10*r - 1/30*r**4 + b*r**3 + 3/50*r**5 - 1/25*r**6 + 1/105*r**7 + 0*r**2 + 0. Factor u(l).
2*l**2*(l - 1)**3/5
Let d = -222 - -383. Let b = d + -1125/7. Find v such that b*v**2 - 2/7*v**3 + 0 + 4/7*v = 0.
-1, 0, 2
Let w = 6168/2467 + -1/4934. Determine h so that 1/2*h**4 + w*h**2 - 2*h**3 - h + 0 = 0.
0, 1, 2
Let h be (-6)/(-39)*(-767)/(-236). Factor h*r - 1/6*r**2 - 1/3.
-(r - 2)*(r - 1)/6
Factor 2*u**2 - 28 - 35*u + 4*u + 21*u.
2*(u - 7)*(u + 2)
Factor -16/7*c + 2/7*c**2 + 0.
2*c*(c - 8)/7
Let j = 27 + -5. Let a = j - 19. Factor 12*p**4 + 20*p**2 + 2*p**5 + 2 + 29*p**3 - 9*p**a + 10*p - 2*p**4.
2*(p + 1)**5
Let k(n) be the first derivative of -n**5/35 - 2*n**4/7 + 915. Factor k(q).
-q**3*(q + 8)/7
Let 3*c**3 + 16/5*c**2 - 1/5*c**4 + 0*c + 0 = 0. Calculate c.
-1, 0, 16
Factor 2/13*j**4 + 0 + 24/13*j**2 - 16/13*j - 12/13*j**3.
2*j*(j - 2)**3/13
Find r such that -24/7*r**5 + 0 - 12/7*r - 4/7*r**4 + 20/7*r**2 + 52/7*r**3 = 0.
-1, 0, 1/3, 3/2
Let g(b) be the first derivative of b**7/70 - b**6/40 - b**5/20 + b**4/8 - 5*b**2/2 - 4. Let m(a) be the second derivative of g(a). Let m(k) = 0. What is k?
-1, 0, 1
Let p(g) be the second derivative of 0*g**2 + 1/10*g**5 + 2/3*g**3 + 1/2*g**4 + 3*g + 0. Solve p(s) = 0.
-2, -1, 0
Let v(g) be the third derivative of -g**9/12096 + g**8/1344 - g**7/504 - g**5/20 - 11*g**2. Let a(o) be the third derivative of v(o). Factor a(k).
-5*k*(k - 2)*(k - 1)
Let q(t) = 7*t**4 + 38*t**3 + 391*t**2 + 690*t + 330. Let k(f) = -8*f**4 - 38*f**3 - 390*f**2 - 691*f - 331. Let l(y) = 6*k(y) + 7*q(y). Solve l(u) = 0.
-18, -1
Let f be (2 - (-38)/(-4))*-2. Determine i so that -f*i**2 + 25*i**3 - 5*i**4 - 26*i**2 + i**2 + 20*i = 0.
0, 1, 2
Determine s, given that -96/5*s + 108/5 + 3*s**2 + 3/5*s**3 = 0.
-9, 2
Let m = -12184 + 12187. What is b in 32/9*b**m - 1/9*b**4 + 2048/9*b - 128/3*b**2 - 4096/9 = 0?
8
Suppose -2*k + 123 = -37. Find u such that 2*u - 79*u**2 - 6 + 3 + k*u**2 = 0.
-3, 1
Let u be 6/14 - (-96)/21. Let c(y) = 2*y**3 + 21*y**2 - 40*y + 27. Let x(p) = -9*p**3 - 105*p**2 + 201*p - 135. Let m(a) = u*x(a) + 24*c(a). Factor m(r).
3*(r - 3)**2*(r - 1)
Factor 3/8*i - 15/2 + 3/8*i**2.
3*(i - 4)*(i + 5)/8
Let j be (-130)/(-25) - (-1)/(-5). Factor 40 + 26*w + j*w**2 + 24*w - 5*w.
5*(w + 1)*(w + 8)
Let t(l) be the second derivative of 5*l**4/12 + 35*l**3/6 - 20*l**2 + 86*l. Factor t(c).
5*(c - 1)*(c + 8)
Solve -11*d**3 + 22 + 14*d**2 + 23*d + 13*d**3 + 19*d - d**3 - 7*d = 0 for d.
-11, -2, -1
Let l = -23818 + 23818. Factor f**2 + 4/3*f**3 - 1/3*f**4 - 6*f + l.
-f*(f - 3)**2*(f + 2)/3
Let 13/3*x + 7/3*x**2 - 1/3*x**3 - 1/3*x**4 + 2 = 0. What is x?
-2, -1, 3
Solve -8*l + 36/5*l**2 - 2/5*l**4 - 8/5*l**3 + 14/5 = 0 for l.
-7, 1
Let w(u) be the first derivative of -u**6/21 + 2*u**5/5 - u**4/2 - 10*u**3/7 + 10. Determine b so that w(b) = 0.
-1, 0, 3, 5
Let g(d) = d**3 - 4*d**2 - 15*d + 50. Let b be g(5). Let r(a) be the third derivative of 5*a**2 - 3/56*a**4 - 2/7*a**3 + 1/140*a**5 + 0*a + b. Factor r(c).
3*(c - 4)*(c + 1)/7
Let p(b) be the third derivative of -b**6/540 - 2*b**5/5 - 27*b**4 - 292*b**2. Let p(x) = 0. What is x?
-54, 0
Let x(p) be the first derivative of -2/5*p**5 - 2*p**2 - 24 + 8/3*p**3 + p**4 - 6*p. Factor x(s).
-2*(s - 3)*(s - 1)*(s + 1)**2
Let a(r) be the first derivative of 3*r**5 + 39*r**4/4 - 11*r**3 - 39*r**2/2 + 18*r - 733. Suppose a(v) = 0. Calculate v.
-3, -1, 2/5, 1
Let s(o) = 2*o**2 - 31*o + 119. Let g be s(6). Let a(b) be the second derivative of 0 - 4*b + 2/11*b**2 - 1/110*b**g + 2/33*b**4 - 5/33*b**3. Factor a(r).
-2*(r - 2)*(r - 1)**2/11
Let v(r) be the second derivative of -r**4/60 - 2*r**3/3 - 32*r**2/5 + 225*r. Factor v(t).
-(t + 4)*(t + 16)/5
Factor -8/7*k**3 + 160/7*k**2 + 6 + 166/7*k.
-2*(k - 21)*(2*k + 1)**2/7
Let u(q) = q**2 + 10*q - 7. Let i be u(-10). Let j = -5 - i. Factor -3*m**2 - m**2 + 2*m**3 + 4*m - 2*m**j.
2*m*(m - 2)*(m - 1)
Let 21/2*x + 147/4 + 3/4*x**2 = 0. Calculate x.
-7
Let m = -363 - -367. Let y(t) be the second derivative of 1/252*t**7 + 0*t**2 + 5*t + 0*t**m + 0 - 1/60*t**5 + 1/180*t**6 + 0*t**3. Solve y(z) = 0 for z.
-2, 0, 1
Factor 0*j**2 + 7/3*j**4 + 0 - j**5 + 0*j - 4/3*j**3.
-j**3*(j - 1)*(3*j - 4)/3
Let c(h) be the third derivative of h**7/105 + h**6/15 + 2*h**5/15 + 37*h**2. Determine i so that c(i) = 0.
-2, 0
Let d(n) = 6*n**2 - 36*n + 24. Let t(o) = -11*o**2 + 66*o - 49. Let b(y) = 5*d(y) + 3*t(y). Factor b(a).
-3*(a - 3)**2
Let q(d) = -3*d**3 + 12*d**2 - 37*d + 26. Let a(h) = 4*h**3 - 11*h**2 + 38*h - 28. Let u(b) = 4*a(b) + 6*q(b). Find v such that u(v) = 0.
1, 2, 11
Let g(f) be the first derivative of -f**4/36 - 2*f**3/9 - f**2/2 + 22*f - 38. Let s(u) be the first derivative of g(u). Solve s(m) = 0 for m.
-3, -1
Let u(g) = 20*g**4 + 15*g**3 - 20*g**2 - 15. Let y(f) = f**4 + f**3 - 1. Let l(k) = u(k) - 15*y(k). Find d such that l(d) = 0.
-2, 0, 2
Determine r, given that -52/9*r - 8/9*r**4 + 8/3 + 8/3*r**3 + 16/9*r**2 - 4/9*r**5 = 0.
-3, -2, 1
Factor 54/7*s**4 + 6*s**2 + 0*s + 0 - 6/7*s**5 - 90/7*s**3.
-6*s**2*(s - 7)*(s - 1)**2/7
Let x(i) = 5*i + 27. Let k be x(-5). Suppose 4*n = 3*v - 22, v + 3*n + 16 - 6 = 0. Find a such that -6*a**v + 13*a + 4 + k - 3*a**3 - 10*a = 0.
-2, -1, 1
Let b be 70/(-100)*408/(-119). Suppose 2*q + 0*q = 10. Factor -3*r**3 - b + 3/5*r**q + 3/5*r**4 - 3/5*r**2 + 24/5*r.
3*(r - 1)**3*(r + 2)**2/5
Let s(p) be the second derivative of p**5/60 + p**4/36 - p**3/9 - 95*p. Find y such that s(y) = 0.
-2, 0, 1
Let z(p) = -2*p**3 + 6*p**2 + 3*p - 4. Suppose 28*x - 26*x + 4 = 0. Let n(i) = -i**3 + 5*i**2 + 2*i - 4. Let s(f) = x*z(f) + 3*n(f). Factor s(m).
(m - 1)*(m + 2)**2
Let n(f) = -2*f**2 - 7*f - 3. Let v be n(-2). Factor 0*k**v + 0*k - 8/11*k**2 + 0 + 2/11*k**4.
2*k**2*(k - 2)*(k + 2)/11
Let i = 101 + -89. Let v be (i - 6)*(15/(-21) - -1). Suppose -3/7*g**2 + v*g - 12/7*g**3 + 3/7 = 0. What is g?
-1, -1/4, 1
Let f = 101881/5 + -20375. Factor 2/5*n - 6/5*n**2 + f - 2/5*n**3.
-2*(n - 1)*(n + 1)*(n + 3)/5
Suppose 2*i = -u + 5*u, 3*i = 3*u. Let j(a) be the first derivative of -5 + 1/10*a**5 - 3/8*a**4 + 0*a + u*a**2 + 1/3*a**3. Find t such that j(t) = 0.
0, 1, 2
Let t(i) = -4*i**3 + i. Let k(j) = -4*j + 19. Let d be k(5). Let a be t(d). Factor 1/4*h**5 + 0*h + 1/4*h**4 - 1/4*h**2 + 0 - 1/4*h**a.
h**2*(h - 1)*(h + 1)**2/4
Let w(a) = -16*a**4 + 82*a**3 - 99*a**2 + 39*a. Let g(z) = -16*z**4 + 84*z**3 - 100*z**2 + 40*z. Let m(o) = -3*g(o) + 4*w(o). Factor m(b).
-4*b*(b - 3)*(b - 1)*(4*b - 3)
Let c(f) be the third derivative of 1/1680*f**8 - 1/525*f**7 + 0*f**3 + 0*f**4 + 0*f - 1/600*f**6 + 0 + 1/150*f**5 - 34*f**2. What is m in c(m) = 0?
-1, 0, 1, 2
Suppose 34/11*n - 2/11*n**4 - 12/11 - 34/11*n**2 + 14/11*n**3 = 0. What is n?
1, 2, 3
Let i = -181 + 183. Suppose -i*o + 9 - 5 = 0. Determine n, given that 4/5*n + 1/5*n**o + 3/5 = 0.
-3, -1
Suppose 5*c + 85 - 25 = 0. Let d be (-26)/12 + (-6)/c + 2. Let 0 - 1/3*r + 0*r**3 + d*r**5 + 2/3*r**2 - 2/3*r**4 = 0. What is r?
-1, 0, 1
Let a(n) be the second derivative of -n**5/150 + n**4/10 - 14*n**3/45 - 8*n**2/5 - 7*n. Factor a(f).
-2*(f - 6)*(f - 4)*(f + 1)/15
Let b = -8365/6 + 4184/3. Find n, given that -1/4*n**5 - n**2 + b*n**4 - 1/4*n + 1/2 + 1/2*n**3 = 0.
-1, 1, 2
Let x(l) be the second derivative of -l**6/6 - 7*l**5/4 - 35*l**4/6 - 20*l**3/3 - 2*l - 36. Factor x(q).
-5*q*(q + 1)*(q + 2)*(q + 4)
Let y = 2839/70 + -565/14. Find u, given that -y*u**4 + 0*u**2 + 1/5*u**5 + 0 + 0*u**3 + 0*u = 0.
0, 1
Suppose -3*c = 3*w - 9, -3*c + 5*w = 2*w - 3. Let c - 2 - 2*k**2 - k - 2 + 5*k = 0. What is k?
1
Let m = -9/11 + 104/33. Suppose -m*q**2 - 2/3 - 3*q = 0. What is q?
-1, -2/7
Let d(x) be the first derivative of -3 - 1/4*x**2 + 1/3*x**3 + 1/8*x**4 - x. Solve d(r) = 0 for r.
-2, -1, 1
Suppose -3*m + 5*g = -406 - 217, 5*m = 5*g + 1045. Let x = 423/2 - m. Suppose 1/4*n**5 - x*n**2 - 5/4*n + n**4 + n**3 - 1/2 = 0. Calculate n.
-2, -1, 1
Let i be (-4 + 116)/(-4)*8/(-272). Factor 18/17*n**3 + 4/17*n + 0 - i*n**2 - 10/17*n**4 + 2/17*n**5.
2*n*(n - 2)*(n - 1)**3/17
Let f(z) be the third derivative of 0 - 1/70*z**5 + 0*z**3 - 1/70*z**6 + 2*z**2 + 0*z**4 + 0*z - 1/245*z**7. Solve f(t) = 0 for t.
-1, 0
Let q(t) be the second derivative of t**6/24 - 8*t**5/15 + 19*t**4/8 - 3*t**3 + 6*t**2 + 10*t. Let o(u) be the first derivative