6, -1, 0, 1
Let b(p) = -p**2 + 3*p + 8. Let g(h) = h + 1. Let u(f) = b(f) - 2*g(f). Solve u(n) = 0.
-2, 3
Let n(r) be the second derivative of 0*r**3 + 0*r**2 - 1/24*r**4 + 1/168*r**7 - 1/30*r**6 - 2*r + 0 + 1/16*r**5. Solve n(x) = 0 for x.
0, 1, 2
Suppose 81*a = 111 + 213. Factor 1/3*v**a + 0 - v**3 + 4/3*v + 0*v**2.
v*(v - 2)**2*(v + 1)/3
Determine b, given that -3*b**4 - 33/2*b + 0*b**2 - 45/2*b**5 + 3 + 39*b**3 = 0.
-1, 1/5, 2/3, 1
Let u(v) be the second derivative of 0 + 39*v + 0*v**2 + 1/63*v**3 - 1/63*v**4 + 1/210*v**5. Solve u(n) = 0 for n.
0, 1
Let l(d) be the second derivative of d**5/60 - 43*d**3/18 - 7*d**2 - 213*d. Suppose l(z) = 0. What is z?
-6, -1, 7
Let g(n) = -n**3 - n**2 + n. Let p(j) = -39*j - 1 - j + 20*j**3 - 2 - 5*j**2 - 7. Let d be (-1)/3 + 56/(-12). Let a(l) = d*g(l) - p(l). Factor a(m).
-5*(m - 2)*(m + 1)*(3*m + 1)
Let w(a) be the second derivative of a**7/840 - a**6/30 + 2*a**5/5 + a**4/2 - 27*a. Let d(x) be the third derivative of w(x). Determine j, given that d(j) = 0.
4
Let p = -1 - -6. Let g = -835 + 837. Factor 2/5*r**3 - 1/5*r - 1/5*r**p + 2/5*r**g - 1/5*r**4 - 1/5.
-(r - 1)**2*(r + 1)**3/5
Let j be (-42)/(-1 - 5/(-20)). Let n be ((-760)/(-308) - 2) + (-16)/j. Determine d, given that -n*d**5 + 4/11*d**2 + 0*d**4 + 0*d + 6/11*d**3 + 0 = 0.
-1, 0, 2
Let q(z) = -2*z**2 - 32*z + 4. Let u be q(-16). Solve 37*s**u - 12*s**2 + 12*s + 45*s**5 - 14*s**4 + 25*s**4 - 93*s**3 = 0.
-2, -2/5, 0, 1/3, 1
Solve -88/3*s**2 - 170/3*s - 28 - 2/3*s**3 = 0 for s.
-42, -1
Factor 4/5*y**5 - 7776/5*y + 11664/5 + 556/5*y**3 - 108*y**2 + 92/5*y**4.
4*(y - 2)**2*(y + 9)**3/5
Let x(l) = -190*l**2 - 80*l + 215. Let t = 5 - 3. Let q(k) = -7*k**2 - 3*k + 8. Let m(j) = t*x(j) - 55*q(j). Suppose m(n) = 0. Calculate n.
-2, 1
Let a = 175 + -169. Let y(p) be the second derivative of 3/2*p**5 - 3/10*p**a - 4*p + 0 - 2*p**2 + 10/3*p**3 - 37/12*p**4. Factor y(r).
-(r - 1)**2*(3*r - 2)**2
Let w(b) be the third derivative of 3/70*b**5 - 4/21*b**4 - 6*b + 0 + 4*b**2 - 1/392*b**8 - 1/147*b**7 + 4/21*b**3 + 11/420*b**6. Solve w(t) = 0 for t.
-2, 1/3, 1
Let l = -1906 - -1918. Factor 3/2*n**4 + 15/2*n**3 + 6*n + 0 + l*n**2.
3*n*(n + 1)*(n + 2)**2/2
Factor 1 + 1/2*j**2 + 3/2*j.
(j + 1)*(j + 2)/2
Let j(k) be the third derivative of 0*k + 0*k**4 - 9/40*k**5 + 1/40*k**6 - 1/1260*k**7 + 0*k**3 - 36*k**2 + 0. Solve j(q) = 0 for q.
0, 9
Let b(x) = -49*x + 306. Let h be b(6). Let g(t) be the third derivative of 0*t**3 + h*t**2 - 1/360*t**6 - 1/72*t**4 + 0*t - 1/90*t**5 + 0. Factor g(c).
-c*(c + 1)**2/3
Let 7/4*o - 1/8*o**4 + 5/8 + 1/4*o**3 + 3/2*o**2 = 0. What is o?
-1, 5
Let d = 43 + -39. Determine z so that 8*z**2 + 8*z**3 - 4*z**5 - 6*z**3 - d*z**2 - 14*z**3 + 12*z**4 = 0.
0, 1
Let f(d) = 387*d - 387. Let m be f(1). Factor m + 1/3*t**2 + 2*t.
t*(t + 6)/3
Let k(b) be the first derivative of -3*b**4/16 - 11*b**3/4 - 21*b**2/8 + 441*b/4 + 148. Factor k(i).
-3*(i - 3)*(i + 7)**2/4
Suppose 8*y - 4*t - 20 = 3*y, -2*y = 2*t - 8. Let a(n) = 3*n**3 + n**2 - n + 1. Let g be a(1). Solve -5 - 6*w**3 + 3*w + 3*w**y - g*w + 2 + 7*w = 0 for w.
-1, 1
Let w(u) = -u**2 - 6*u - 6. Let p be w(-4). Find o such that -3*o**p + 5*o**2 + 10*o**3 - 9*o**3 = 0.
-2, 0
Let w(a) be the third derivative of 1/54*a**4 + 0*a - 20*a**2 - 1/270*a**5 + 1/9*a**3 + 0. Factor w(h).
-2*(h - 3)*(h + 1)/9
Let q(c) be the second derivative of 8*c**2 - 8/3*c**3 - 2*c + 1/3*c**4 - 4. Factor q(x).
4*(x - 2)**2
Factor 68 - 105*z + 34*z**2 + 40 - 22*z**2 - 15*z**2.
-3*(z - 1)*(z + 36)
Let a(t) be the first derivative of 3*t**6/11 + 102*t**5/55 + 32*t**4/11 - 112*t**3/33 - 80*t**2/11 + 96*t/11 + 138. Suppose a(w) = 0. Calculate w.
-3, -2, 2/3
Let g(x) be the second derivative of x**4/6 + x**3/2 + x. Let u be g(-2). Factor -6*z**4 + 6*z**u - 4*z**5 - 3*z**3 - 2*z**2 + 3*z**5 + 4*z + 2*z**4.
-z*(z - 1)*(z + 1)*(z + 2)**2
Let q = 1559 + -3117/2. Let u(y) be the first derivative of -1/3*y**6 + 4/5*y**5 - q*y**4 + 0*y**2 - 7 + 0*y + 0*y**3. Factor u(g).
-2*g**3*(g - 1)**2
Factor -18 - 24*s - 3/8*s**3 - 51/8*s**2.
-3*(s + 1)*(s + 4)*(s + 12)/8
Let t(s) be the second derivative of s**4/4 + 14*s**3 + 81*s**2/2 + 3*s - 7. Find p, given that t(p) = 0.
-27, -1
Let h(i) be the first derivative of 52*i**3/3 - 22*i**2 - 8*i + 216. Factor h(y).
4*(y - 1)*(13*y + 2)
Let v = 261/436 + -38/109. Factor -3/4*a + v*a**2 + 1/2.
(a - 2)*(a - 1)/4
Let 2112*r + 4624 + 1551*r - 8*r**3 + 12*r**3 + 825*r - 135*r**2 - 3*r**3 = 0. What is r?
-1, 68
Suppose a - 9*a + 16 = 0. Factor 5*z**2 + 3*z**3 - 6*z - 2*z**2 - 3*z**a + 3*z**2.
3*z*(z - 1)*(z + 2)
Let v(n) be the first derivative of n**5/390 + 3*n**4/52 + 8*n**3/39 + 19*n**2/2 + 20. Let u(w) be the second derivative of v(w). Factor u(y).
2*(y + 1)*(y + 8)/13
Let p(d) be the first derivative of 4*d**3/3 - 11*d**2 + 24*d - 71. Find k, given that p(k) = 0.
3/2, 4
Let x(q) = -5*q**5 + 7*q**4 - 11*q**3 - 9*q**2 + 3*q - 5. Let k(i) = i**4 + i**3 + i**2 + 1. Let m(y) = 20*k(y) + 4*x(y). Suppose m(u) = 0. What is u?
-3/5, 0, 1
Let d(n) be the third derivative of n**5/390 + n**4/13 + 20*n**3/39 + 24*n**2. Determine a, given that d(a) = 0.
-10, -2
Factor 4/5*y**4 - 12/5 + 44/5*y + 24/5*y**3 - 56/5*y**2 - 4/5*y**5.
-4*(y - 1)**4*(y + 3)/5
Let q(m) be the third derivative of m**5/60 - m**4/12 - 4*m**3/3 - 5*m**2 + 1. Factor q(f).
(f - 4)*(f + 2)
Determine d, given that -4/7*d**2 - 144/7 - 48/7*d = 0.
-6
Let q(k) be the third derivative of k**6/480 - 31*k**4/96 + 5*k**3/4 + k**2 + 1. What is d in q(d) = 0?
-6, 1, 5
Let v be 33/(-110) + (-1590)/(-300). Let u = -1659 + 21609/13. Factor 10/13*m**v + 34/13*m**4 + 22/13*m**2 + 4/13*m + u*m**3 + 0.
2*m*(m + 1)**3*(5*m + 2)/13
Let x(y) be the first derivative of -35*y**4/4 - 55*y**3 - 80*y**2 + 60*y + 152. Factor x(g).
-5*(g + 2)*(g + 3)*(7*g - 2)
Let t(x) be the third derivative of -5*x**8/672 - x**7/84 + x**6/48 + x**5/24 + x**2 + 62. Let t(v) = 0. What is v?
-1, 0, 1
Let l = 308008 + -195584948/635. Let d = l + -1/127. Determine p so that -1/5*p**3 - 3/5*p**2 + d*p**4 + 2/5 + 1/5*p = 0.
-1, 1, 2
Factor -514*a + 6*a**3 + 3*a**2 - 228*a**2 + 625*a.
3*a*(a - 37)*(2*a - 1)
Let b(x) = -6*x + 9*x - 7*x + 2. Let n be b(1). Let p(t) = -2*t**3 - 2*t**2 - t - 1. Let o(k) = -k**3 + k**2 + k - 1. Let c(q) = n*p(q) + 2*o(q). Factor c(f).
2*f*(f + 1)*(f + 2)
Let o(k) = -6*k**4 + 10*k**3 - 2*k**2. Let s(r) = -r**5 + 14*r**4 - 20*r**3 + 2*r**2. Let q(j) = -5*o(j) - 2*s(j). Factor q(p).
2*p**2*(p - 1)**2*(p + 3)
Let l(m) = -m**4 - m**3 - m**2 + m. Suppose 6 = -13*x + 16*x. Let y(p) = -p**5 + 2*p**4 + 2*p**3 - p. Let r(i) = x*y(i) + 2*l(i). Solve r(t) = 0.
-1, 0, 1
Let f(t) be the second derivative of -t**5/170 - t**4/51 + 8*t**3/51 + 45*t. Factor f(d).
-2*d*(d - 2)*(d + 4)/17
Let t be 75/42 - 2/7. Suppose 26*c - 10*c = -25*c. Factor c + 3/2*q - t*q**2.
-3*q*(q - 1)/2
Factor -1/2*n**4 + 0 + 2*n**2 + 0*n + 3/2*n**3.
-n**2*(n - 4)*(n + 1)/2
Let l(f) = -f**4 + f**3. Let r(s) = -8 - 13*s**2 - 17*s**3 - 7*s**4 + 40*s**3 - 23*s**2 + 28*s. Let d(j) = 3*l(j) - r(j). Let d(u) = 0. Calculate u.
1, 2
Suppose -3*c = c. Suppose c*z - 28 = -4*z. What is q in -2 + 3*q**2 + z + q**2 + 16*q + 7 = 0?
-3, -1
Let b = 100 - 64. Suppose 4*r + 2*x - b = 0, -5*r + 2*x + x + 23 = 0. Factor 4*z**2 - 4*z**4 + r*z**3 + 9*z**4 - 15*z**3 - z**4.
4*z**2*(z - 1)**2
Let i(d) = -2*d**2 + 7*d + 114. Let g be i(-6). What is p in 0 + 4/11*p**2 + g*p + 2/11*p**3 = 0?
-2, 0
Suppose c = -3*w + 15, 4*w = -5*c - 0*w + 75. Suppose 5*o = -a + c, -4*o - 6*a = -a - 33. What is h in 0*h + 0 + 1/3*h**5 - 1/3*h**3 + 2/3*h**o - 2/3*h**4 = 0?
-1, 0, 1, 2
Let q(y) be the third derivative of y**7/70 - y**6/8 + 2*y**5/5 - y**4/2 - 4*y**2 - 4. Factor q(n).
3*n*(n - 2)**2*(n - 1)
Let j be (-3)/20*(-12)/3. Solve 0*d**2 + j*d**4 + 0 + 0*d + 3/5*d**3 = 0.
-1, 0
Factor 25*n**3 + 7*n**3 - 24*n**4 + 24*n**2 - 156*n + 120*n + 4*n**5.
4*n*(n - 3)**2*(n - 1)*(n + 1)
Let l(x) = x**3 - x**2 + 1. Let n(a) = -4*a**3 - 24*a**2 - 36*a. Let u(w) = -16*l(w) - n(w). Determine k, given that u(k) = 0.
-1, 1/3, 4
Let n = 9159 + -100739/11. Factor -14/11*y + 4/11*y**2 + n.
2*(y - 1)*(2*y - 5)/11
Let f = 141667/6 + -23611. Determine h so that -1/2*h - 2/3 + f*h**2 = 0.
-1, 4
Let a(c) be the second derivative of -2*c**5/85 - 15*c**4/34 - 11*c**3/