p - 1)*(p + 3)/7
Let w(q) be the first derivative of 4*q**3/3 - 4*q**2 - 14. Suppose w(m) = 0. Calculate m.
0, 2
Solve -2/11*t**2 - 1/11*t + 2/11 + 1/11*t**3 = 0.
-1, 1, 2
Let w(q) = 4*q**2 - 2*q + 1. Suppose 5*f = 4*t + 2*f - 4, 0 = -4*t + 4*f + 4. Let l be w(t). Factor -u**3 + 3*u**4 + l*u**3 - u**4.
2*u**3*(u + 1)
Let s(p) be the first derivative of -p**4/12 + p**3/9 - 1. Factor s(w).
-w**2*(w - 1)/3
Suppose 3*p + 2 = 4*p. Let m(y) be the second derivative of 0 - 1/6*y**3 - 1/12*y**4 + 3*y + y**p. Let m(r) = 0. What is r?
-2, 1
Suppose -5*o - 19 = -t + 6, o + 4*t = 16. Let p be 1/2 + o/24. Factor 0 + p*c**3 + 0*c - 1/3*c**2.
c**2*(c - 1)/3
Factor 6*a**4 + 6*a**3 + 3*a - 18 - 51*a**3 + 27*a**2 + 27*a**2.
3*(a - 6)*(a - 1)**2*(2*a + 1)
Let b(z) = z**3 + 3*z**2 + 3*z + 2. Let k be b(-2). Let r be 3 + -1 + k/3. Factor f**2 + 0*f - 3*f + r + 5*f - 5*f**2.
-2*(f - 1)*(2*f + 1)
Factor 0*h**2 + 0 - 1/4*h**3 + 1/4*h.
-h*(h - 1)*(h + 1)/4
Let g be (-3 - 8)*2/(-2). Let q = g - 9. Determine b so that 1/3*b - 1/3*b**q + 0 = 0.
0, 1
Let u(x) be the third derivative of -x**6/30 + 2*x**5/15 - x**4/6 - 2*x**2. Let u(p) = 0. Calculate p.
0, 1
Let q(l) be the first derivative of 3/26*l**4 - 2/13*l + 2/39*l**3 + 5 - 3/13*l**2. Factor q(d).
2*(d - 1)*(d + 1)*(3*d + 1)/13
Factor 105*k - 107*k + 5*k**2 - k**3 - 2*k**2 + 0*k**2.
-k*(k - 2)*(k - 1)
Suppose 2*o = 5 + 7. Let c(i) be the first derivative of 0*i - 214/5*i**5 - 17*i**4 - 3 - 8*i**2 + 88/3*i**3 + 35*i**o. Suppose c(h) = 0. Calculate h.
-2/3, 0, 2/7, 2/5, 1
What is r in 3/7*r**4 + 0 + 3/7*r**3 - 6/7*r**2 + 0*r = 0?
-2, 0, 1
Let d = 0 - -2. Factor 0*w**4 - 4*w**2 + 3*w**d + 2*w**2 - w**4 + w - w**3.
-w*(w - 1)*(w + 1)**2
Let a(q) be the third derivative of q**7/630 - q**6/90 + q**5/60 + q**4/18 - 2*q**3/9 + 12*q**2. Factor a(f).
(f - 2)**2*(f - 1)*(f + 1)/3
Let p be 7/16*(-3 + 216/56). Factor -1/8*x**3 + 0 - 1/4*x - p*x**2.
-x*(x + 1)*(x + 2)/8
Let m be (-82)/615 + 1 + 32/15. Solve -105/2*v**m - 39*v**2 + 0 - 6*v + 147/4*v**4 = 0 for v.
-2/7, 0, 2
Let c = 17 - 11. Factor -c*i**2 - i**3 - 6*i**2 + 11*i**2.
-i**2*(i + 1)
Suppose 0 = -w - 2*o - 8 + 2, 4*w + 9 = -3*o. Suppose -n = -w*n. Find l, given that n*l + 2*l + l**2 - 3*l**2 = 0.
0, 1
Let k be (8/12)/(20/(-99)). Let z = k + 81/20. Factor 1/2 + 1/4*h**2 - z*h.
(h - 2)*(h - 1)/4
Let o(f) be the second derivative of 0 - 1/70*f**5 + 0*f**4 + 1/7*f**3 + 2*f + 2/7*f**2. Let o(t) = 0. Calculate t.
-1, 2
What is b in -11/3*b**3 + 4*b**2 + 0 - 4/3*b + b**4 = 0?
0, 2/3, 1, 2
Let g = 6/17 + 5/34. Let -o**3 + 3/4*o**5 - 1/2*o**4 + 0 + g*o**2 + 1/4*o = 0. What is o?
-1, -1/3, 0, 1
Let p(u) = -5*u**2 - 10*u - 9. Let s(z) = z**2 + z. Let a(d) = -p(d) - 4*s(d). Factor a(j).
(j + 3)**2
Let n(l) = 5*l**3 + 35*l**2 + 78*l + 58. Let o(b) = -85*b**3 - 595*b**2 - 1325*b - 985. Let i(v) = 35*n(v) + 2*o(v). What is c in i(c) = 0?
-3, -2
Let b(r) = r**3 - r**2 + 1. Let k(l) = 16*l**2 + 12*l. Let u(y) = -4*b(y) - k(y). Factor u(z).
-4*(z + 1)**3
Let g(n) be the first derivative of 8*n**3/21 + 3*n**2/7 - 2*n/7 + 4. Solve g(b) = 0.
-1, 1/4
Let a(u) = -u**3 + 6*u**3 + 3*u**2 + 4 + 1 - 5*u - 4*u**4 - 2. Let z(j) = -1. Let x(b) = -a(b) - 2*z(b). Find o, given that x(o) = 0.
-1, 1/4, 1
Let d(h) be the third derivative of 0*h**4 + 0*h**3 - 1/240*h**5 + 0 + 2*h**2 + 0*h. Factor d(i).
-i**2/4
Let c = 19 - 6. Let l = -9 + c. Determine d, given that 0 + 0*d + 2/7*d**l + 0*d**2 + 2/7*d**3 = 0.
-1, 0
Factor 8*c - 2*c**3 - 2*c**3 - 44*c - 24*c**2.
-4*c*(c + 3)**2
Factor -2/5*k**3 + 0*k + 2/5*k**4 + 0*k**2 + 0.
2*k**3*(k - 1)/5
Let i = 149/3 - 49. Let f(x) be the first derivative of -i*x**3 - 4*x**2 - 2 - 8*x. Factor f(m).
-2*(m + 2)**2
Let a be (-7)/(-35) + 51/45. Suppose 0 = 2*b + 3*b. Factor 5/3*i**2 - 1/3*i + b - a*i**3.
-i*(i - 1)*(4*i - 1)/3
Suppose 3*v + 9 = 3*o, -5*v + 4 = 3*o - 21. Suppose -a + o = 3*k + k, -5*a + 25 = 0. What is z in 2*z**3 + 8*z - 3*z**2 + k*z**3 - 5*z**2 = 0?
0, 2
Factor 18/7 + 2/7*i**2 - 12/7*i.
2*(i - 3)**2/7
Let h(y) be the second derivative of -y**7/112 + y**6/80 + 3*y**5/80 - y**4/16 - y**3/16 + 3*y**2/16 + 18*y. Factor h(w).
-3*(w - 1)**3*(w + 1)**2/8
Let x be -2 + (-4)/2 - -13. Let m(v) = 3*v**2 - v - 4. Let j(c) = -13*c**2 + 4*c + 17. Let i(a) = x*m(a) + 2*j(a). Factor i(q).
(q - 2)*(q + 1)
Factor 4/9 - 2/3*b + 2/9*b**3 + 0*b**2.
2*(b - 1)**2*(b + 2)/9
Let c(g) be the first derivative of 2*g**5/65 - g**4/13 + 2*g**3/39 - 12. Determine w, given that c(w) = 0.
0, 1
Let v(n) = -n**3 + 3*n + 1. Let l be v(-2). Let k = 16 + -12. Factor 0*t**2 + 0*t**l - 3*t**k + 2*t**3 + 0*t**2 + t**2.
-t**2*(t - 1)*(3*t + 1)
Let r(j) = -j**2 + j + 2. Let u(z) = z**2 - z - 2. Let s(n) = -3*r(n) - 4*u(n). Suppose s(c) = 0. What is c?
-1, 2
Let l = -3 + 5. Let t be 3/((-15)/l)*-5. Let -8/9 - 16/9*n - 10/9*n**t - 2/9*n**3 = 0. Calculate n.
-2, -1
Suppose 0 = 5*o + 5*p - 395, 4*p - p = -o + 81. Solve o - 5*y**2 - 78 + 2*y + 4*y**3 - y**4 = 0.
0, 1, 2
Let q = -3/122 - 1920/61. Let a = q - -32. Factor m**2 - a*m**4 + 1/2*m**5 - 1/2 - m**3 + 1/2*m.
(m - 1)**3*(m + 1)**2/2
Factor 30*n**2 - 4*n + n - 33*n**2.
-3*n*(n + 1)
Let l be (-12)/(-66) - 58/(-44). Determine i so that l*i**3 + 1/4*i**5 + i**2 + 1/4*i + i**4 + 0 = 0.
-1, 0
Let j(c) be the second derivative of c**7/147 - 4*c**6/105 + 3*c**5/35 - 2*c**4/21 + c**3/21 - 12*c - 3. Suppose j(g) = 0. What is g?
0, 1
Let b(d) = d**3 + d**2. Let z(c) = c**3 + 10*c**2 + 7*c - 2. Let g(j) = -24*b(j) + 3*z(j). Let g(p) = 0. What is p?
-1, 2/7, 1
Let n be 35 - 40 - 1*-5. Let n - 1/7*k + 1/7*k**3 + 0*k**2 = 0. What is k?
-1, 0, 1
Suppose -26*b - 3 + 3 = 0. Factor b - 1/3*v**3 - 2/3*v**2 - 1/3*v.
-v*(v + 1)**2/3
Let r = 18 + -16. Let t be (r/(-6))/((-7)/18). Determine p, given that -4/7 + 4/7*p**2 - t*p = 0.
-1/2, 2
Let s(v) be the third derivative of -v**2 + 1/12*v**4 + 0 + 1/15*v**5 + 0*v**3 + 0*v. Let s(q) = 0. What is q?
-1/2, 0
Let g be 2/9 + 325/117. Solve 6*r**2 - 2*r**3 - 6*r**4 - 2*r**5 + r**g + 2*r**3 + 4*r - 3*r**3 = 0 for r.
-2, -1, 0, 1
Suppose 33*h = 38*h - 25. Let g = 0 + h. What is r in 0 + 2/7*r**3 + 0*r**2 + 0*r + 0*r**4 - 2/7*r**g = 0?
-1, 0, 1
Let k(c) be the third derivative of -c**7/42 + c**6/36 + c**5/3 - 5*c**4/9 - c**2. Suppose k(m) = 0. What is m?
-2, 0, 2/3, 2
Let i(q) = -105*q**5 + 350*q**4 - 85*q**3 + 20*q - 20. Let c(r) = 15*r**5 - 50*r**4 + 12*r**3 - 3*r + 3. Let k(o) = -20*c(o) - 3*i(o). Factor k(w).
5*w**3*(w - 3)*(3*w - 1)
Let d = 239/3 + -79. Let x(t) be the third derivative of 2*t**2 - 1/4*t**4 + 0 + 0*t - 1/30*t**5 - d*t**3. Find c such that x(c) = 0.
-2, -1
Suppose 0*f = 4*f. Factor -3*g + 3*g**3 - g**2 + g**2 + f*g**2.
3*g*(g - 1)*(g + 1)
Let b be (-4)/(-4)*6 + -2 + -1. Factor 0*y**2 + y - y**b + 1/2*y**4 - 1/2.
(y - 1)**3*(y + 1)/2
Let n(p) be the first derivative of p**3/12 + p**2/8 - 3*p/2 - 13. Factor n(a).
(a - 2)*(a + 3)/4
Let c(m) = -m**2 - 13*m - 9. Let n be c(-12). Suppose -3*x + 14 = a, -n*x + 14 = -a + x. Factor 2/3 + 2/3*g**a + 4/3*g.
2*(g + 1)**2/3
Let u(n) be the first derivative of -3/7*n**2 + 4/7*n - 4/21*n**3 - 6 + 3/14*n**4. Factor u(j).
2*(j - 1)*(j + 1)*(3*j - 2)/7
Let c(v) be the second derivative of -3/4*v**2 + 9/8*v**4 + 1/5*v**6 + 33/40*v**5 + 2*v + 1/4*v**3 + 0. Determine y, given that c(y) = 0.
-1, 1/4
Determine s so that 0*s - 5/6*s**4 - 1/2*s**3 + 0 + 1/3*s**2 = 0.
-1, 0, 2/5
Let x(j) be the second derivative of 2*j**6/135 + 7*j**5/90 + 2*j**4/27 - 4*j**3/27 - 5*j. Solve x(t) = 0 for t.
-2, 0, 1/2
Let g(y) = -y**2 - y + 1. Let m(s) = 8*s**2 - 36*s + 96. Let t(i) = -4*g(i) - m(i). Solve t(k) = 0.
5
Let z be 4/(-10) + (-6)/(-10)*2. Factor -z*f - 2/5*f**2 - 2/5.
-2*(f + 1)**2/5
Let p be 6/27 - (-8)/(-36). Factor 0*g**2 + p*g - 3/4*g**3 + 0.
-3*g**3/4
Suppose -34 = -3*h + 14. Find k such that -16*k**4 + 12*k**3 + 0 + 4*k**5 - h*k + 0 + 16*k**2 = 0.
-1, 0, 1, 2
Let m(h) = h**2 + h + 3. Let a be m(0). Factor -4*t**2 + 5*t**a + 2 + 2*t**2 + 0 - 5*t - 7*t**2 + 7*t**4.
(t - 1)*(t + 1)**2*(7*t - 2)
Let c(j) = j**2 + j + 21. Let m be c(0). Let t = m + -18. Let 1/3*g**2 - 1/3*g**5 - 1/3*g**4 + 1/3*g**t + 0 + 0*g = 0. Calculate g.
-1, 0, 1
Let g(u) = u - 6. Let k(h) = -h**3 - 13*h**2 - 12*h + 8. Let n be k(-12). Let c be g(n). Let 0*y - 2/7*y**c - 2/7*y**3 + 0 = 0. What is y?
-1, 0
Find d s