**g + 1/10*b - 1/10*b**3 + 0.
-b*(b - 1)*(b + 1)**2/10
Let z(t) = -t + 11. Let h(x) = x - 12. Let f(p) = -3*h(p) - 2*z(p). Let q be f(11). Factor 0 + 0*c - 1/4*c**q - 1/4*c**4 + 1/4*c**2 + 1/4*c**5.
c**2*(c - 1)**2*(c + 1)/4
Find j such that 160 + 166*j + 121*j - 5*j**5 + 80*j**2 - 30*j**4 - 40*j**3 - 47*j = 0.
-2, 2
Let w(p) = p**3 + 2*p**2 - 2*p - 2. Let x be w(-2). Let -8*a - 6*a**2 + 10*a**2 - 3*a**2 + 3*a**x = 0. What is a?
0, 2
Let d(g) be the third derivative of 0*g**3 + 1/60*g**4 + 1/1050*g**7 + 0*g - 1/300*g**6 - 14*g**2 + 0 - 1/300*g**5. Factor d(n).
n*(n - 2)*(n - 1)*(n + 1)/5
Let c(p) be the second derivative of p**4/4 + p**3/2 - 9*p**2 - 102*p. Determine a so that c(a) = 0.
-3, 2
Let p be (-3 - 9) + (185/(-15))/(-1). Determine g, given that -p*g**5 - 6*g - 3*g**4 - 29/3*g**3 - 13*g**2 + 0 = 0.
-3, -2, -1, 0
Let c(z) be the second derivative of -z**4/48 - 11*z**3/3 - 87*z**2/8 - 49*z - 1. Factor c(q).
-(q + 1)*(q + 87)/4
Let k(x) be the third derivative of 0*x**3 - 8*x**2 - 13/6*x**4 - 1/15*x**5 + 0 + 0*x. Factor k(b).
-4*b*(b + 13)
Let k(s) be the second derivative of -s**5/4 - 5*s**4/6 + 10*s**3/3 + 20*s**2 + 52*s - 2. Suppose k(f) = 0. What is f?
-2, 2
Let j be 39/(-26) + 9/2. Suppose j*b = -7*b. Let 1/3*v**2 + b - 8/3*v**3 + 5/3*v**4 + 2/3*v = 0. What is v?
-2/5, 0, 1
Let s(x) be the third derivative of 1/8*x**4 + 0*x - 1/10*x**5 + 0 + 1/70*x**7 - 1/20*x**6 + 1/2*x**3 - 25*x**2 + 1/112*x**8. Factor s(n).
3*(n - 1)**2*(n + 1)**3
Let p = 1776 - 1773. Let v(x) be the first derivative of -2 - 8/7*x + 2/21*x**p + 3/7*x**2. Let v(n) = 0. What is n?
-4, 1
Let a be (-7 - -17)/(-5) - 2/(-1). Let y(t) be the third derivative of -3*t**2 - 1/15*t**3 - 1/40*t**4 + 0*t - 1/300*t**5 + a. Find k, given that y(k) = 0.
-2, -1
Let v(y) = -y**2 + 61*y - 27. Let l(q) = q - 3. Let a(d) = -36*l(d) + 4*v(d). Factor a(g).
-4*g*(g - 52)
Let z(u) = 5*u**3 + 348*u**2 + 6460*u - 14440. Let p(r) = -r**3 - 70*r**2 - 1292*r + 2888. Let i(g) = -11*p(g) - 2*z(g). Let i(a) = 0. What is a?
-38, 2
Factor 6*u**2 - u**2 + 232*u - 3364 - 9*u**2.
-4*(u - 29)**2
Suppose 27 = 3*z + 15. Suppose -5*v + 3*h = -8 - z, -16 = -5*v + 4*h. Factor 0*a**2 + a**3 + 0 + v*a + 1/2*a**4.
a**3*(a + 2)/2
Let c(i) be the second derivative of i**5/45 - 5*i**4/54 - i**3/9 + 40*i. Factor c(q).
2*q*(q - 3)*(2*q + 1)/9
Let w = -16 - -21. Suppose w = 4*p - 7. What is n in 6 - 2*n + 11*n - 18 + p*n**2 = 0?
-4, 1
Let v(q) = -q**5 - 2*q**4 + 8*q**3 + 2*q**2 + 13*q - 4. Let p(t) = -t**5 - 2*t**4 + 9*t**3 + t**2 + 14*t - 5. Let s(y) = 6*p(y) - 7*v(y). Factor s(o).
(o - 2)*(o + 1)**4
Let c = -2/779 - -3130/5453. Suppose 0 + 6/7*u**2 + 2/7*u**3 + c*u = 0. Calculate u.
-2, -1, 0
Let a(n) = n**3 + 6*n**2 + 8*n + 2. Let l be a(-4). What is t in l + 2/9*t**3 + 10/3*t + 14/9*t**2 = 0?
-3, -1
Let l be (-9)/21 - (1776/126)/(-8). Factor -1/3*b - 4/3*b**2 - 2*b**3 - 1/3*b**5 + 0 - l*b**4.
-b*(b + 1)**4/3
Suppose -3*d + 74 = -46. Suppose 0 = -5*x + 3*x + d. What is z in -z**2 + 5*z**2 + 12 + x*z - z**2 - 8*z = 0?
-2
Let y(k) be the third derivative of -k**7/70 + 29*k**6/40 - 27*k**5/20 - 29*k**4/8 + 14*k**3 + 215*k**2. Find m such that y(m) = 0.
-1, 1, 28
Let g(r) = 11*r**5 - 9*r**4 - 4*r**3 - 9*r**2 + 2*r. Let k(m) = 5*m**5 - 4*m**4 - 2*m**3 - 4*m**2 + m. Let d(f) = -4*g(f) + 9*k(f). Factor d(v).
v*(v - 1)**2*(v + 1)**2
Let l = 111 + -219/2. Let j(b) be the first derivative of -4 - l*b**4 - 6/5*b**5 + 0*b**2 - 2/3*b**3 + 0*b - 1/3*b**6. Suppose j(m) = 0. What is m?
-1, 0
Let g(s) be the third derivative of s**7/504 - s**6/240 - s**5/60 - 11*s**4/24 + 26*s**2. Let h(r) be the second derivative of g(r). Factor h(t).
(t - 1)*(5*t + 2)
Let k(o) be the second derivative of -o**5/150 - o**4/45 + 7*o**3/45 - 4*o**2/15 - 40*o. Determine z so that k(z) = 0.
-4, 1
Let u(g) be the first derivative of -11*g**4/4 + 62*g**3/3 - 75*g**2/2 - 36*g + 391. Factor u(x).
-(x - 3)**2*(11*x + 4)
Let b(r) be the second derivative of r + 0 + 3/8*r**3 + 3/80*r**5 + 0*r**2 + 1/4*r**4. Suppose b(u) = 0. What is u?
-3, -1, 0
Suppose -20*t**4 + 133*t**2 + 5*t**5 - 133*t**2 + 15*t**3 = 0. Calculate t.
0, 1, 3
Let j(b) be the first derivative of b**6/5 - b**5/5 - b**4/2 + 2*b**3/3 - b + 18. Let p(v) be the first derivative of j(v). What is q in p(q) = 0?
-1, 0, 2/3, 1
Let h be (1 + (-108)/8)*(-36)/(-15). Let f = -28 - h. Factor -1/4*o**3 + 0*o - 1/4*o**f + 0.
-o**2*(o + 1)/4
Factor 5*j**3 + 82*j + 90*j**2 + 145*j + 313*j + 1080.
5*(j + 6)**3
Factor 0*i - 1/11*i**3 + 2/11*i**2 + 0.
-i**2*(i - 2)/11
Let m(k) = 7*k**2 - 46*k + 676. Let z(f) = -f**2 - f. Let c(s) = -m(s) - 6*z(s). Factor c(p).
-(p - 26)**2
Suppose 1 = -c - 0*c, -2*i = 2*c - 6. Factor -4 - 2*z + 92*z**2 - 91*z**2 + i.
z*(z - 2)
Suppose 3*w - 21 = -2*k, 4*k + 2*w = 2*k + 18. Factor -3*g**3 + 6*g**3 + k*g**2 + 0*g**3.
3*g**2*(g + 2)
Determine x so that -65/6 + 4/3*x + 1/6*x**2 = 0.
-13, 5
Let m(t) be the first derivative of -t**5/5 - 7*t**4/4 - 6*t**3 - 12*t**2 - 4*t + 42. Let l(a) = -a + 1. Let w(c) = 12*l(c) - 3*m(c). Factor w(x).
3*(x + 1)*(x + 2)**3
Suppose -7 = -5*n + j - 10, 5*n + j = 3. Solve 1/12*f**3 - 1/6*f + n - 1/12*f**2 = 0.
-1, 0, 2
Let v(n) be the second derivative of -3*n**5/20 + 18*n**4 - 141*n**3/2 + 105*n**2 - 8*n + 35. Determine y so that v(y) = 0.
1, 70
Let t(m) be the first derivative of 2*m**6/105 + m**5/14 + m**4/14 - m**3/21 - m**2/7 - m - 5. Let o(q) be the first derivative of t(q). Solve o(g) = 0 for g.
-1, 1/2
Let j(q) be the third derivative of q**6/480 + 19*q**5/240 + 25*q**4/48 + 4*q**3/3 + 2*q**2 + 116*q. Let j(t) = 0. Calculate t.
-16, -2, -1
Let u(n) = n - 3. Suppose 4*f - 4*y = -7*y + 13, -f = 4*y. Let t be u(f). Factor t - w + w**3 - w - 3 - w.
(w - 2)*(w + 1)**2
Suppose -42*p + 300 = 18*p. Solve -8/11*q**2 + 6/11*q**3 + 4/11*q**4 + 0 - 8/11*q - 2/11*q**p = 0.
-1, 0, 2
Let q = -6 + 15. Suppose q*x + 4*x = 39. Determine b, given that -1/3*b**2 - 1/3*b**4 + 0 + 2/3*b**x + 0*b = 0.
0, 1
Let o(l) = -l**2 - 36*l + 3. Let n be o(-36). Let z(r) be the second derivative of 0*r**n + 2*r + 0*r**2 + 1/110*r**5 + 0 - 1/66*r**4. Let z(y) = 0. What is y?
0, 1
Suppose -4*f - 16*t + 15*t + 13 = 0, 2*f + 6 = 2*t. Let m(l) be the second derivative of -9*l + 1/7*l**3 + 1/42*l**4 + 0*l**f + 0. Solve m(q) = 0 for q.
-3, 0
Let m(f) be the third derivative of -1/27*f**3 + 0 - 2/135*f**5 - 9*f**2 + 0*f - 5/108*f**4. Factor m(r).
-2*(r + 1)*(4*r + 1)/9
Let q(v) be the first derivative of 0*v**3 - 1/3*v**4 + 13 + 0*v + 14/15*v**5 - 5/9*v**6 + 0*v**2. Factor q(s).
-2*s**3*(s - 1)*(5*s - 2)/3
Let o(d) = -12*d - 5. Let l be o(-3). Determine k so that -k**2 - l - 54 - 15 + 20*k = 0.
10
Let a(b) be the second derivative of -b**6/180 - b**5/20 + b**4/3 - 2*b**3 + 12*b. Let x(y) be the second derivative of a(y). Factor x(r).
-2*(r - 1)*(r + 4)
Let i(k) = -k**2 - k - 1 - k + k + 2*k. Let u(s) = 3*s**2 - 15*s - 3. Let p(w) = 5*i(w) + u(w). Suppose p(o) = 0. Calculate o.
-4, -1
Let q(d) be the second derivative of d**7/28 + d**6/40 - 3*d**5/10 - d**4/4 + 3*d - 17. Solve q(h) = 0 for h.
-2, -1/2, 0, 2
Suppose -a - 2*s - 12 = 0, -a + 24 = 3*a - 4*s. What is j in -21/2*j**2 + a - 15/2*j**5 + 21/2*j**4 + 3*j + 9/2*j**3 = 0?
-1, 0, 2/5, 1
Let b(y) be the second derivative of 5*y**9/3024 + y**8/42 + y**7/24 - y**3/2 - 9*y. Let a(w) be the second derivative of b(w). Factor a(t).
5*t**3*(t + 1)*(t + 7)
Suppose -140*z = 2*z - 284. Determine k, given that -50/7 - 72/7*k**z + 120/7*k = 0.
5/6
Let o(t) be the second derivative of 11/100*t**5 - 7/60*t**4 - 2/105*t**7 - 7/30*t**3 + 1/5*t**2 + 9*t + 0 + 1/30*t**6. Determine d so that o(d) = 0.
-1, 1/4, 1, 2
Let z(a) = -2*a**3 + a**2 + a. Let g(h) = 8*h**3 + 165*h**2 - 3701*h + 3528. Let w(d) = g(d) + 5*z(d). Factor w(t).
-2*(t - 42)**2*(t - 1)
Let u(b) = 13*b**2 - 5*b + 2. Let o be u(1). Let a be (o + -9)*((-2)/(-1))/12. Determine y so that -1/6*y**2 - a*y + 1/3 = 0.
-2, 1
Suppose -j = 3*y + 126, 2*y = -3*j - j - 514. Let f = j - -131. Suppose 1/4*l**5 + 1/4*l**3 + 0*l - 1/2*l**4 + 0*l**f + 0 = 0. Calculate l.
0, 1
Let q(v) be the first derivative of v**6/36 - 2*v**5/3 + 151*v**4/24 - 266*v**3/9 + 212*v**2/3 - 224*v/3 + 607. Solve q(b) = 0.
1, 4, 7
Let q(s) be the third derivative of -1/22*s**6 + 3*s**2 + 3/385*s**7 + 14/165*s**5 + 0 - 2/3