5*t.
t*(t - 1)/5
Let a(m) be the third derivative of -m**7/70 + m**6/20 - 2*m**2. Factor a(b).
-3*b**3*(b - 2)
Let p(g) be the first derivative of g**7/2100 - g**6/600 + g**5/600 + g**3/3 + 2. Let s(d) be the third derivative of p(d). Let s(b) = 0. Calculate b.
0, 1/2, 1
Let t(z) be the third derivative of -z**8/84 - 4*z**7/105 + 2*z**5/15 + z**4/6 + 5*z**2. Suppose t(h) = 0. What is h?
-1, 0, 1
Let a(t) = 12*t**2 - 3*t - 1. Let n(o) = 12*o**2 - 2*o. Let p(v) = 5*a(v) - 6*n(v). Let j(y) = -13*y**2 - 4*y - 6. Let r(i) = 5*j(i) - 6*p(i). Factor r(f).
f*(7*f - 2)
Let c(i) be the third derivative of -i**7/10080 + i**6/2880 - i**4/6 - 4*i**2. Let m(k) be the second derivative of c(k). Let m(f) = 0. What is f?
0, 1
Find m such that -35*m**2 - 60*m - 82*m - 23*m + 50 = 0.
-5, 2/7
Let d be 3 - (0 + 3) - -84. Suppose 4*t = d - 12. Solve 7 - 7*x - 1 + 47*x + t*x**2 + 2 = 0 for x.
-2, -2/9
Let m(i) = -3*i**2 + 12*i + 9. Let w(x) = -9*x**2 + 36*x + 28. Let c(r) = 17*m(r) - 6*w(r). Find a such that c(a) = 0.
-1, 5
Let l(z) be the first derivative of 1/20*z**4 - 1/15*z**3 + 3 + 1/5*z - 1/10*z**2. Suppose l(s) = 0. What is s?
-1, 1
Factor 2/7*b**2 + 0 - 4/7*b.
2*b*(b - 2)/7
Let w(m) be the first derivative of -m**3 + 6*m**2 + 15*m + 22. Suppose w(u) = 0. Calculate u.
-1, 5
What is f in 0 - 2/9*f**3 + 2/9*f**2 + 4/9*f = 0?
-1, 0, 2
Let d(b) be the first derivative of -1 + 0*b**2 + 0*b - 7/15*b**6 - 18/25*b**5 - 1/5*b**4 + 0*b**3. Factor d(h).
-2*h**3*(h + 1)*(7*h + 2)/5
Let g be 3/(-9) + 5/15. Let q(r) be the second derivative of 2*r + 0*r**4 + g*r**2 + 0 + 1/24*r**3 - 1/80*r**5. Factor q(i).
-i*(i - 1)*(i + 1)/4
Factor 4 + 4*m - 2 + 2*m**2 + 2*m**2 - 10.
4*(m - 1)*(m + 2)
Suppose 0 = -3*v + 4*z + 20, v = 2*v + 4*z + 4. Let m(b) be the second derivative of 0 + b**2 + 1/6*b**v - 2*b + 2/3*b**3. Factor m(j).
2*(j + 1)**2
Let i(c) = 4*c**5 - c**4 + 5*c**2 - 5*c + 5. Let w(j) = -4 + 4*j**4 + 2*j**4 - 3*j**5 - 4*j**2 - 5*j**4 + 4*j. Let y(u) = 4*i(u) + 5*w(u). Factor y(x).
x**4*(x + 1)
Let d(b) = -5*b**2 - 2. Let n(j) = j + 1. Let l(c) = d(c) + 2*n(c). Factor l(v).
-v*(5*v - 2)
Let w(g) be the first derivative of -g**4/42 + 4*g**2/7 - 7*g + 8. Let s(q) be the first derivative of w(q). Factor s(x).
-2*(x - 2)*(x + 2)/7
Let j = -6 - -9. Factor 5 - j*w**2 + 8*w + 5*w**2 - 3 + 4.
2*(w + 1)*(w + 3)
Determine g, given that -15/2*g**2 + 3*g + 0 - 3/2*g**4 + 6*g**3 = 0.
0, 1, 2
Let c be 0 + ((-1)/2)/(5/(-30)). Let b(d) be the third derivative of 1/9*d**c + d**2 + 0*d - 1/18*d**4 + 0 + 1/90*d**5. Factor b(z).
2*(z - 1)**2/3
Let z(b) be the third derivative of -b**8/120960 - b**7/10080 - b**6/2160 + b**5/15 - 4*b**2. Let f(d) be the third derivative of z(d). Factor f(u).
-(u + 1)*(u + 2)/6
Let q be 6/(-8) - 23/(-4). Factor q + 2*i - 2 + 0*i - 2*i**3 - i**4 - 2.
-(i - 1)*(i + 1)**3
Let u(s) be the first derivative of -3*s**5/5 - 3*s**4/4 - 11. Factor u(i).
-3*i**3*(i + 1)
Let a(z) be the second derivative of 2*z**7/147 - 2*z**6/35 - z**5/35 + 11*z**4/21 - 8*z**3/7 + 8*z**2/7 + 6*z - 1. What is k in a(k) = 0?
-2, 1, 2
Factor -4*s**2 + 4*s**3 - s**2 - 8 + 4*s**4 - 20*s - 7*s**2.
4*(s - 2)*(s + 1)**3
Let l(k) = k**3 + 18*k**2 - 36*k + 28. Suppose -4 = -3*i - 13. Let m(r) = 18*r**2 - 36*r + 27. Let z(w) = i*l(w) + 4*m(w). Factor z(x).
-3*(x - 2)**3
Let k(c) be the second derivative of c**4/10 + 4*c**3/15 + c**2/5 + 8*c. Determine s so that k(s) = 0.
-1, -1/3
Let n(q) = 3*q**4 - 8*q**3 + q**2 + 13*q + 1. Let k(v) = -2*v**4 + 4*v**3 - v**2 - 7*v. Let i(x) = 5*k(x) + 3*n(x). Factor i(j).
-(j - 1)*(j + 1)**2*(j + 3)
Let x = -3 + 8. Let y(b) be the second derivative of -9*b**3 - 2*b**2 + 0 - 3*b - 142/5*b**x - 133/6*b**4 - 16*b**6 - 64/21*b**7. Let y(u) = 0. What is u?
-2, -1, -1/4
Suppose -d = -5*j - 9, -7*d = -10*d - 5*j + 7. Factor d + 1/4*s**2 + 2*s.
(s + 4)**2/4
Let i(x) be the first derivative of 0*x**2 - 1/3*x**3 + 0*x - x**4 + 2. Determine g, given that i(g) = 0.
-1/4, 0
Let h(p) = p**2 - 12*p - 13. Let w be h(13). Let f be (-524)/(-16) + w - -4. Factor -3*t + 0 - f*t**3 - 21*t**2.
-3*t*(7*t + 2)**2/4
Let j be 1 - (3 + 24) - -2. Let y be (-2)/(-3) + j/(-18). Suppose 0*o**3 + 1/2*o**4 + 1/2 + 0*o - o**y = 0. Calculate o.
-1, 1
Suppose 0 = 2*i + 2*s - 10, -4*i + 44 = -3*s + s. Let n be (-6)/i + 32/12. Factor -3*o + 5*o**2 - 9*o**2 - 2*o**n.
-3*o*(2*o + 1)
Let n(b) be the first derivative of b**4 - 16*b**3/3 + 10*b**2 - 8*b + 5. Factor n(i).
4*(i - 2)*(i - 1)**2
Let m(h) be the third derivative of -h**5/20 + h**4/8 - 7*h**2. Suppose m(k) = 0. What is k?
0, 1
Let y = -37 + 39. Let k be ((-44)/24)/(-11)*y. Let 1/3*u**5 - 2/3*u**2 + 1/3 - 2/3*u**3 + 1/3*u**4 + k*u = 0. What is u?
-1, 1
Suppose -a - p = -0*a - 6, -3*a - 4*p + 21 = 0. Suppose d + 0 - 2 = 0. Determine t, given that 6*t - a*t**d + t - 2 + 0 = 0.
1/3, 2
Let r(d) = -5*d**2 + 7*d + 10. Let g(m) = 9*m**2 - 13*m - 18. Let t(p) = -6*g(p) - 11*r(p). Factor t(h).
(h - 1)*(h + 2)
Let n = 13 + -12. Let -c**2 + 4*c**2 - 3 - n - c**3 = 0. What is c?
-1, 2
Let n(f) = f**5 + 9*f**4 - 9*f**3 - f**2 - 3. Let y(i) = -8*i**4 + 8*i**3 + 2. Let l(a) = 2*n(a) + 3*y(a). Solve l(x) = 0.
0, 1
Let h(l) be the third derivative of -l**7/280 - 9*l**6/160 + 21*l**5/80 - 11*l**4/32 + 42*l**2. Factor h(o).
-3*o*(o - 1)**2*(o + 11)/4
Let s be 9/6*32/18 + -2. Factor s - y + 1/3*y**2.
(y - 2)*(y - 1)/3
Suppose 1 + 1 = -2*k - q, 0 = 4*k - 3*q + 24. Let i = k + 4. Factor 4*o**2 - i - 5*o**4 - 1 + 3*o**4.
-2*(o - 1)**2*(o + 1)**2
Let h(c) be the second derivative of -c**7/10080 + c**6/960 - c**5/240 - c**4/3 - 4*c. Let q(i) be the third derivative of h(i). Let q(n) = 0. What is n?
1, 2
Let i(t) be the first derivative of 0*t**2 + 1/216*t**6 - 1/45*t**5 - 1 - 1/18*t**4 + 0*t + 1/3*t**3. Let z(y) be the third derivative of i(y). Factor z(u).
(u - 2)*(5*u + 2)/3
Find z such that 2*z**2 - 2/3*z + 2/3*z**3 - 2 = 0.
-3, -1, 1
Let b be -3 - 36/(-8) - (-1)/(-1). Let g(a) be the first derivative of -1/3*a**3 + 2 - b*a**2 + 0*a. Let g(r) = 0. What is r?
-1, 0
Let b = 41 + -38. Let j = 0 + 2. Determine n so that -25/4*n**5 - 35/2*n**4 - 69/4*n**b - 7*n**j + 0 - n = 0.
-1, -2/5, 0
Factor -11*x**3 + x**4 + 3*x**3 - 5*x**4.
-4*x**3*(x + 2)
Let a(n) be the third derivative of -n**5/15 - 11*n**4/6 - 30*n**2. Suppose a(o) = 0. Calculate o.
-11, 0
Factor -16 + 28*d**2 - 14*d**3 + 11*d**3 + 15*d**3 + 0*d**2.
4*(d + 1)*(d + 2)*(3*d - 2)
Determine m, given that -7*m**2 - 17*m**2 - 2*m - 2*m + 8*m = 0.
0, 1/6
Let x = 40 - 37. Let f(y) be the second derivative of 0 + 1/36*y**4 + 0*y**x - 1/6*y**2 + 2*y. Factor f(o).
(o - 1)*(o + 1)/3
Let y(q) be the first derivative of -q**5/15 - q**4/4 - 2*q**3/9 + 37. Solve y(z) = 0 for z.
-2, -1, 0
Let s(l) be the third derivative of l**8/1008 - l**6/120 + l**5/90 + 5*l**2. Factor s(m).
m**2*(m - 1)**2*(m + 2)/3
Let q(j) = -j**2 - 6*j - 4. Let b be q(-4). Suppose -g = -b*k - 5, -2*k - 1 - 4 = -g. Factor 4*p**5 - 5*p**g + p**3 + 2*p**5 - 2*p**3.
p**3*(p - 1)*(p + 1)
Let d(q) = -3*q**3 - 2*q**2 + q - 2. Let l(t) = -t**3 + t - 1. Let x(k) = 5*d(k) - 10*l(k). Determine r so that x(r) = 0.
-1, 0
Let y = -1/190 - -124/95. Let f = y + 1/5. Factor 1/2*a**2 + 1 - f*a.
(a - 2)*(a - 1)/2
Let a(k) be the third derivative of -k**7/84 + k**6/20 - k**5/30 - 4*k**2. Factor a(f).
-f**2*(f - 2)*(5*f - 2)/2
Factor 2/3*f**2 + 1/3*f**3 - 7/3*f + 4/3.
(f - 1)**2*(f + 4)/3
Suppose -5*h - 37 = -4*p, -2*p - p = -4*h - 29. Solve 2*s**2 + 2 + p*s - 3*s - 4 = 0 for s.
-1, 1
Let j = 4 + -2. Find a such that 5*a**2 - 3*a**2 + 0*a**j + 2*a - 4*a**2 = 0.
0, 1
Suppose l - 5*p + 25 = 0, -2*l - p + 5 = 2*l. Let h(q) be the third derivative of l - q**2 + 1/15*q**3 + 0*q - 1/150*q**5 + 0*q**4. Factor h(d).
-2*(d - 1)*(d + 1)/5
Factor -1/5*f**5 - 1/5*f**3 - 8/5 + 22/5*f - 17/5*f**2 + f**4.
-(f - 4)*(f - 1)**3*(f + 2)/5
Let p(i) be the third derivative of i**6/24 + 7*i**5/12 - i**2. Factor p(j).
5*j**2*(j + 7)
Suppose 4 = y - 1. Determine r, given that y*r + r**2 - 3*r - r = 0.
-1, 0
Let d(j) = 12*j**4 + 8*j**3 - 4*j**2 - 4*j - 4. Let y(k) = -13*k**4 - 9*k**3 + 4*k**2 + 5*k + 5. Let o(q) = 5*d(q) + 4*y(q). Solve o(x) = 0.
-1, 0, 1/2
Solve -1/5*x**2 - 1/5*x + 2/5 = 0 for x.
-2, 1
Suppose -3*s + 10 = 4*v - 3*v, 0 = 4*v + 2*s - 60. Factor 4*n**3 - 3*n**2 - 2*n + v*n**2 - 2*n**4