- 36*n(g). Factor b(t).
4*t**4*(t - 1)
Let f = 225 + -5399/24. Let j(b) be the third derivative of -f*b**4 - 3*b**2 + 1/60*b**5 + 0*b + 0*b**3 + 0. Factor j(n).
n*(n - 1)
Let j(a) be the third derivative of -a**6/140 - a**5/42 + 11*a**4/84 - a**3/7 - 5*a**2. Factor j(o).
-2*(o - 1)*(o + 3)*(3*o - 1)/7
Factor -18*i**2 + 3*i**4 - 4*i + 5*i**3 - 10*i**2 + 24*i**2.
i*(i - 1)*(i + 2)*(3*i + 2)
Suppose 0 = -3*g + 2*m + 7, 2*m = -2*g + g + 5. Let b(c) be the second derivative of 0*c**2 - 1/24*c**g + 0 - 2*c + 1/12*c**4. Find f such that b(f) = 0.
0, 1/4
Let z(c) = 17*c**4 - 48*c**3 + 104*c**2 - 96*c + 32. Let d(g) = -4*g**4 + 12*g**3 - 26*g**2 + 24*g - 8. Let w(q) = 9*d(q) + 2*z(q). Factor w(p).
-2*(p - 2)**2*(p - 1)**2
Let r be (-5)/10*6 + -237. Let a be ((-2)/(-12))/((-15)/r). Determine f so that -4/3*f**2 - 2/3 + 8/3*f - a*f**3 + 2*f**4 = 0.
-1, 1/3, 1
Let m be (-2)/(1/(4/(-16))). Let p(d) be the second derivative of -1/30*d**6 + 1/42*d**7 - d + 0 + 1/6*d**4 - m*d**2 + 1/6*d**3 - 1/10*d**5. Factor p(w).
(w - 1)**3*(w + 1)**2
Let h(p) be the second derivative of -p**4/8 - 3*p**3/4 - 15*p. Let h(f) = 0. What is f?
-3, 0
Suppose 16*u = 11*u + 15. Let f(r) be the first derivative of u + 0*r + 0*r**2 + 1/9*r**3 + 0*r**4 - 1/15*r**5. Factor f(b).
-b**2*(b - 1)*(b + 1)/3
Factor 1/4*o**5 + 0*o**4 + 0*o + 0*o**2 + 0 - 1/4*o**3.
o**3*(o - 1)*(o + 1)/4
Let s(m) be the first derivative of m**4/4 - 3*m**2/2 + 2*m - 16. Suppose s(q) = 0. Calculate q.
-2, 1
Let v(x) be the first derivative of x**7/2520 - x**5/360 - x**3 - 1. Let w(s) be the third derivative of v(s). Determine m so that w(m) = 0.
-1, 0, 1
Solve 2/13*r**4 + 0 + 14/13*r**3 - 2/13*r**2 - 2/13*r**5 - 12/13*r = 0 for r.
-2, -1, 0, 1, 3
Let a(o) be the second derivative of o**5/5 - 13*o**4/36 + o**2/6 + 10*o. Factor a(m).
(m - 1)*(3*m - 1)*(4*m + 1)/3
Let j(z) = -z + 11. Let q be j(8). Suppose 0*k = -q*k. Suppose -3 + s**2 + 4 + k*s - 2*s = 0. Calculate s.
1
Factor -32/5*q + 8/5*q**3 + 4/5*q**4 - 16/5 - 12/5*q**2.
4*(q - 2)*(q + 1)**2*(q + 2)/5
Let v = -137/21 + 48/7. Let b(m) be the first derivative of -1 + v*m**2 + 1/3*m + 1/9*m**3. Suppose b(f) = 0. Calculate f.
-1
Let z = -5 - -7. Factor 3*x**2 - 2*x**2 + 7*x - z - 8*x.
(x - 2)*(x + 1)
Let o(g) be the second derivative of -8*g**5/75 + 4*g**4/45 + g**3/3 - 3*g**2/5 - 21*g. Suppose o(z) = 0. Calculate z.
-1, 3/4
Let p be 1/(-4)*1 + 15/28. Factor 0*q - p*q**2 + 0.
-2*q**2/7
Let a be (1 - (-159)/(-80)) + 1. Let y(j) be the second derivative of -1/120*j**6 - j + 0*j**2 + a*j**5 - 1/24*j**3 + 1/48*j**4 + 0. Factor y(c).
-c*(c - 1)**2*(c + 1)/4
Let i = -1 + 8. Let u(l) = 8*l**2 - 2*l - 6. Let r(n) = -7*n**2 + 2*n + 5. Let p(k) = i*r(k) + 6*u(k). Factor p(y).
-(y - 1)**2
Let z = 13 - 11. Suppose 8 - 2 = -2*d, 5*g + 5 = -5*d. What is p in -p**z - 3*p + p**2 - 1 + 4*p**g = 0?
-1/4, 1
Let z = 97/3 - 482/15. Factor 2/5*t**2 + 0 + 1/5*t + z*t**3.
t*(t + 1)**2/5
Let i(g) = g + 2. Suppose 2*b = -2*b. Let z be i(b). Let 2/9*y**z - 2/9*y + 0 = 0. Calculate y.
0, 1
Let g(h) be the second derivative of h**7/21 - 2*h**6/15 + h**4/3 - h**3/3 - 6*h. Let g(x) = 0. Calculate x.
-1, 0, 1
Let u(r) be the second derivative of -r**4/18 - 2*r**3 - 27*r**2 + 6*r. Solve u(f) = 0 for f.
-9
Let o(r) = 0*r + 2*r + 4*r**2 - 7*r - 9. Let c(l) = -10*l**2 + 12*l + 22. Let p(w) = 5*c(w) + 12*o(w). Factor p(t).
-2*(t - 1)*(t + 1)
Determine o, given that 5/7*o + 1/7*o**3 + 2/7 + 4/7*o**2 = 0.
-2, -1
Suppose 4*r + b = 9, -5*r - 3*b + 12 = -b. Find z such that -z**2 + z**r - 14*z + z**2 + 4 - 9*z**2 = 0.
-2, 1/4
Suppose -3*r + 9*r - 12 = 0. Let m(h) be the third derivative of 0 + 1/60*h**5 + 4*h**r - 1/8*h**4 + 1/3*h**3 + 0*h. Let m(x) = 0. What is x?
1, 2
Let o = -24/7 - -127/35. Factor 1/5*i**2 + 0 + o*i.
i*(i + 1)/5
Let t = -122/3 - -41. Solve -2/3 + m + 0*m**2 - t*m**3 = 0.
-2, 1
Let i(n) be the third derivative of -n**7/120 + 11*n**6/160 - 23*n**5/120 + n**4/8 + n**3/3 + 10*n**2. Find m, given that i(m) = 0.
-2/7, 1, 2
Let i(d) = -5*d**2 - 23*d + 16. Let l(t) = t**2 + 6*t - 4. Let r(p) = 2*i(p) + 9*l(p). Let m be r(7). Suppose 7 + m*k**2 + 3 - 10 + 6*k = 0. What is k?
-2, 0
Let p(q) be the second derivative of -q**5/150 + q**4/45 - q**3/45 + 5*q. Factor p(k).
-2*k*(k - 1)**2/15
Suppose -u - 4*u = -15. Let -5*c**3 + 0 - 1 + c**2 - c + 6*c**u = 0. Calculate c.
-1, 1
Find i such that 144*i**2 + 6 + 51*i + 89*i**4 - 55*i**4 + 12*i**5 + 186*i**3 + 80*i**4 + 15*i**5 = 0.
-1, -2/9
Let h(p) be the first derivative of 0*p**3 + 0*p**5 + 2 - 1/3*p**6 + 0*p + p**4 - p**2. Let h(t) = 0. Calculate t.
-1, 0, 1
Let f(h) = 2*h**2 - 6*h - 3. Let k(i) be the third derivative of -i**5/60 + i**4/8 + i**3/3 - 4*i**2. Let d(s) = 4*f(s) + 7*k(s). Factor d(n).
(n - 2)*(n - 1)
Let w(d) = -8*d**4 + 4*d**3 - 4*d + 8. Let f(u) = 15*u**4 - 8*u**3 + 8*u - 15. Suppose -y = 2*y - 33. Let c(v) = y*w(v) + 6*f(v). Solve c(q) = 0 for q.
-1, 1
Let p(v) be the third derivative of -4*v**2 + 2/3*v**4 + 0 - 23/75*v**5 + 0*v - 8/15*v**3 + 7/150*v**6. Factor p(t).
4*(t - 2)*(t - 1)*(7*t - 2)/5
Let f = -3 + 9. Let 7*x - f*x + x**3 + 1 + 3*x**2 + 2*x = 0. Calculate x.
-1
Factor 2/3*r**3 - 2/15*r - 2/5*r**4 + 0 - 2/15*r**2.
-2*r*(r - 1)**2*(3*r + 1)/15
Suppose 2*b + 22 = 4*b - 3*j, -3 = b + 2*j. Let i = 20 - 18. Factor -2/5*w**i + 4/5*w + 0 - 6*w**3 - 14/5*w**b - 38/5*w**4.
-2*w*(w + 1)**3*(7*w - 2)/5
Let a(p) = -p**2 + 5*p - 21. Let j(v) = -2*v + 10. Let m(f) = 2*a(f) + 5*j(f). Factor m(i).
-2*(i - 2)*(i + 2)
Let m(x) be the third derivative of 0*x**3 + 0*x + 0 - 2*x**2 - 1/90*x**5 - 1/120*x**6 + 0*x**4. Factor m(b).
-b**2*(3*b + 2)/3
Let s(w) be the third derivative of 0*w**3 + 0 + 0*w**4 - 1/1176*w**8 + 0*w**7 + 2*w**2 + 1/420*w**6 + 0*w + 0*w**5. Determine f so that s(f) = 0.
-1, 0, 1
Let g = 41/90 + 2/45. Let b be 26/8 - (-3 - -4). Factor -7/4*j**3 + 0 - g*j + b*j**2.
-j*(j - 1)*(7*j - 2)/4
Suppose 2*i + i - 36 = 0. Let m be ((-1)/3)/((-10)/i). Factor 0 + m*t**2 - 2/5*t.
2*t*(t - 1)/5
Factor 6/5 + 3/5*k - 3/5*k**2.
-3*(k - 2)*(k + 1)/5
Let r be (4/(-10))/((-5)/25). Solve 0 + 2*z**3 - 2*z + 3 - 5 + z**2 + z**r = 0 for z.
-1, 1
Let j(g) be the second derivative of g**4/3 + 4*g**3/3 + 2*g**2 - 40*g. Factor j(w).
4*(w + 1)**2
Let o(m) = 34*m**2 + 6*m - 16. Let x(r) = -r**2 + r + 1. Let b(a) = -o(a) - 12*x(a). Determine k, given that b(k) = 0.
-1, 2/11
Let k(t) be the first derivative of t**7/42 - t**6/10 + 3*t**5/20 - t**4/12 + 4*t + 3. Let p(q) be the first derivative of k(q). Factor p(g).
g**2*(g - 1)**3
Let q = 5 + -5. Let z(b) be the second derivative of 0*b**4 + 1/40*b**5 + 0*b**2 + 0*b**3 + q + b + 0*b**6 - 1/84*b**7. Suppose z(n) = 0. What is n?
-1, 0, 1
Let h = 4 + -1. Solve -6*q**h + 8*q**2 + 2*q**3 + 4*q**3 + 4*q**3 - 4*q - 8 = 0 for q.
-2, -1, 1
Let b be 4 - 4 - (-1 + (-3)/(-6)). Factor y + 1/2*y**2 + b.
(y + 1)**2/2
Let o(t) = t**2 + 2*t - 75. Let n be o(8). Factor 76/7*c**2 + 50/7*c**3 + 8*c + 16/7 + 16/7*c**4 + 2/7*c**n.
2*(c + 1)**2*(c + 2)**3/7
Let x(n) be the third derivative of n**7/1155 + n**6/165 + n**5/110 - n**4/33 - 4*n**3/33 + 13*n**2. Suppose x(a) = 0. Calculate a.
-2, -1, 1
Let v(m) = -m**2 + 7*m - 6. Let c(f) = -3*f**2 + 20*f - 17. Let d(k) = 3*c(k) - 8*v(k). Factor d(p).
-(p - 3)*(p - 1)
Let p(u) be the first derivative of -1/9*u**3 + 1/3*u**2 - 1/3*u + 1. Factor p(n).
-(n - 1)**2/3
Let q(b) = 2*b - 7. Let w be q(5). Suppose -6*p**w + 6*p**3 - p**4 + p**2 + 0*p**2 = 0. What is p?
-1, 0, 1
Let k(x) be the first derivative of -5*x**3/3 + 20*x**2 - 80*x - 9. Factor k(v).
-5*(v - 4)**2
Suppose g = 2*m + 13, -m + 2*g = -2 + 4. Let j = 10 + m. Factor 0*f + 2/7*f**j + 0.
2*f**2/7
Let j(l) be the second derivative of 1/72*l**4 + 0 - 5*l + 0*l**2 + 0*l**3. Find y, given that j(y) = 0.
0
Let b(l) be the second derivative of 5/3*l**4 + l + 5/3*l**3 + l**2 + 0 + 1/3*l**6 + 1/21*l**7 + l**5. Find f such that b(f) = 0.
-1
Let t = -560 + 560. Factor 2/5*r**3 + 1/5*r**2 + t*r + 1/5*r**4 + 0.
r**2*(r + 1)**2/5
Let u be 9*(-10 - 279/(-27)). What is m in -1/4*m + 0 - 1/4*m**u - 1/2*m**2 = 0?
-1, 0
Let o(f) be the third derivative of f**6/90 + f**5/9 + f**4/6 - 2*f**3 - 10*f**2. Factor o(w).
4*(w - 1)*(w + 3)**2/3
Suppose 0 = z - o + 2, 2*z - 4*o + 7 = -1. Factor -2/7*f**5 - 2/7*f**4 + 0*f + 2/7*f**2 + z + 2/7*f**3.
-