
Let n(m) = 5*m - 17. Let c be n(4). Factor 58*i**3 - 19*i**3 - 9*i**c - 25*i - 20*i**2 - 15*i**3 + 10.
5*(i - 2)*(i + 1)*(3*i - 1)
Let k(l) = l**3 + 14*l**2 + 29*l + 212. Let w be k(-13). Solve 4/5*a**w + 0*a**2 - 2/5*a**3 + 0 + 0*a - 2/5*a**5 = 0 for a.
0, 1
Let b be 12*(-22)/(-165)*(-25)/(-10). Factor 0 + 2/11*c**5 + 0*c**b + 0*c**2 - 2/11*c**3 + 0*c.
2*c**3*(c - 1)*(c + 1)/11
Let t(h) = 5*h**2 - 40*h + 295. Let l(n) = -n**2 + 6*n - 42. Let c(m) = 20*l(m) + 3*t(m). Suppose c(w) = 0. Calculate w.
-3, 3
Let s(w) be the third derivative of 1/21*w**4 - 255/392*w**8 + 26*w**2 + 0*w**3 + 0 + 2/5*w**7 + 0*w + 19/84*w**6 - 8/35*w**5. Suppose s(m) = 0. Calculate m.
-2/5, 0, 2/17, 1/3
Let p(q) be the first derivative of q**8/2940 - q**6/315 + q**4/42 + 8*q**3 + 25. Let j(r) be the third derivative of p(r). Let j(f) = 0. Calculate f.
-1, 1
Suppose 5*n - 4 = 4*n. Factor -n - 3 + 3 - p**2 - 4*p + 0*p.
-(p + 2)**2
Let i(x) be the second derivative of -x**7/14 - 61*x**6/10 - 1527*x**5/10 - 1349*x**4/2 - 2581*x**3/2 - 2523*x**2/2 - 2*x + 56. Factor i(w).
-3*(w + 1)**3*(w + 29)**2
Find w such that 2/9*w**2 - 8/9 - 2/3*w = 0.
-1, 4
Let z(y) be the second derivative of -y**6/120 - y**5/10 + 5*y**4/8 - y**3/6 - 15*y. Let k(a) be the second derivative of z(a). Factor k(i).
-3*(i - 1)*(i + 5)
Let -2/11*i**3 + 0 + 4*i + 42/11*i**2 = 0. Calculate i.
-1, 0, 22
Let v be (-15)/20 - 15/(-4). Factor 4*b**5 - 6*b**2 - 7*b**5 + 9 + 18*b**v - 3*b**4 - 15*b + 0*b**4.
-3*(b - 1)**3*(b + 1)*(b + 3)
Let l(k) = k**3 - 2*k**2 + k + 3. Let v(t) = -4*t**3 - 137*t**2 - 674*t - 942. Let p(r) = l(r) - v(r). Factor p(f).
5*(f + 3)**2*(f + 21)
Factor 4*c - 327 + 655 - 2*c**2 - 322.
-2*(c - 3)*(c + 1)
Let r(d) = -36*d**3 + 52*d**2 - 16*d. Let a(c) = 4*c + 1. Let j be a(-2). Let k(u) = -24*u**3 + 35*u**2 - 11*u. Let o(x) = j*k(x) + 5*r(x). Factor o(f).
-3*f*(f - 1)*(4*f - 1)
Let f(v) = v + 1. Let p(g) = g**2 + 26*g + 4. Let c(t) = -4*f(t) + p(t). Find a, given that c(a) = 0.
-22, 0
Let p(c) = -c - 7. Let j(z) = -2*z - 8. Let l(x) = -4*j(x) + 5*p(x). Let v be l(2). Factor 2/7*w**v + 0*w + 0 + 4/7*w**4 + 0*w**2 + 2/7*w**5.
2*w**3*(w + 1)**2/7
Suppose -33*l + 18*l = -75. Let b(u) be the first derivative of 1/5*u**5 + 0*u - 1/4*u**4 + 0*u**2 + 0*u**3 - l. Factor b(v).
v**3*(v - 1)
Let i(h) be the third derivative of -5*h**8/1008 + h**7/42 + 11*h**6/36 + 19*h**5/18 + 15*h**4/8 + 35*h**3/18 - 80*h**2. Let i(g) = 0. Calculate g.
-1, 7
Let x(c) = c**3 - 3*c**2 - 5*c + 6. Let q be x(4). Suppose -5 - 1 = -q*l. Find t, given that -2*t + 0*t**3 - 2*t**l + 4*t = 0.
-1, 0, 1
Let v(b) = 9*b + 20. Let z be v(-5). Let o be 10/z - (-3 - (-34)/15). Find g such that -g**3 + 0 - 2/3*g + 1/3*g**5 - o*g**4 + 5/3*g**2 = 0.
-2, 0, 1
Let q(a) = -a**3 + 62*a**2 - 160*a + 168. Let m(t) = -2*t**3 + 59*t**2 - 160*t + 166. Let k(u) = 4*m(u) - 3*q(u). Determine j, given that k(j) = 0.
2, 4
Let b be 550/372 - (3 - (-10)/(-5)). Let c = b - -2/93. Factor 3/2*n - 1/2 - 3/2*n**2 + c*n**3.
(n - 1)**3/2
Let r(y) be the third derivative of 0*y - 10*y**2 + 0 + 1/8*y**4 + 1/6*y**3 + 1/20*y**5 + 1/120*y**6. Factor r(f).
(f + 1)**3
Let g(y) be the first derivative of 1/24*y**3 + 1 + 1/32*y**4 + 0*y - 1/16*y**2 - 1/40*y**5. Factor g(t).
-t*(t - 1)**2*(t + 1)/8
Let l(i) = i**2 + i**2 + 2 + 10*i - i**2 + 0*i**2. Let f be l(-10). Factor -2/9*n + 0 + 2/9*n**3 - 2/9*n**4 + 2/9*n**f.
-2*n*(n - 1)**2*(n + 1)/9
Let h(o) be the second derivative of 1/3*o**3 + 5/9*o**4 - 1/9*o**7 + 0*o**2 - 2*o + 2/15*o**5 - 2/9*o**6 + 1. Suppose h(c) = 0. What is c?
-1, -3/7, 0, 1
Let y(i) = -2*i**2 + 3*i**2 - 5*i**2 + 3*i**2 - 5*i - 2. Let a be y(-4). Solve -2*s**3 + s**2 + 5*s + 2 + 3*s**a + 3*s**3 = 0 for s.
-2, -1
Factor 6*b**2 + 2040*b**4 - 1019*b**4 - 1018*b**4 + 7*b**3 + 2*b**3.
3*b**2*(b + 1)*(b + 2)
Let t(q) = 4*q**2 - 3*q**2 + 0 - 2 + 4*q + 9*q**2 - 4*q**2. Let u(a) = 2*a - 4*a**2 + 5*a**2 - a. Let i(o) = -t(o) + 4*u(o). What is d in i(d) = 0?
-1, 1
Let s(j) = -27*j**3 + 35*j**2 - 17*j. Let x(a) = a**4 + 27*a**3 - 34*a**2 + 18*a. Let b(w) = 6*s(w) + 5*x(w). Factor b(m).
m*(m - 3)*(m - 2)*(5*m - 2)
Factor 52/3*c**2 + 0 - 50/3*c - 2/3*c**3.
-2*c*(c - 25)*(c - 1)/3
Suppose -4*o + 3*o = 5*s - 91, -2*o = 3*s - 56. Determine j so that -2*j**4 + 583*j**2 - 599*j**2 + s + 12*j**3 - 4*j - 8*j = 0.
-1, 1, 3
Factor -66/23*f - 2/23*f**5 - 18/23*f**4 - 18/23 - 4*f**2 - 60/23*f**3.
-2*(f + 1)**3*(f + 3)**2/23
Solve 0 + 39/2*r**2 + 5/6*r**3 + 23/3*r = 0.
-23, -2/5, 0
Factor 28/11 - 2/11*p**2 - 26/11*p.
-2*(p - 1)*(p + 14)/11
Factor -2*o**2 - 2*o**2 - 3 - 8 + 4*o + 11.
-4*o*(o - 1)
Suppose -y = 5*c - 48, 25 = 3*c + 3*y + 1. Let z(w) = -w. Let k(p) = -4*p**3 - 24*p**2 - 46*p - 16. Let o(h) = c*z(h) - k(h). Factor o(r).
4*(r + 1)**2*(r + 4)
Let h be -1 - 4/(12/(-45)). Suppose -3*r - 21 = -3*m, -3*m - r - 3*r = h. Factor -3*s**2 + 2 - s**2 + m*s**2.
-2*(s - 1)*(s + 1)
Suppose -4/7*y**4 - 96/7*y**2 - 32/7*y**3 - 128/7*y - 64/7 = 0. What is y?
-2
Suppose 0 = 119*x - 816 + 340. Solve -10/3*l**3 - 2/3*l**x - 4/3 - 6*l**2 - 14/3*l = 0.
-2, -1
Factor 0 - 135*w + 5/2*w**2.
5*w*(w - 54)/2
Let g be 19035/329 - 58 - 8/(-14). Suppose g*q**5 + 48/7*q**2 - 48/7*q - 12/7*q**4 + 0*q**3 + 0 = 0. Calculate q.
-2, 0, 2
Let b(t) be the third derivative of -t**6/960 - 3*t**5/320 - t**4/32 + 11*t**3/3 - 2*t**2. Let u(l) be the first derivative of b(l). Factor u(x).
-3*(x + 1)*(x + 2)/8
Suppose 217 = -28*y + 301. Factor 0 + 2/9*g**y + 2/9*g**4 - 4/9*g**2 + 0*g.
2*g**2*(g - 1)*(g + 2)/9
Let k(a) = -5 + 3*a - 7*a**2 + 1 - a. Let x(c) = -36*c**2 + 9*c - 21. Let v(h) = -h**2 - 13*h - 34. Let g be v(-10). Let j(m) = g*x(m) + 21*k(m). Factor j(t).
-3*t*(t - 2)
Let -9 - 3/4*j**3 - 57/4*j - 6*j**2 = 0. Calculate j.
-4, -3, -1
Let v(p) be the second derivative of p**4/12 - 30*p**3 + 4050*p**2 + 196*p. Solve v(s) = 0 for s.
90
Let o be (393/(-2620))/((2/3)/(50/(-15))). Suppose 3/4*y**2 + 6*y - 21/4*y**3 + 3 - 15/4*y**4 - o*y**5 = 0. What is y?
-2, -1, 1
Let q(v) be the first derivative of 3*v**4/8 - 99*v**3 + 9801*v**2 - 431244*v - 296. Find o such that q(o) = 0.
66
Suppose 3*n + 3*b = -187 + 208, -5*b + 35 = -2*n. Suppose n + 0*j + 0*j**2 + 2/5*j**4 + 2/5*j**3 = 0. Calculate j.
-1, 0
Let o(d) be the second derivative of 9*d**6/10 + 9*d**5/2 + 37*d**4/4 + 10*d**3 + 6*d**2 + 2*d - 25. Factor o(x).
3*(x + 1)**2*(3*x + 2)**2
Let f = 60 - 60. Let z be f + 0 + (-3)/(-12). Factor -z - 1/2*k - 1/4*k**2.
-(k + 1)**2/4
Suppose -5*y - 3*d = 18, -d - 8 + 36 = -4*y. Let z be (y + -1)*4/(-28)*3. Factor -2/3*o**z + 10/9*o**2 + 2/3 + 22/9*o.
-2*(o - 3)*(o + 1)*(3*o + 1)/9
Factor 2/9*x**5 + 2/9 + 10/9*x + 10/9*x**4 + 20/9*x**2 + 20/9*x**3.
2*(x + 1)**5/9
Let -26*y - 8/13*y**3 - 344/13*y**2 - 84/13 = 0. Calculate y.
-42, -1/2
Let o(d) be the second derivative of 7*d**6/240 - d**5/60 - 5*d**2/2 + d. Let b(s) be the first derivative of o(s). Factor b(i).
i**2*(7*i - 2)/2
Suppose 5*v + 5 = d + 4*v, -2*d = -5*v - 16. Determine h so that 20 - 14 + 77*h**3 + 115*h**d - 34*h + 64*h**4 - 12*h**2 = 0.
-3, -1/2, 1/4
Let a(q) = -7 + 0*q + 6*q**3 - 5*q - 5*q**3 - 3*q**2. Let s be a(5). Determine x so that 33*x**2 + s*x + 6*x - 36 - 37*x**2 = 0.
3
Let g be 6/9*15 - 3/1. Let i be 1/g*112/48. What is w in -1/3*w**2 + i*w + 0 = 0?
0, 1
Factor 10*d + 1/2*d**2 + 50.
(d + 10)**2/2
Factor 4*w**2 + 2*w + w**3 + 104*w**2 - 33*w + 3*w**3 - 81*w.
4*w*(w - 1)*(w + 28)
Let t = 29 - 29. Let z(s) be the third derivative of 0 - 1/90*s**5 + t*s**3 - 4*s**2 + 0*s**4 + 0*s. Factor z(u).
-2*u**2/3
Let p(a) be the third derivative of -a**8/84 - 2*a**7/21 + 13*a**6/30 - 7*a**5/15 + 20*a**2 + 4. Factor p(q).
-4*q**2*(q - 1)**2*(q + 7)
Let g(y) be the third derivative of 0 + 7/6*y**4 + 0*y + 4*y**3 + 0*y**5 - 1/30*y**6 - 30*y**2. Determine f so that g(f) = 0.
-2, -1, 3
Let z = 65/63 - 8/9. Suppose -3*g = 2*k + 17, 5*k = -1383*g + 1384*g + 17. Factor -1/7*w + 2/7 - z*w**k.
-(w - 1)*(w + 2)/7
Let y(d) be the first derivative of 0*d**4 + 0*d**2 + 2 + 0*d + 1/30*d**5 + 1/180*d**6 + 4/3*d**3. Let k(j) be the third derivative of y(j). Factor k(q).
2*q*(q + 2)
Suppose -5*m = -3*y + 14 + 2, 3*m = -6. Let p(a) = -a**3 + 3*a - 2. Let x(o) = 2*o**3 - 6*o + 4. Let j(q) = y*x(q) + 5*p(q). Suppose j(i) = 0. What is i?
-2, 1
Factor 8/5*h**2 + 4*h**4 + 28/5*h*