t**4. Solve q(y) = 0.
-1, 0, 1
Let p(q) be the second derivative of q**7/1260 + q**6/540 - q**5/90 + q**3/2 - q. Let t(h) be the second derivative of p(h). Factor t(w).
2*w*(w - 1)*(w + 2)/3
Let x(g) be the first derivative of 0*g - 4/3*g**3 - 1 - g**2. Factor x(w).
-2*w*(2*w + 1)
Suppose 18 - 3 = 3*s. Suppose 2*a - 7 = -j + 4*a, -4 = 2*j + s*a. Factor 4*r**3 - j*r**3 - 3*r**3 - 4*r**2.
-2*r**2*(r + 2)
Let s(k) be the third derivative of -3/8*k**4 + k**3 + 0 - k**2 + 0*k + 1/20*k**5. Factor s(i).
3*(i - 2)*(i - 1)
Let c be 35/14 + (5 - 6). What is d in c + 9/4*d**3 - 9/4*d - 3/2*d**2 = 0?
-1, 2/3, 1
Suppose -32/3 - 28/3*s**4 + 8*s**2 + 76/3*s**3 - 112/3*s = 0. Calculate s.
-1, -2/7, 2
Let z(x) be the third derivative of 1/336*x**8 + x**2 + 1/24*x**6 + 0*x + 0*x**3 + 2/105*x**7 + 0 + 1/30*x**5 + 0*x**4. Let z(b) = 0. What is b?
-2, -1, 0
Let z(f) = 2*f**2 + f. Let b(o) = 13*o**2 - 9*o + 14. Let q(d) = b(d) - 6*z(d). Let q(m) = 0. Calculate m.
1, 14
Let n = -116 - -1046/9. Let x be 1*((-40)/(-18) - 2). Determine f so that -n*f - x*f**2 + 0 = 0.
-1, 0
Let n = 2/125 + 1986/875. Determine z so that -2/7 - 32/7*z**2 - n*z = 0.
-1/4
Let t(i) be the first derivative of 0*i - 1/6*i**4 + 1/30*i**5 + 1/3*i**3 - 3/2*i**2 - 2. Let d(j) be the second derivative of t(j). What is p in d(p) = 0?
1
Let h(n) be the first derivative of -4/15*n**3 - 1/10*n**4 + 2 - 1/5*n**2 + 0*n. Solve h(r) = 0 for r.
-1, 0
Let d(k) be the second derivative of -6*k + 1/60*k**5 + 0 + 1/6*k**2 - 1/18*k**3 - 1/36*k**4. Factor d(y).
(y - 1)**2*(y + 1)/3
Let u(i) = -i**3 + 7*i**2 - 6*i + 2. Let s be u(6). Factor -c**2 - s + 3*c + 3 - 4*c**3 + 0 + c.
-(c - 1)*(c + 1)*(4*c + 1)
Let w = 2096/149225 + 2/1175. Let d = 260/381 - w. Factor -2/3*n**2 + d - 2/3*n**3 + 2/3*n.
-2*(n - 1)*(n + 1)**2/3
Suppose 0 = -4*r + 4*i + 1 - 9, -5*r + 4*i - 12 = 0. Let o be (-46)/(-4) + -3 + r. Suppose 3 + 3/2*u**2 + o*u = 0. Calculate u.
-2, -1
Find t, given that 3/4*t - 3/4*t**3 - 3/4 + 3/4*t**2 = 0.
-1, 1
Let j(p) be the third derivative of 0 + 0*p**5 + 1/720*p**6 + 1/6*p**3 - 2*p**2 + 0*p + 0*p**4. Let v(q) be the first derivative of j(q). Factor v(o).
o**2/2
Determine v, given that -4/3 + 2*v**3 - 2*v + 2/3*v**4 + 2/3*v**2 = 0.
-2, -1, 1
Let v be (-1)/(-4) - (-14)/8. Determine p, given that 0*p**2 + p - v*p**3 - 2*p**2 + 2*p**4 - p + 2*p**5 = 0.
-1, 0, 1
Let s(h) = h**2 - 1. Let y(t) = -4*t**2 - 3*t + 1. Let p(v) = -10*s(v) - 2*y(v). Solve p(r) = 0.
-1, 4
Let a(r) be the third derivative of -1/15*r**5 + 0*r + 2/105*r**7 + 1/24*r**4 + 0*r**3 - 1/112*r**8 + 6*r**2 + 0 + 1/60*r**6. Let a(y) = 0. Calculate y.
-1, 0, 1/3, 1
Let g(v) be the third derivative of v**8/21 - 2*v**7/15 - v**6/5 + 7*v**5/15 + v**4/3 + 15*v**2. Solve g(r) = 0 for r.
-1, -1/4, 0, 1, 2
Let l(s) be the first derivative of -2*s**3/21 + 4*s**2/7 - 8*s/7 - 2. Suppose l(x) = 0. What is x?
2
Let d(q) be the first derivative of -q**6/12 + 3*q**5/10 - 3*q**4/8 + q**3/6 + 6. Suppose d(i) = 0. What is i?
0, 1
Let n(f) be the third derivative of -2*f**7/315 + f**6/30 - 2*f**5/45 - 29*f**2. Suppose n(d) = 0. What is d?
0, 1, 2
Let q(s) be the first derivative of -12/5*s**5 + 5/6*s**6 + 9/4*s**4 + 3 + 0*s**2 + 0*s - 2/3*s**3. Determine l, given that q(l) = 0.
0, 2/5, 1
Let y be 1/2*2 - -15. Suppose -4 = 4*i - y. Let 0*n - 1/4*n**2 + 0 - 1/4*n**5 + 1/4*n**i + 1/4*n**4 = 0. What is n?
-1, 0, 1
Suppose -9 = -2*n - 1. Factor -7*j**n + 13*j**4 + 3*j**2 - 6*j**2 + 3*j**3.
3*j**2*(j + 1)*(2*j - 1)
Let a = 12 + -6. Let 0*u**2 + 2*u**5 + 6*u**4 + 2*u**2 + u**5 - u**5 + a*u**3 = 0. Calculate u.
-1, 0
Let s(p) = 3*p**2 - p + 10. Let r(u) be the first derivative of u**3/3 + 3*u - 1. Let x(o) = -7*r(o) + 2*s(o). Factor x(l).
-(l + 1)**2
Let y be -2 - (-6 - -5)*(2 + 3). Let o = -1329/5 + 267. Find h, given that 0*h + 2/5*h**2 + o*h**y + 0 = 0.
-1/3, 0
What is a in -32/3 - 20/3*a - 2/3*a**2 = 0?
-8, -2
Let w(u) be the third derivative of u**7/4200 + u**6/300 + 3*u**5/200 + u**4/6 - 4*u**2. Let i(j) be the second derivative of w(j). Factor i(b).
3*(b + 1)*(b + 3)/5
Let z be (-8)/14*(-70)/20. Suppose z*p - 5 = -5*c, -c - p - 2*p = 12. Factor -6*j**3 + 3*j**4 - c*j**2 + 3*j**5 + 0*j**3 + 3 - 3*j**2 + 3*j.
3*(j - 1)**2*(j + 1)**3
Factor 2*a + 6*a**2 - 3*a**4 - 2*a**2 - 2*a**5 - a**4.
-2*a*(a - 1)*(a + 1)**3
Let p = -2 + 4. Suppose -9 = -7*c + 4*c. Solve -3*y - y**3 + 0*y**c + 4*y**2 + p - 2*y = 0.
1, 2
Suppose 4*u = 6*u - 8. Suppose -u = -4*x + 4. Determine t, given that 0 - 1/5*t**x + 1/5*t**3 + 0*t = 0.
0, 1
Let g(j) be the third derivative of -j**8/504 + j**7/63 - j**6/60 - j**5/10 - 10*j**2. Factor g(m).
-2*m**2*(m - 3)**2*(m + 1)/3
Let m(s) = -s**3 - 6*s**2 - 5*s + 2. Let a be m(-5). Factor 1/2*j**2 + a - 2*j.
(j - 2)**2/2
Suppose -v + 18 = 8*v. Determine g so that -2*g**3 + v + 2*g - 1/2*g**4 - 3/2*g**2 = 0.
-2, -1, 1
Let a = 83/3472 - 2/651. Let x(b) be the second derivative of 0 - 1/120*b**6 + 0*b**2 + 1/80*b**5 - 1/24*b**3 + a*b**4 + b. Factor x(j).
-j*(j - 1)**2*(j + 1)/4
Let f be -1 - (3/(-2) + 12/(-8)). Suppose 1/2*n + 0 - 3/4*n**f + 1/4*n**3 = 0. Calculate n.
0, 1, 2
Let u = 274/105 + -17/21. Let p(k) be the first derivative of 14/25*k**5 - 2/3*k**3 + u*k**2 + 3 - 9/10*k**4 - 4/5*k. Suppose p(y) = 0. What is y?
-1, 2/7, 1
Let p = 3/64 + 55/192. Factor -1/3*j**2 + 1/3*j**3 + 0*j + 0 + 1/3*j**4 - p*j**5.
-j**2*(j - 1)**2*(j + 1)/3
Let y(q) = q**2 + q - 2. Let a be y(-5). Solve -128*m + 30*m**2 + 5 + 27 + 146*m**2 - 125*m**3 + 29*m**3 + a*m**4 = 0 for m.
2/3, 2
Suppose -3*c = c + 3*u - 12, u - 12 = -4*c. Let x be (4/(-12))/((-2)/114). Factor 4 + 9*g**3 + x*g**c + 2*g - 10*g**2 - 24*g**2.
2*(g - 1)*(2*g - 1)*(7*g + 2)
Suppose 20*p**4 + 95*p**3 + 5/4*p**5 - 385/4*p + 205/2*p**2 - 245/2 = 0. Calculate p.
-7, -2, -1, 1
Suppose 1 = -2*r - 1. Let o(v) = -v**3. Let w(h) = -2*h**3 - 6*h**2 + 2*h. Let m(s) = r*w(s) - 6*o(s). Factor m(p).
2*p*(p + 1)*(4*p - 1)
Determine a, given that 25*a + 8 + 250*a**2 + 256*a**2 - 511*a**2 + 22 = 0.
-1, 6
Let v(u) be the second derivative of 3*u**5/100 - 3*u**3/10 - 3*u**2/5 + 17*u. Find l such that v(l) = 0.
-1, 2
Let u be 4*2*4/64. Determine r so that -r**2 + 1 - 1/2*r + u*r**3 = 0.
-1, 1, 2
Let m(t) be the second derivative of -t**5/20 + t**4/3 - t**3/2 - 26*t. Factor m(k).
-k*(k - 3)*(k - 1)
Suppose -5*h - 14*h + 57 = 0. Factor 2/7 + 162/7*l**4 + 108/7*l**2 - 24/7*l - 216/7*l**h.
2*(3*l - 1)**4/7
Let c(l) be the second derivative of l**8/2520 + l**7/1260 - l**6/540 - l**5/180 + 4*l**3/3 - 2*l. Let h(t) be the second derivative of c(t). Factor h(j).
2*j*(j - 1)*(j + 1)**2/3
Suppose 0 = -5*r - 35. Let t = -4 - r. Solve 2*u**2 + t*u**2 - u + 0*u - 4*u**3 = 0 for u.
0, 1/4, 1
Factor -u - 5*u + 26 - 26 + 23*u**2 - 7*u**3.
-u*(u - 3)*(7*u - 2)
Let r(y) be the third derivative of 1/63*y**8 + 2*y**2 + 0*y**3 + 0*y**4 + 0*y + 2/45*y**5 - 1/10*y**6 + 0 + 2/105*y**7. Determine o so that r(o) = 0.
-2, 0, 1/4, 1
Let d(x) = 3*x + 30. Let c be d(-10). Let a(o) be the second derivative of o**2 + 7/12*o**4 - 3/2*o**3 - o + c. Find t, given that a(t) = 0.
2/7, 1
Factor -p**4 + 5*p**4 - 3*p**4 - 5*p**5 - 6*p**4.
-5*p**4*(p + 1)
Let n(c) be the first derivative of c**4/14 + 4*c**3/7 + 12*c**2/7 + 16*c/7 - 62. Let n(g) = 0. What is g?
-2
Let l(o) = o**5 - 2*o**4 + 4*o**3 + 3*o - 3. Let d(a) = -a**4 + 5*a**3 + 4*a - 4. Let v(x) = 3*d(x) - 4*l(x). Factor v(s).
-s**3*(s - 1)*(4*s - 1)
Suppose 0 = -v + 5*v - 8. Factor 0 + 2*f**v - 1/2*f.
f*(4*f - 1)/2
Let r(g) = 2*g**2 + 2*g. Let l be r(-2). Suppose -5*j + 3*b - 12 = 0, 3*b - 7 = j + 5. Find w, given that 7/4*w**2 + 2*w**3 + j + 1/4*w - 4*w**l = 0.
-1/4, 0, 1
Let n(g) be the first derivative of g**4/20 + 2*g**3/5 - 3*g**2/2 + 8*g/5 - 66. Factor n(h).
(h - 1)**2*(h + 8)/5
Suppose -4*p = -3*p - 5. Determine a so that -a**p + 4*a**2 - 3*a**5 + 2*a**4 + 7*a**4 - 6*a**3 - 3*a**2 = 0.
0, 1/4, 1
Let s(q) = -4*q - 5. Let r be s(-2). Factor -1/2*o**r + 1/2*o**2 - 1/2*o**4 + 1/2*o + 0.
-o*(o - 1)*(o + 1)**2/2
Let w(b) be the first derivative of -1/2*b**2 + 4 - 1/3*b**3 + 2*b. Factor w(x).
-(x - 1)*(x + 2)
Suppose -p + 36 = 4*n - 5*p, -4*n = 5*p. Let j = n + -3. Factor -4/7*d**4 - 2/7*d**3 + 0*d**j + 0*d + 0 - 2/7*d**5.
-2*d**3*(d + 1)**2/7
Suppose 21*j = 19*j. Suppose j = -x - c + 5, c = 4*x + 5 - 0. Factor