derivative of 5*q**3/3 - 5*q**2 + 5*q + 5. Factor s(f).
5*(f - 1)**2
Suppose 4*l - 5*x = 41, -4*l - 12 + 48 = -4*x. Factor 0*k + 0 + 0*k**3 + 0*k**2 - 4/3*k**l - 2/3*k**5.
-2*k**4*(k + 2)/3
Let c(w) be the second derivative of -1/70*w**5 - 2*w - 1/42*w**4 + 0 + 0*w**3 + 0*w**2. Factor c(x).
-2*x**2*(x + 1)/7
Let g(k) be the third derivative of -k**6/140 - 3*k**5/140 - k**4/56 + 2*k**2. Solve g(f) = 0 for f.
-1, -1/2, 0
Let x(b) be the third derivative of -b**7/42 - b**6/4 - 11*b**5/12 - 5*b**4/4 - 36*b**2. Determine p, given that x(p) = 0.
-3, -2, -1, 0
Suppose 10 = -5*j - 10. Let s be 4 + -2 + (-2 - j). Factor 156*x - 138*x**4 - 420*x**2 - 16 + 824*x**4 - s*x + 98*x**3.
2*(x + 1)*(7*x - 2)**3
Let k(i) = -i**2 + 3*i + 3. Let r be k(3). Suppose 0*j = -r*j. Determine y, given that 1/5*y**2 + j + 1/5*y = 0.
-1, 0
Let o = -21 - -15. Let k be o/(-12) + (-5)/18. Factor k*z - 2/3*z**2 + 4/9.
-2*(z - 1)*(3*z + 2)/9
Let y = 18/65 + 4/455. Factor 0*x**4 + 4/7*x**3 - y*x - 2/7*x**5 + 0*x**2 + 0.
-2*x*(x - 1)**2*(x + 1)**2/7
Let o(c) be the first derivative of -c - 1/3*c**3 + c**2 + 1. What is y in o(y) = 0?
1
Suppose -2/5*c**2 + 0 - 2/5*c**3 + 2/5*c + 2/5*c**4 = 0. Calculate c.
-1, 0, 1
Let n = -2/1653 - -583/26448. Let c(u) be the second derivative of 1/80*u**5 - u - n*u**4 + 0 - 1/24*u**3 + 1/8*u**2. Solve c(m) = 0 for m.
-1, 1
Let z be (8/4)/6*15. Let h(m) be the first derivative of 1/6*m**3 + 3/8*m**4 + 1/12*m**6 + 2 + 0*m**2 + 3/10*m**z + 0*m. Find a, given that h(a) = 0.
-1, 0
Let d be (-4)/18*(-2 - 16). Let i(o) be the first derivative of -o**3 - d + o**4 + 0*o - 1/2*o**2. Factor i(j).
j*(j - 1)*(4*j + 1)
Suppose 0 = -4*p - b + 17, -2*b = -p - p + 16. Let l = p + -1. Factor 2*s**2 - s**l - 2*s**2 - s**3.
-s**3*(s + 1)
Factor 0 - 1/2*b + 1/8*b**2.
b*(b - 4)/8
Suppose -47*g + 45*g = 0. Let m be (-4)/(-1 + g + -13). Factor -m*l**2 - 6/7 - 8/7*l.
-2*(l + 1)*(l + 3)/7
Let v(p) be the third derivative of -p**6/120 - 3*p**2. Factor v(l).
-l**3
Let y(u) be the third derivative of u**6/120 + 3*u**5/20 + u**4 + 8*u**3/3 + 16*u**2. Factor y(s).
(s + 1)*(s + 4)**2
Let p(y) = y**3 - 7*y**2 + 3*y + 3. Let h(i) = 4*i**3 - 22*i**2 + 10*i + 10. Let m(u) = 3*h(u) - 10*p(u). Find n such that m(n) = 0.
-2, 0
Let l(h) be the first derivative of 8 + 2/9*h + 1/27*h**6 - 4/27*h**3 - 1/9*h**4 + 1/9*h**2 + 2/45*h**5. Find o such that l(o) = 0.
-1, 1
Let n(l) be the third derivative of l**5/30 - l**4/6 + l**3/3 - 8*l**2. Let n(k) = 0. What is k?
1
Let f be (-261)/(-36) - (-5)/(-4). Let n(j) be the first derivative of 3 - 4/9*j**3 + 0*j + 1/18*j**f + 1/2*j**4 - 4/15*j**5 + 1/6*j**2. What is k in n(k) = 0?
0, 1
Let f(p) be the first derivative of 3*p**4/4 + 3*p**3 + 3*p**2 - 15. Suppose f(h) = 0. What is h?
-2, -1, 0
Let n(m) be the first derivative of 1/6*m**4 + 1/9*m**3 - 3 + 1/15*m**5 + 0*m + 0*m**2. Solve n(f) = 0 for f.
-1, 0
Let 1/3*c**2 + 0*c + 1/3*c**3 + 0 = 0. What is c?
-1, 0
Factor 13/3*x**2 - 7/3*x**5 - 2/3*x + 0 + 23/3*x**4 - 9*x**3.
-x*(x - 1)**3*(7*x - 2)/3
Let w(p) be the third derivative of -p**7/210 - p**6/30 - p**5/20 + p**4/6 + 2*p**3/3 + 39*p**2. What is h in w(h) = 0?
-2, -1, 1
Let x = -17/28 - -6/7. Let l be (-1)/(-2) + -1 - -1. Factor -1/4*g + l - x*g**2.
-(g - 1)*(g + 2)/4
Let j = 13 - 8. Factor -j*t**3 + 2*t**2 + 2*t**3 + 5*t**3 - 4*t.
2*t*(t - 1)*(t + 2)
Let t(l) be the first derivative of 2*l**5/35 + l**4/7 - 8*l**3/21 - 2*l**2/7 + 6*l/7 - 21. Suppose t(f) = 0. Calculate f.
-3, -1, 1
Let y = 19 + -17. Factor p**4 + 3*p**5 + 6*p - 3*p**2 - 9*p**3 + 2*p**4 + 0*p**y.
3*p*(p - 1)**2*(p + 1)*(p + 2)
Factor -5*t**2 - 9*t**2 + 12*t**4 + 11*t**2 - 4*t**2 - 2*t + 7*t**3.
t*(t + 1)*(3*t - 2)*(4*t + 1)
Let n(v) be the second derivative of 2*v**7/3 - 2*v**6/3 - 23*v**5/5 + v**4/3 + 32*v**3/3 + 8*v**2 - 12*v. Suppose n(c) = 0. What is c?
-1, -2/7, 1, 2
Suppose 0*a - 5*a = -30. Factor -a - 2*h**2 - 5 - 8*h + 3.
-2*(h + 2)**2
Let m(l) = -2*l**2 + 2*l + 4. Let z(u) = u - 2. Let n be (-2)/3 - 17/(-3). Let v be z(n). Let a(c) = -2*c**2 + c + 3. Let q(s) = v*m(s) - 4*a(s). Factor q(i).
2*i*(i + 1)
Let a(l) = 235*l**2 - 112*l + 12. Let q(x) = 469*x**2 - 223*x + 24. Suppose -b - 6 = -4*b. Suppose -3*d = b*d + 20. Let t(r) = d*q(r) + 7*a(r). Factor t(p).
-3*(7*p - 2)*(11*p - 2)
Suppose 5*q = -q + 24. Factor -1/4*t**5 + 1/4*t**q + 1/2*t**3 + 0*t**2 + 0 + 0*t.
-t**3*(t - 2)*(t + 1)/4
Let l(v) be the second derivative of 1/12*v**4 + 1/168*v**7 + 3*v + 1/30*v**6 + 1/24*v**3 + 0*v**2 + 0 + 3/40*v**5. Factor l(m).
m*(m + 1)**4/4
Let u(o) = -o**2 + 4*o + 3. Let t be u(5). Let q be (t/(-7))/((-48)/(-84)). Factor q*z - z**4 + z**2 + 0 - 1/2*z**5 + 0*z**3.
-z*(z - 1)*(z + 1)**3/2
Let v(f) be the third derivative of 0*f - 1/80*f**5 + 1/480*f**6 + 1/48*f**4 - 6*f**2 + 0*f**3 + 0. Factor v(g).
g*(g - 2)*(g - 1)/4
Let t = -204 - -209. Suppose -1/2*w**t + 0*w**3 + 1/2*w - w**4 + 0 + w**2 = 0. What is w?
-1, 0, 1
Let r(v) be the second derivative of -v**7/252 - v**6/45 - v**5/20 - v**4/18 - v**3/36 + 5*v. Suppose r(s) = 0. What is s?
-1, 0
Let 11 - 14*n + 1 + 2*n - 3 + 3*n**2 = 0. What is n?
1, 3
Let p(c) = -c**2 - 8*c + 5. Let u be p(-11). Let l = u - -57/2. What is s in 1/2 - l*s**3 - 1/2*s**2 + 1/2*s = 0?
-1, 1
Let n(o) = o + 14. Let a be n(-9). Determine f, given that 5*f**4 - f**4 - 4*f**4 - 3*f**a = 0.
0
Let k = 7 - 3. Suppose -k*m + m**2 + m - 1 + m**3 + 2*m + 0*m = 0. Calculate m.
-1, 1
Let h be (-154)/99 + (-4)/(-2). Factor 2/9 - 2/3*r + h*r**2.
2*(r - 1)*(2*r - 1)/9
Let j(f) be the second derivative of -f**6/300 - 7*f**2/2 + 7*f. Let g(r) be the first derivative of j(r). Solve g(a) = 0 for a.
0
Let n be 7 - 2/(10/35). Solve 2*w**3 + 10/9*w**5 + 4/9*w**2 + 8/3*w**4 + 0*w + n = 0 for w.
-1, -2/5, 0
Let k(l) be the first derivative of 3*l**5/5 - 15*l**4/4 + 9*l**3 - 21*l**2/2 + 6*l + 4. Factor k(g).
3*(g - 2)*(g - 1)**3
Let q(b) be the first derivative of -b**3/12 + b**2/4 - b/4 + 34. Determine z so that q(z) = 0.
1
Let a be (1 + 23/(-5) - -2) + 2. Suppose 0*v**2 - a*v**3 + 0 + 0*v - 1/5*v**4 = 0. Calculate v.
-2, 0
Let l be -3 + (23/(-2))/(28/(-8)). Factor 4/7*q - l - 2/7*q**2.
-2*(q - 1)**2/7
Suppose -4*u + 4*w + 21 = -15, -3*u = -w - 27. Let f = -5 + u. Determine p, given that 2*p**3 + 2*p**4 + 22*p**f + 3*p - 7*p**3 - 13*p**3 - 9*p**5 = 0.
-1/3, 0, 1
Let o(p) be the third derivative of 2*p**2 - 1/18*p**4 + 0*p + 0*p**3 - 1/90*p**5 + 0. Factor o(j).
-2*j*(j + 2)/3
Let l(p) be the third d