
-6, -2/5, 1
Let a(t) be the third derivative of -t**7/6300 + t**6/600 - 17*t**4/12 - 24*t**2. Let b(o) be the second derivative of a(o). Factor b(h).
-2*h*(h - 3)/5
Let p(r) be the second derivative of -r**4/36 - 13*r**3/18 - 11*r**2/3 + 2*r + 48. Factor p(j).
-(j + 2)*(j + 11)/3
Let j(i) be the third derivative of 0 + i**4 - 29*i**2 - 30*i**3 + 0*i - 1/75*i**5. Factor j(h).
-4*(h - 15)**2/5
Determine f, given that -9/5*f**4 + 0*f + 3/5*f**5 - 3/5*f**2 + 0 + 9/5*f**3 = 0.
0, 1
Let b(k) be the first derivative of -2*k**7/105 + 2*k**6/75 + k**5/25 - k**4/15 + 6*k - 10. Let r(j) be the first derivative of b(j). Factor r(m).
-4*m**2*(m - 1)**2*(m + 1)/5
Suppose -5*a - 9 = 4*y, -3*a = y + 5 - 1. Let p(c) = -5*c**2 + 7*c**2 + 0 - c + 0. Let w(z) = -1. Let r(f) = a*p(f) - w(f). Factor r(m).
-(m - 1)*(2*m + 1)
Suppose 0*u - 6 = 3*k - 3*u, 3*k - 19 = -2*u. Solve -11*m**2 - 2*m**3 - 16 - m**2 - 24*m + 0*m**k = 0 for m.
-2
Let w(m) = -m**2 - 29*m + 2. Let r(v) = v**2 + 22*v - 3. Let u(d) = -4*r(d) - 3*w(d). Solve u(k) = 0 for k.
-3, 2
Let v(p) = p**3 - 18*p**2 + 15*p. Let o(n) = -n**3 - n. Let u(a) = -5*o(a) - v(a). Factor u(t).
2*t*(t + 5)*(2*t - 1)
Determine g so that -2/5*g**3 + 0*g + 0 + 1/5*g**2 + 1/5*g**4 = 0.
0, 1
Let g = -17 - -23. Suppose -j - j + g = 0. Suppose -5*o - 3*o**2 + j*o**3 - o + 3*o**4 + 3*o**3 = 0. Calculate o.
-2, -1, 0, 1
Let i = -20 - -22. Let s be (-1 - i/3)*(-12)/50. Solve -s*z - 1/5 - 1/5*z**2 = 0.
-1
Suppose 0*b + b**2 + 3*b - 355 + 348 - 9*b = 0. What is b?
-1, 7
Let g(l) = 9*l**2 + 15*l. Let a(c) = c**3 + 18*c**2 + 31*c. Let m(t) = 3*a(t) - 7*g(t). Factor m(s).
3*s*(s - 4)*(s + 1)
Let i(f) = -6*f - 33. Let b be i(-6). Let k(t) be the third derivative of 0*t + 1/10*t**5 + 5*t**2 + 5/12*t**4 + 0 + 2/3*t**b. Factor k(q).
2*(q + 1)*(3*q + 2)
Find c such that 72*c**2 - 179*c - 2*c**3 - 159*c - 20*c**2 = 0.
0, 13
Let r(f) = -f**2 + 11*f - 4. Let l(t) = -t**2 + 15*t - 2. Let d(p) = 5*l(p) - 6*r(p). Factor d(a).
(a + 2)*(a + 7)
Let f(j) = -17*j**2 - 20*j - 8. Let w be 14/6 + (-7)/21. Let o(i) = 6 + i - 4 - 1 + i**w. Let u(p) = -f(p) - 5*o(p). Let u(s) = 0. Calculate s.
-1, -1/4
Let u = -38104009/11 + 3461055. Let z = u - -2948. Factor -2/11*q**4 - 26/11*q**2 - 8/11 - z*q - 12/11*q**3.
-2*(q + 1)**2*(q + 2)**2/11
Let b(k) = -2*k**2 - k. Let i(q) = 11*q**2 - 27*q + 25. Let t(x) = -3*b(x) - i(x). Determine a so that t(a) = 0.
1, 5
Find j such that 16*j - 16*j**2 - 18*j - 3*j**4 + 82*j**2 + 2*j - 63*j**3 = 0.
-22, 0, 1
Let o(m) be the third derivative of 17*m**5/30 - 13*m**4/18 + m**3/3 - 6*m**2 - 14. Factor o(w).
2*(3*w - 1)*(17*w - 3)/3
Let o be (8840/918)/65*(0 - -3). Solve -o + 4/9*z + 4/9*z**2 - 4/9*z**3 = 0 for z.
-1, 1
Let u be (-17 + 3740/221)*-2. Factor 4/13*i + 6/13*i**2 + u*i**3 + 0.
2*i*(i + 1)*(i + 2)/13
Suppose 5*o = -2*o + o. Let u(s) be the second derivative of -6*s + 0*s**2 + 0*s**4 + 1/30*s**6 + 1/42*s**7 + o + 0*s**5 + 0*s**3. Solve u(m) = 0 for m.
-1, 0
Suppose 4*z = 5*o - 24, -5*o + z + 12 = -9. Suppose -c + 6*c = 10*c. Let c - 1/3*k**2 - 2/3*k**3 + 2/3*k + 1/3*k**o = 0. Calculate k.
-1, 0, 1, 2
Suppose 6*u = 3*u + 3. Suppose -u + 10 = 3*s. Factor -9*z**3 - 3*z + 0 + 1 + 11*z**s - z**2 + z.
(z - 1)*(z + 1)*(2*z - 1)
Let f be (-252)/(-980)*14/6. Find w such that -1/5*w**2 - 2/5 - f*w = 0.
-2, -1
Let p(x) be the second derivative of 0 + 1/30*x**4 + 1/15*x**3 - 1/50*x**5 - 4*x + 0*x**2 - 1/75*x**6. Factor p(z).
-2*z*(z - 1)*(z + 1)**2/5
Let g = 52 - 44. Let 17*m**5 + 3*m + 6*m**2 - g*m**5 - 12*m**5 - 6*m**4 = 0. Calculate m.
-1, 0, 1
Let n(j) = 2*j**2 + 6*j - 10. Let d(w) = 4*w**2 + 12*w - 21. Let f(s) = 4*d(s) - 10*n(s). Factor f(r).
-4*(r - 1)*(r + 4)
Factor 4*f**3 + 597*f + 4*f**5 - 533*f - 4*f**4 + 96*f**2 - 20*f**4.
4*f*(f - 4)**2*(f + 1)**2
Let l(p) = 66 + 4 + 24 - 20*p + p**2 + 11. Let x(a) = a**2 - 20*a + 104. Let o(u) = 4*l(u) - 5*x(u). Factor o(v).
-(v - 10)**2
Let r(l) be the first derivative of 19 + 2/39*l**3 + 4/13*l - 3/13*l**2. Find b such that r(b) = 0.
1, 2
Determine c, given that -4/9*c**4 + 4/9 - 2/3*c**5 + 20/9*c**3 + 0*c**2 - 14/9*c = 0.
-2, -1, 1/3, 1
Let z(j) be the third derivative of j**5/160 + j**4/64 - j**3/8 - 33*j**2. Solve z(r) = 0.
-2, 1
Let t(a) be the first derivative of -a**4/8 + 5*a**3/3 - 17*a**2/4 + 4*a + 69. Determine d, given that t(d) = 0.
1, 8
Let k = -22 + 35. Let v(d) = -15*d**3 + 10*d**2 - 29*d - 5. Let b(a) = -7*a**3 + 5*a**2 - 14*a - 2. Let x(q) = k*b(q) - 6*v(q). Suppose x(z) = 0. What is z?
1, 2
Let o(v) = 2*v**5 + 6*v**4 + 4*v**3 + 2*v**2 - 2. Let z(s) = -10*s**5 - 30*s**4 - 19*s**3 - 10*s**2 + 11. Let r(u) = 22*o(u) + 4*z(u). Factor r(k).
4*k**2*(k + 1)**3
Let w = -75 - -21. Let f be (w - -4)/(-7 - -3). Factor 1/2*b**2 - 5*b + f.
(b - 5)**2/2
Factor -10/3*n - 5/3*n**4 + 0 + 1/3*n**5 + 17/3*n**2 - n**3.
n*(n - 5)*(n - 1)**2*(n + 2)/3
Factor -12*z**2 + 3/2*z**3 - 15 + 51/2*z.
3*(z - 5)*(z - 2)*(z - 1)/2
Let i(b) = 2*b**2 + b**3 + 65*b - 66*b + 0*b**2. Let v be i(-2). Factor -2*q + 4*q**4 + 10*q - 5*q**2 - 4*q**2 + 5*q**v - 8*q**3.
4*q*(q - 2)*(q - 1)*(q + 1)
Let m(c) = -10*c - 26. Let t be m(-3). Let s(g) be the second derivative of 1/45*g**6 + 5*g - 1/6*g**t + 2/3*g**2 - 1/30*g**5 + 0 + 1/9*g**3. Solve s(n) = 0.
-1, 1, 2
Let -6/5 - 1/5*g - 1/5*g**3 + 4/5*g**2 = 0. Calculate g.
-1, 2, 3
Let f(o) be the third derivative of o**7/42 - 5*o**6/24 + o**5/3 - 78*o**2. Factor f(p).
5*p**2*(p - 4)*(p - 1)
Suppose 0 = t - 3*q - 0 - 3, -t = -2*q - 3. Find l, given that -4*l**2 - 10*l + 10 + 5*l + 2 - t*l = 0.
-3, 1
Let s(h) = -11*h**3 + 7*h**2 + 11*h + 13. Let n(y) = 6 - 2*y - 23*y**3 + 3*y**2 + 8*y + 18*y**3 + 0*y. Let c(a) = -5*n(a) + 2*s(a). Factor c(z).
(z - 2)*(z + 1)*(3*z + 2)
Let n(f) be the first derivative of 7*f**7/90 + 91*f**6/270 + 17*f**5/30 + f**4/2 - 4*f**3 - 15. Let k(t) be the third derivative of n(t). Factor k(y).
4*(y + 1)*(7*y + 3)**2/3
Let b(a) be the first derivative of -2*a**5/65 + 8*a**3/39 + 354. Factor b(j).
-2*j**2*(j - 2)*(j + 2)/13
Let s(j) be the third derivative of -j**7/70 + j**6/40 + j**5/20 - j**4/8 - 27*j**2 + 3. What is r in s(r) = 0?
-1, 0, 1
Let n be (120/96 + 5/(-4))/(-2). Determine p, given that n + 1/4*p**2 - 1/4*p = 0.
0, 1
Solve 5*g**3 - 16/3*g - 7/3*g**4 - 5/3*g**2 + 4 + 1/3*g**5 = 0.
-1, 1, 2, 3
Suppose -2*s - 15 = -5 - 50. Solve 64/3*o**4 - 8/3*o + 0 - s*o**2 - 32*o**3 = 0.
-1/4, 0, 2
Let f(p) = -4*p**5 + 10*p**4 + p**3 - 5*p**2 + 5*p - 10. Let s(b) = -b**5 + b**4 - b**3 - b**2 + b - 2. Let t(a) = -f(a) + 5*s(a). Factor t(m).
-m**3*(m + 2)*(m + 3)
Let p(h) be the first derivative of 1/3*h**3 - 1/4*h**4 - 5 + 0*h**2 + 0*h. Factor p(w).
-w**2*(w - 1)
Let m be (1 - 6) + 2 + 18. Solve 49 + 27*s + m*s - 7*s + 0*s**3 + s**3 - 13*s**2 = 0.
-1, 7
Factor -10*n**3 - 9532*n**2 + 12*n**4 - 13*n**4 + 9516*n**2.
-n**2*(n + 2)*(n + 8)
Find b, given that 292/9*b**2 + 16 + 4/3*b**4 + 116/3*b + 100/9*b**3 = 0.
-3, -4/3, -1
Factor 0 - 14/3*r + 2/3*r**2.
2*r*(r - 7)/3
Factor -2/17*o**5 - 50/17*o**3 - 56/17*o + 16/17 + 16/17*o**4 + 76/17*o**2.
-2*(o - 2)**3*(o - 1)**2/17
Let w(t) be the first derivative of -44/3*t**3 + 8*t - 4*t**4 - 10 - 10*t**2. Factor w(z).
-4*(z + 1)*(z + 2)*(4*z - 1)
Suppose -j - 13 = -3*f, -5*f - 12 + 35 = -j. Let t be 3*j/(-10)*-5. Suppose -4*v**3 - 12*v**2 + t*v**3 + 9*v**2 + 0*v**3 = 0. What is v?
-3, 0
Let q(f) be the second derivative of f**6/15 - f**5/10 - 7*f**4/2 + f**3/3 + 20*f**2 - 126*f. What is o in q(o) = 0?
-4, -1, 1, 5
Let f be (-1)/4 - (-594)/1944. Let a(g) be the third derivative of 0*g + 0*g**4 + 0 + 2*g**2 - f*g**3 + 1/180*g**5. Factor a(l).
(l - 1)*(l + 1)/3
Let h(d) be the second derivative of d**6/9 + 89*d**5/90 + 29*d**4/9 + 4*d**3 - 8*d**2/9 - 2*d - 6. Factor h(i).
2*(i + 2)**3*(15*i - 1)/9
Let s = -30 - -66. Let a = s + -34. Suppose -h + h**3 + 0 + 1/2*h**4 - 1/2*h**a = 0. What is h?
-2, -1, 0, 1
Let s = -2659 + 29251/11. Solve 14/11*b**2 + s + 10/11*b + 6/11*b**3 = 0.
-1, -1/3
Let l(w) be the third derivative of -w**5/150 + 23*w**4/30 - 529*w**3/15 - 17*w**2 + w. Solve l(x) = 0.
23
Let 1/3 + 1/6*o**4 - 5/6*o**3 - 7/6*o + 3/2*o**2 = 0. What is o?
1, 2
Let v(b) = b**3 - 6*b**2 - 3*b - 4. Let p(a) be the first derivative of -3*a**4/4 + 4*a**3 + 3*a**2 + 9*a + 8. Let l(g) = -4*p(g) - 9*v(g). Solve l(u) = 0.