2 + 5*f**2 + 3*f + f - 6 + 0*f.
2*(f - 1)*(f + 3)
Let d(z) = -z**2 + 1. Let q(u) = -9*u + 15. Let g(p) = 17*p - 29. Let c(w) = -6*g(w) - 11*q(w). Let f(m) = -c(m) - d(m). Factor f(h).
(h - 2)*(h + 5)
Let i(q) = 1. Let d(p) = p**3 + 13*p**2 - 14*p - 1. Let u be d(-14). Let h(f) = 2*f**2 - 8*f + 6. Let r(g) = u*h(g) - 2*i(g). Factor r(v).
-2*(v - 2)**2
Let u = 19 + -37. Let c(m) = 11*m**3 + 9*m**2 - 15*m + 13. Let p(y) = y**3 + y**2 - y + 1. Let x(g) = u*p(g) + 2*c(g). Suppose x(f) = 0. What is f?
-2, 1
Let v be (-2)/6*(-36)/6. Suppose -6*l + 4*l + 4*j = -4, -4*j = v*l - 4. Factor -l*z**3 - 4*z**3 + 24*z**2 - 2*z**5 - 8*z - 20*z**3 + 12*z**4.
-2*z*(z - 2)**2*(z - 1)**2
Let q = 67 + -66. Let x be (7/21*(0 + 0))/q. Solve x*j + 2/15 - 2/15*j**2 = 0 for j.
-1, 1
Let p(b) be the second derivative of b**7/336 + 49*b**6/240 + 623*b**5/160 + 527*b**4/96 - 13*b**3 - 36*b**2 - 559*b + 2. Solve p(y) = 0 for y.
-24, -1, 1
Factor 10/7*q + 2/7*q**3 + 8/7*q**2 + 4/7.
2*(q + 1)**2*(q + 2)/7
Let s be (1/3)/((-3)/(-36)). Let p be (-2)/(2/s + -1). Factor -2*b**2 + 0*b**2 - 2*b + 0*b**2 + p.
-2*(b - 1)*(b + 2)
Suppose 0 = -12*c + 14*c + 4. Let g be (c - -3)/(3/6). Suppose 0*a + 6/7*a**3 + 0 - 3/7*a**g - 3/7*a**4 = 0. Calculate a.
0, 1
Let c(x) be the second derivative of -7*x**6/165 - 47*x**5/110 - 21*x**4/22 - 13*x**3/33 + 10*x**2/11 + 52*x - 3. Suppose c(k) = 0. What is k?
-5, -1, 2/7
Let w(z) be the second derivative of z**7/168 - z**6/20 - 11*z**5/80 + 5*z**4/4 + 25*z**3/6 - 81*z + 1. Suppose w(k) = 0. What is k?
-2, 0, 5
Let w = -10440 + 10442. Factor -5/3*y - 1/3*y**3 - 2*y**w + 0.
-y*(y + 1)*(y + 5)/3
Determine q so that 5*q**3 - 7*q**3 + 7*q**4 + 36 - 36 = 0.
0, 2/7
Let p(b) = 2*b**3 - 4 + 2*b**2 - b - 7*b + 1 - 3. Let d(k) = 6*k**3 + 7*k**2 - 25*k - 19. Let j(q) = 2*d(q) - 7*p(q). What is u in j(u) = 0?
-1, 2
Suppose m**2 - 2/3*m**3 - 7 + 20/3*m = 0. What is m?
-3, 1, 7/2
Let m(b) be the second derivative of -1/8*b**3 - 9/16*b**2 + 1/32*b**4 + 0 - 2*b. Factor m(t).
3*(t - 3)*(t + 1)/8
Let h(z) be the first derivative of 2*z**3/33 - 7*z**2/11 + 20*z/11 - 147. Find d, given that h(d) = 0.
2, 5
Suppose 6 = -919*s + 921*s. Let 0*b + 1/2*b**4 + 1/2*b**s + 0*b**2 + 0 = 0. Calculate b.
-1, 0
Let z be (15/(-6))/(80/(-224)) + 33/(-5). Factor -12/5*f**3 + 26/5*f**2 + z - 16/5*f.
-2*(f - 1)**2*(6*f - 1)/5
Let l(j) be the third derivative of -j**5/12 + 25*j**4/8 - 35*j**3/3 + 127*j**2. Determine k, given that l(k) = 0.
1, 14
Let -2/11*u**2 - 48/11 + 50/11*u = 0. Calculate u.
1, 24
Suppose 0 = -d + 4*q + 27, 2*q + 72 = 2*d + 12. Factor 12*k**5 + k**3 + 21*k**3 - 4*k**2 - 2*k**3 + 3*k**4 - d*k**4.
4*k**2*(k - 1)**2*(3*k - 1)
Let r be (1036/(-24))/(-7) - 2/12. Let a(n) be the first derivative of -n**2 + 4*n - 2/3*n**3 + r. Suppose a(s) = 0. What is s?
-2, 1
Let l(a) be the second derivative of 1/90*a**5 + 0 + 1/27*a**4 - 2/3*a**2 - 7*a - 5/27*a**3. Let l(r) = 0. What is r?
-3, -1, 2
Let q = 7 - 4. Suppose 0 = 4*z - q*z - 5. Let 2*s**4 + 0*s**5 - 4*s**3 - s**z + 5*s**3 - s**4 - s**2 = 0. What is s?
-1, 0, 1
Let i(y) be the third derivative of -y**6/60 + y**5/15 + y**4/3 - 8*y**3/3 - 139*y**2. Determine m so that i(m) = 0.
-2, 2
Let v(z) = 3*z**3 + 2*z**2 + 8*z + 9. Let d be v(-1). Suppose 4/3*m**5 - m**3 + 0*m**4 + d*m + 0 + 1/3*m**2 = 0. Calculate m.
-1, 0, 1/2
Let u(o) be the third derivative of -1/1260*o**7 - 1/672*o**8 + 1/360*o**5 + 0 - 1/72*o**4 + 1/144*o**6 + 0*o - 19*o**2 + 0*o**3. Let u(m) = 0. Calculate m.
-1, 0, 2/3, 1
Let i(x) = x**3 + 7*x**2 + 6*x. Let o be i(-6). Suppose -7*s - z + 3 = -5*s, 4*s + 5*z + 3 = o. Let -s*f + 0 + 3/2*f**2 = 0. Calculate f.
0, 2
Factor n - 22*n**2 + 4*n**5 + 14*n**2 - 9*n**3 + n**3 + 4*n**4 + 3*n + 4.
4*(n - 1)**2*(n + 1)**3
Factor 1/3*r**2 + 2/3 + 3*r**4 - 3*r + 7*r**3.
(r + 1)*(r + 2)*(3*r - 1)**2/3
Suppose 5*k = -5*i + 2*i + 22, 0 = -k - 4*i + 18. Factor -131*d + 80*d**2 - 44*d - 5*d**3 + 125 - 25*d**k.
-5*(d - 5)**2*(d - 1)
Let w(l) be the second derivative of l**7/12600 + l**6/1200 + 11*l**4/12 + 18*l. Let n(s) be the third derivative of w(s). Factor n(p).
p*(p + 3)/5
Let h = 6 - 3. Let c = -20 - -167. Determine d so that 73*d - c*d**h + 12 + 37*d - 38*d + 63*d**2 = 0.
-2/7, 1
Suppose 14*i - 3 = -73. Let p(v) = -v**3 + v**2 - 2*v - 1. Let a(t) = 2*t**3 + 10*t**2 - 11*t + 14. Let y(g) = i*p(g) - a(g). Factor y(f).
3*(f - 3)*(f - 1)**2
Let x(g) = g**3 + 4*g**2 + g + 1. Let r(y) = -6*y**3 - 7*y**2 + 41*y + 27. Let q(w) = r(w) + 5*x(w). Suppose q(k) = 0. What is k?
-2, -1, 16
Let z = 507 + -501. Let r(x) be the second derivative of 2/5*x**z + 2*x + 8/3*x**4 - 7/5*x**5 + 2*x**2 - 1/21*x**7 - 3*x**3 + 0. Factor r(y).
-2*(y - 2)*(y - 1)**4
Let s be (4 + (-9)/6)/(2/4). Let m(b) be the second derivative of 1/78*b**4 + 1/39*b**3 + b - 1/13*b**2 - 1/130*b**s + 0. Factor m(u).
-2*(u - 1)**2*(u + 1)/13
Factor -6*b**2 - 89*b**5 + 6*b**4 - 3*b**3 + 7*b**3 - 5*b + 90*b**5.
b*(b - 1)*(b + 1)**2*(b + 5)
Let u be (2/13)/(336/364). Factor -u*l**3 + 1/6*l**4 + 0*l**2 + 0*l + 0.
l**3*(l - 1)/6
Suppose -2*a - 9 = -v + 16, 0 = 3*a + 15. Suppose -6 + 0 - v*y**2 - 6*y**2 - 27*y + 0 = 0. What is y?
-1, -2/7
Suppose 0 = -28*c + 25*c + 417. Find t, given that 285*t**4 + 17*t**2 - 75*t**5 - 342*t**3 + c*t**2 + 74*t - 98*t = 0.
0, 2/5, 1, 2
Let b(m) be the first derivative of 21 + 0*m**2 + 2/3*m**3 + 0*m + 1/5*m**5 - 3/4*m**4. Factor b(w).
w**2*(w - 2)*(w - 1)
Let q(i) = i**3 + 2*i**2 - 6*i - 7. Suppose 0 = 21*k - 25*k - 12. Let c be q(k). Factor -2*d**3 - 4/9*d**c - 14/9*d**4 + 0 + 0*d.
-2*d**2*(d + 1)*(7*d + 2)/9
Let 1176/5 + 6/5*q**2 + 168/5*q = 0. Calculate q.
-14
Let l(k) be the third derivative of k**9/241920 - k**8/80640 - k**5/5 + 14*k**2. Let o(p) be the third derivative of l(p). Find n such that o(n) = 0.
0, 1
Let c = 97 - 92. Find i such that -i**4 - 15*i**3 + 13*i**4 + 19*i**c - 16*i**5 = 0.
-5, 0, 1
Suppose 5*h = 15, -3*p = -3*h + 3 + 3. Let b be p/(-7) + (-3)/(-7). Factor 11/7*v**2 - b + 9/7*v.
(v + 1)*(11*v - 2)/7
Solve -136/5*y**2 + 0 - 4/5*y**5 - 128/5*y**3 + 136/5*y**4 + 132/5*y = 0.
-1, 0, 1, 33
Let f(d) = -5*d**3 - 19*d**2 - 42*d - 24. Let q(j) = -36*j**3 - 132*j**2 - 294*j - 168. Let y(s) = -15*f(s) + 2*q(s). Factor y(p).
3*(p + 1)*(p + 2)*(p + 4)
Let p(x) be the first derivative of -5*x**3/9 - 10*x**2 + 65*x/3 - 94. Find f such that p(f) = 0.
-13, 1
Let x(h) = h**3 + h**2 - h - 4. Let a be x(0). Let u be (2 + 8/(-1))*1/a. Factor 3/4*s**4 - 3/2*s**3 - 3/4 + 0*s**2 + u*s.
3*(s - 1)**3*(s + 1)/4
Suppose -156*c**2 + 1065*c**5 - 72*c - 22*c**4 - 14*c**4 - 1069*c**5 - 116*c**3 = 0. What is c?
-3, -2, -1, 0
Factor 10 - 7*p - 2*p**2 - 14 + 2*p - p.
-2*(p + 1)*(p + 2)
Let o(n) be the third derivative of 2/21*n**3 + 2/105*n**5 + 5/84*n**4 + 0 - 8*n**2 + 0*n + 1/420*n**6. Factor o(f).
2*(f + 1)**2*(f + 2)/7
Let n(q) = 3*q**4 - 44*q**3 - 17*q**2 + 122*q - 72. Let p(o) = -o**4 + 15*o**3 + 6*o**2 - 41*o + 24. Let a(u) = -3*n(u) - 8*p(u). Factor a(m).
-(m - 12)*(m - 1)**2*(m + 2)
Suppose 5*q - 3*o + 21 = 63, 4*q + 3*o - 39 = 0. Let p = q - 4. Let 3*n + n - p*n - n**2 + 0*n**2 = 0. Calculate n.
-1, 0
Let i(v) = -3*v**2 - 11*v + 27. Let q(d) = d**3 - d**2 + 3. Let l be q(0). Let o(s) = 2*s**2 + 5*s - 13. Let r(t) = l*i(t) + 5*o(t). Factor r(z).
(z - 4)**2
Let d = -1/4948 - -7423/4948. Solve -9/4 + d*v - 1/4*v**2 = 0 for v.
3
Let n(p) be the third derivative of 2*p**2 + 0*p + 0 + 3/2*p**3 + 5/8*p**4 + 3/40*p**6 - 11/20*p**5. Find i, given that n(i) = 0.
-1/3, 1, 3
Let 33/2*j**2 - 2*j**3 + 14*j - 9/2 = 0. What is j?
-1, 1/4, 9
Suppose -4*x - 202 = -2*b, 3*x - 116 = -2*b + 51. Find z such that 2*z**4 - 3*z - 2*z**2 - z - 91 + 4*z**3 + b = 0.
-2, -1, 0, 1
Let g(m) be the first derivative of 0*m**4 - 1/45*m**6 + 0*m - 2/75*m**5 + 0*m**2 + 10 + 0*m**3. Factor g(o).
-2*o**4*(o + 1)/15
Let u(z) be the first derivative of -z**7/3360 + z**6/1440 + z**5/240 - 11*z**3 + 21. Let x(r) be the third derivative of u(r). Determine a so that x(a) = 0.
-1, 0, 2
Find k such that -35/2*k + 1225/4 + 1/4*k**2 = 0.
35
Let b(v) be the first derivative of 2/17*v**2 + 0*v + 1/34*v**4 - 2/17*v**3 - 28. Let b(d) = 0. What is d?
0, 1, 2
Let b be ((3 + 10/(-20)*6)/(-5))/(-3). Determine n so that 20/3*n**2 + 0*n + b + 4/3*n**3 = 0.
-5, 0
Determine x so that -1/4*x**4 - 3/2*x**2 