3 + 8*b + 10. Factor z(g).
-2*(g - 1)*(g + 2)**2
Let m(t) be the second derivative of -t**8/168 + t**6/60 - 4*t**2 - 6*t. Let u(a) be the first derivative of m(a). Find g such that u(g) = 0.
-1, 0, 1
Suppose -5*n + 2*c - 5 = -23, 0 = 2*n + c. Factor 2*x**4 + 4*x**3 - x**2 + x**4 - x - n*x**4 - 3*x**3.
x*(x - 1)*(x + 1)**2
Let j(d) = -2*d**2 + 2*d + 2. Let a be j(3). Let t = -2 - a. Suppose -8/7 - t*i - 14*i**2 = 0. Calculate i.
-2/7
Let h = 402 + -402. Factor 0*w**2 + h + 0*w + 0*w**3 - 4/13*w**4 + 6/13*w**5.
2*w**4*(3*w - 2)/13
Factor -8/7*w**4 - 10/7*w**2 - 16/7*w**3 - 2/7*w + 0.
-2*w*(w + 1)*(2*w + 1)**2/7
Let t(m) be the third derivative of 1/42*m**4 + 0*m - 1/210*m**6 + 2/21*m**3 + 2*m**2 - 1/1470*m**7 - 1/140*m**5 + 0. Factor t(h).
-(h - 1)*(h + 1)*(h + 2)**2/7
Let g(d) be the third derivative of d**7/10080 + d**6/960 + d**5/240 + d**4/3 - 3*d**2. Let m(i) be the second derivative of g(i). Factor m(v).
(v + 1)*(v + 2)/4
Suppose 0*u = -3*k + 2*u + 8, -u - 19 = -4*k. Suppose -4*p - 4*r + r - k = 0, 0 = -p - r - 2. Factor -1/4*a**2 + 1/4*a**5 + 0 + 3/4*a**3 + p*a - 3/4*a**4.
a**2*(a - 1)**3/4
Let x(n) be the first derivative of -1/2*n**2 + 0*n**4 + 0*n + 1 + 2/5*n**5 - 2/3*n**3 + 1/6*n**6. Determine q so that x(q) = 0.
-1, 0, 1
Let s(b) = -6*b**2 + 6*b - 3. Let p(o) = 5*o**2 - 7*o + 4. Let q(n) = 5*n**2 - 8*n + 5. Let x(h) = -3*p(h) + 2*q(h). Let t(y) = -4*s(y) + 5*x(y). Factor t(i).
-(i - 2)*(i + 1)
Let b(q) be the third derivative of -q**6/720 + q**4/48 - 5*q**3/6 + 2*q**2. Let k(c) be the first derivative of b(c). Factor k(h).
-(h - 1)*(h + 1)/2
Suppose 0 = 12*i - 15*i + 9. Suppose -3/2*r**i + 0*r + 0 + 3/4*r**4 + 0*r**2 = 0. What is r?
0, 2
Let p(d) be the first derivative of -d**3/12 - 4. Find z such that p(z) = 0.
0
Let z = -9/17 - -35/34. Let k = 57/196 - 2/49. Factor z*n + 0 + k*n**2.
n*(n + 2)/4
Suppose 0 = f - 4*f + 9. Let 8*z - 30*z - 14*z - 27*z**2 + f - 15 = 0. What is z?
-2/3
Let t(c) = -2*c**3 - 4*c**2. Let s(u) = -9*u**3 - 16*u**2 - u. Let a(v) = 6*s(v) - 26*t(v). Find z such that a(z) = 0.
0, 1, 3
Let g = 104/285 + 2/57. Suppose -2/5*o**2 - 6/5 - 2*o + g*o**3 = 0. Calculate o.
-1, 3
Suppose -n - 8 = -v, -3*v + 5 = n - 3. Suppose k**v + k**2 - 7*k**3 + 4*k**3 + 5*k**3 = 0. What is k?
-1, 0
Let y = 342/11 + -13007/418. Let n = y - -79/114. Factor -8/3*z + 0 + 8/3*z**2 - n*z**3.
-2*z*(z - 2)**2/3
Let g be 4*(9/3)/6. What is n in -2*n - 2*n - 4*n**2 + g*n = 0?
-1/2, 0
Let t(j) be the second derivative of j**10/15120 - j**9/2520 + j**8/1120 - j**7/1260 - j**4/4 - 3*j. Let x(s) be the third derivative of t(s). Factor x(v).
2*v**2*(v - 1)**3
Let y = -213 + 213. Factor 0*r + 7/5*r**4 - 2/5*r**2 - r**3 + y.
r**2*(r - 1)*(7*r + 2)/5
Suppose 6*d - 16*d = 0. Let z(m) be the third derivative of -m**2 + 16/15*m**3 + 4/25*m**5 - 8/15*m**4 + 0*m + d - 2/75*m**6 + 1/525*m**7. Factor z(k).
2*(k - 2)**4/5
Let n(v) = v + 3. Let t(c) = c + 3. Let w(l) = 4*n(l) - 5*t(l). Let k be w(-7). Suppose 2*s**2 - 2*s + 2*s**4 + 0*s**2 + 2*s**3 - k*s**4 = 0. Calculate s.
-1, 0, 1
Let m(c) be the first derivative of -16/15*c**5 + 1 + 0*c - 7/3*c**4 + 2/3*c**2 - 8/9*c**3. Solve m(b) = 0.
-1, 0, 1/4
Suppose 0*g = -u + 5*g - 18, 3*u + 10 = 4*g. Let b be (-1)/1 - (u - 5). Suppose -6/5*f**3 + 0 + 6/5*f**b + 2/5*f**4 - 2/5*f = 0. Calculate f.
0, 1
Let i(y) be the first derivative of -16*y**5/5 + 6*y**4 - y**3/3 - 3*y**2 - y + 12. Determine o, given that i(o) = 0.
-1/4, 1
Let x(t) be the first derivative of 2/3*t**3 - 7 + 0*t - 1/4*t**4 - 1/2*t**2. Factor x(m).
-m*(m - 1)**2
Suppose 0 = 3*m + 2 - 14. Factor -2*g**5 - g**4 + 4*g**4 + 3*g**5 - 4*g**m.
g**4*(g - 1)
Let q(w) be the first derivative of -9*w**5/5 + 3*w**4 + 2*w**3 - 6*w**2 + 3*w - 2. Let q(l) = 0. What is l?
-1, 1/3, 1
Factor -2*n**5 + 16*n**4 + 6*n**2 - 56*n + 16 - 52*n**3 + 25*n**2 + 2*n**3 + 45*n**2.
-2*(n - 2)**3*(n - 1)**2
Let v(l) be the second derivative of -l**7/5040 - l**6/360 - l**5/60 + 5*l**4/12 - 5*l. Let s(h) be the third derivative of v(h). Solve s(g) = 0 for g.
-2
Let z(i) be the third derivative of -7*i**2 + 1/210*i**5 + 0*i + 0 + 1/28*i**4 + 0*i**3. Factor z(j).
2*j*(j + 3)/7
Let f = -21 + 27. Let r(i) be the second derivative of 0 + 1/24*i**4 - 2*i + 0*i**2 - 1/60*i**f - 1/12*i**3 + 1/40*i**5. Factor r(z).
-z*(z - 1)**2*(z + 1)/2
Factor -20*m**2 + 2*m**3 - 2*m**3 + 24*m**2 - 4*m**4.
-4*m**2*(m - 1)*(m + 1)
Find x such that -3/7*x**5 + 0*x + 9/7*x**4 + 0*x**3 - 12/7*x**2 + 0 = 0.
-1, 0, 2
Let h(n) be the third derivative of n**5/20 - 7*n**4/8 - 46*n**2. Factor h(b).
3*b*(b - 7)
Factor -1/2*m**2 + 3/2*m**3 - 3/2*m - 1/2*m**4 + 1.
-(m - 2)*(m - 1)**2*(m + 1)/2
Let f(j) = -2*j**2 + 14*j + 60. Let t be f(10). Solve 1/3*v**2 + 0*v + t*v**3 - 1/3*v**4 + 0 = 0 for v.
-1, 0, 1
Let w(v) be the third derivative of -v**8/672 + v**7/105 - v**6/48 + v**5/60 - 3*v**2. Find z, given that w(z) = 0.
0, 1, 2
Let y(q) be the third derivative of -q**8/1344 - q**7/840 + q**6/480 + q**5/240 + q**2. Factor y(b).
-b**2*(b - 1)*(b + 1)**2/4
Let b(c) be the second derivative of -c**7/840 + c**5/120 + c**3 - 5*c. Let p(k) be the second derivative of b(k). Find s such that p(s) = 0.
-1, 0, 1
Suppose -7*j = 2*j. Let k(f) be the third derivative of -9/2*f**3 + 3/4*f**4 - 1/20*f**5 + f**2 + 0 + j*f. Find m, given that k(m) = 0.
3
Let w(f) = -f**3 + 1. Let b = -5 + 8. Let p(q) = q**4 - 4*q**3 + 3*q**2 - q + 1. Let y(l) = b*w(l) - 3*p(l). Factor y(g).
-3*g*(g - 1)**3
Factor -2/5*z**3 - 6/5*z + 2/5 + 6/5*z**2.
-2*(z - 1)**3/5
Let j(g) be the second derivative of 0*g**5 + 0 + 0*g**3 + 0*g**2 + 3*g - 1/30*g**6 + 0*g**4. Factor j(l).
-l**4
Suppose w = -5*v + 36, w + 4*w - 3*v - 96 = 0. Let p = 23 - w. Determine c, given that 6/5*c + 3/5 + 3/5*c**p = 0.
-1
Factor -4/11*h - 2/11*h**5 + 10/11*h**4 + 0 - 18/11*h**3 + 14/11*h**2.
-2*h*(h - 2)*(h - 1)**3/11
Let i(v) = -7*v - 11. Let o be i(-2). Let t(w) be the third derivative of 0*w - w**2 + 5/36*w**4 + 0 + 2/9*w**o - 1/30*w**5. Find n such that t(n) = 0.
-1/3, 2
Let q = -12 + 14. Suppose -6 = 2*x - 2*c, -3*x + 28 = x + 4*c. Factor -3*g + g**3 + g**x + q*g - 2*g**2 + g**4.
g*(g - 1)*(g + 1)**2
Find b such that -16/7 + 0*b + 4/7*b**2 = 0.
-2, 2
Let q(b) = b**2 - 8*b + 8. Let c be q(7). Factor -w**2 - 2*w + 0 - c + 0*w**2.
-(w + 1)**2
Suppose -3*h**3 + 75 + 4*h - 75 - h**3 = 0. What is h?
-1, 0, 1
Let r = 42 + -22. Suppose 2*x = 3*y + y + r, 4*y = 3*x - 22. Factor -s**4 - 2*s**x - 1 + 5*s**2 - s**2.
-(s - 1)**2*(s + 1)**2
Let t = 1 + 3. Solve 3/4*i**2 + 0 - 9/4*i**3 + 9/4*i**t - 3/4*i**5 + 0*i = 0 for i.
0, 1
Let f(j) be the second derivative of 5*j**5/4 - 5*j**4/4 - 80*j**3/3 - 30*j**2 - 2*j. Factor f(c).
5*(c - 3)*(c + 2)*(5*c + 2)
Let g be (-60)/80*-2*2. Let u(b) be the first derivative of -2/5*b - 1/10*b**2 + 1/15*b**g - 3. Suppose u(k) = 0. Calculate k.
-1, 2
Factor 8/7 + 0*p - 2/7*p**2.
-2*(p - 2)*(p + 2)/7
Suppose 5*z + 18 = 58. Let l = z + -7. Determine b, given that 8*b**4 - 11/2*b + 2*b**3 + 7/2*b**5 - l - 7*b**2 = 0.
-1, -2/7, 1
Let n(b) = 10*b + 6. Let w(u) = u**2 - 51*u - 29. Let d(i) = -11*n(i) - 2*w(i). Factor d(q).
-2*(q + 2)**2
Let i be -1 + -1 - 15/(-6). Let m(a) be the second derivative of i*a**2 - 1/6*a**3 + 1/20*a**5 - a + 0 - 1/12*a**4. Factor m(n).
(n - 1)**2*(n + 1)
Let x be (-18)/135 - (-1)/3. Determine h, given that -x*h**5 - 1/5*h**4 + 0*h + 0 + 0*h**3 + 0*h**2 = 0.
-1, 0
Let f(v) = -v**3. Let x(t) be the second derivative of 3*t**5/20 + t**3/6 + 3*t. Let i(r) = -4*f(r) - x(r). Factor i(j).
j*(j - 1)*(j + 1)
Suppose -16*o**2 + 8*o + 1/2*o**5 + 0 + 12*o**3 - 4*o**4 = 0. Calculate o.
0, 2
Suppose n + 6 - 8 = 0. Factor -2*w**2 + 0*w**n + w**4 - 2*w**3 + 3*w - w + w**4.
2*w*(w - 1)**2*(w + 1)
Let w(i) = -i**2 - 6*i + 3. Let q be w(-3). Let y = -7 + q. Factor -d**4 + 6*d**y - 10*d + 3 - 12*d**2 - 5 + 15*d**4 + 4*d**3.
2*(d - 1)*(d + 1)**3*(3*d + 1)
Let i(d) = d - 1. Let h be i(4). Let p be (1/h)/(6/60). Factor 2/3*v**5 - 2/3 + p*v - 20/3*v**2 - 10/3*v**4 + 20/3*v**3.
2*(v - 1)**5/3
Let z(h) be the second derivative of h**6/6 - 5*h**4/6 + 5*h**2/2 + h. Factor z(g).
5*(g - 1)**2*(g + 1)**2
Let t be 220/(-12) + (-1 - -1). Let s = t - -19. What is c in 0*c**2 + 0*c + s*c**4 + 2/3*c**3 + 0 = 0?
-1, 0
Suppose -4*b = -0*b - 20. Suppose 5*o + 5*a = 4*a + 9, 15