*o - 3. Let g(a) be the first derivative of l(a). Factor g(u).
-u**2*(u + 1)
Suppose -r + 0*r = 2*b - 9, -4*b = -2*r - 14. Let v(a) be the first derivative of 1 + 3/2*a**b - 2/3*a**3 + 2*a - 3*a**2. Determine o so that v(o) = 0.
-1, 1/3, 1
Let p(t) be the first derivative of t**8/6720 - t**7/3360 - t**6/1440 + t**5/480 - 2*t**3 + 5. Let w(r) be the third derivative of p(r). Solve w(s) = 0 for s.
-1, 0, 1
Let c(j) = -2*j + 2. Let q be c(3). Let o = 6 + q. Find p such that -2*p**3 - p - p**4 + p**3 + p**2 + o*p = 0.
-1, 0, 1
Let d = 51 - 51. Suppose 0 + d*q**4 - 6/5*q**3 + 3/5*q + 0*q**2 + 3/5*q**5 = 0. Calculate q.
-1, 0, 1
Let u(a) = -a**2 + 6*a + 7. Let m(w) = w**3 - 7*w**2 - 7*w - 1. Let s be m(8). Let f be u(s). Factor -2/3*i**3 + 0 + f*i + 2/3*i**2 + 2/3*i**5 - 2/3*i**4.
2*i**2*(i - 1)**2*(i + 1)/3
Let z(w) be the third derivative of -w**9/68040 + w**7/5670 - w**5/540 - w**4/4 + 4*w**2. Let t(m) be the second derivative of z(m). Let t(n) = 0. Calculate n.
-1, 1
Let k be 231/92*2/3. Let b = k - 4/23. Factor -1/2*r**4 + r + b*r**3 - 1/2*r**5 + 5/2*r**2 + 0.
-r*(r - 2)*(r + 1)**3/2
Determine a, given that 4/7*a**4 + 12/7*a**3 + 12/7*a**2 + 4/7*a + 0 = 0.
-1, 0
Let t(z) = -z**2 - 7*z - 6. Let m be t(-6). Let a be (-2 - (-27)/12) + m. Factor 0*i**2 + 1/4*i**3 + 0 - a*i**4 + 0*i.
-i**3*(i - 1)/4
Let m(u) = 7*u - 2. Let o be m(1). Let c(p) be the second derivative of 2/3*p**3 + p + 2/5*p**o + 1/15*p**6 + 0 + 5/6*p**4 + 0*p**2. What is n in c(n) = 0?
-2, -1, 0
Let k(a) be the second derivative of 0 + 1/25*a**5 + 1/105*a**7 - 1/5*a**3 + 1/25*a**6 - 1/5*a**2 - 1/15*a**4 + 3*a. What is l in k(l) = 0?
-1, 1
Let f(n) = 9*n**2 + 24. Let i(p) = -p**2 - 3. Let q(t) = -4*f(t) - 33*i(t). Factor q(l).
-3*(l - 1)*(l + 1)
Let g(i) be the first derivative of -2*i**3/21 + i**2/7 - 28. Factor g(t).
-2*t*(t - 1)/7
Let d = 405 - 1199/3. Factor -13/3*s**2 - d*s - 4/3 - s**3.
-(s + 2)**2*(3*s + 1)/3
Let c = 70 + -66. Let a(y) be the first derivative of 2*y + 2/5*y**5 - 1/3*y**6 - y**2 + y**c + 4 - 4/3*y**3. Factor a(g).
-2*(g - 1)**3*(g + 1)**2
Suppose -2*j = 3*j - 30. Let n(a) = 5*a + 9 + 155*a**2 + 335*a**3 + 2 + 0. Let g(p) = -168*p**3 - 78*p**2 - 2*p - 6. Let i(d) = j*n(d) + 11*g(d). Factor i(y).
2*y*(9*y + 2)**2
Let k(m) = 3*m**5 - m**4 - 2*m**3 + 2*m + 2. Let c(n) = -7*n**5 + 3*n**4 + 5*n**3 - 5*n - 5. Let v(w) = 2*c(w) + 5*k(w). Find j, given that v(j) = 0.
-1, 0
Let b be 75/12 - 2/8. Solve -9*r**2 + 9*r - b + 5*r**2 + r**2 = 0.
1, 2
Let b = 556/3 - 185. Factor b + 1/3*x**3 + x + x**2.
(x + 1)**3/3
Let w(m) be the third derivative of 1/168*m**8 + 3*m**2 + 0*m**6 - 1/12*m**4 + 1/15*m**5 + 0 + 0*m - 2/105*m**7 + 0*m**3. Factor w(d).
2*d*(d - 1)**3*(d + 1)
Suppose -u - 6 = -n - n, 5*n - 2 = -4*u. Let c be 1 + -1 + n/1. Solve -3*t**2 + 4*t**c + 8*t + 0 - 3*t**2 - 8 = 0.
2
Let u be ((-6)/9)/(1/(-3)). Find m such that m**u - 2*m**2 - 2*m**3 + 5*m**2 + 4*m**3 + 2*m = 0.
-1, 0
Find i such that 2/5*i**4 + 0 - 2/5*i**2 - 4/5*i**3 + 4/5*i = 0.
-1, 0, 1, 2
Let q(f) be the third derivative of 0*f - 3/2*f**3 + 0 + 1/20*f**5 + 10*f**2 + 1/4*f**4. Factor q(i).
3*(i - 1)*(i + 3)
Let q(n) be the third derivative of 0 + 1/112*n**8 + 3/8*n**4 - 1/10*n**5 + 0*n**7 + n**3 - 7*n**2 - 1/10*n**6 + 0*n. Find p, given that q(p) = 0.
-1, 1, 2
Let a(v) be the first derivative of -v**5 + 5*v**4/4 - 21. Determine b so that a(b) = 0.
0, 1
Let f(o) be the second derivative of 0*o**6 + 1/1260*o**7 + 1/12*o**4 + o + 0*o**5 + 0 + 0*o**2 + 0*o**3. Let q(c) be the third derivative of f(c). Factor q(w).
2*w**2
Let f = -46 + 46. Find z such that 1/2*z**3 - 1/2*z + f*z**2 + 0 = 0.
-1, 0, 1
Suppose 4*h + 7 = -4*u + u, -3*h - 14 = 4*u. Let g = 8 + u. Find w such that -2/7*w + 0 + 2/7*w**g + 0*w**2 = 0.
-1, 0, 1
Suppose c = -y + 9, c = 3*c + 5*y - 33. Suppose -3*l = c*t - 1 - 0, 0 = 4*l - 2*t - 16. Suppose -2*m + m**l + m**3 + 0*m = 0. What is m?
-1, 0, 1
Let d(x) be the first derivative of 2*x**6/3 - 4*x**4 + 8*x**3/3 + 6*x**2 - 8*x - 6. Let d(j) = 0. Calculate j.
-2, -1, 1
Let k(u) = u. Let l be k(3). Let h(m) be the third derivative of 2/3*m**l + 0*m - 3*m**2 + 1/12*m**4 + 0 - 1/30*m**5. Suppose h(i) = 0. Calculate i.
-1, 2
Let k be 6*(-12)/18*-1. Let c(i) be the first derivative of -2*i**3 - 2*i**2 - 1/5*i**5 - i - 3 - i**k. Factor c(x).
-(x + 1)**4
Suppose -6/5*v**3 + 12/5 - 12/5*v**2 + 6/5*v = 0. What is v?
-2, -1, 1
Suppose 0 = -5*s + 5*x - 10, -4*s + x + 27 = 4*x. Let n(r) be the first derivative of 16/3*r**s + 2*r**2 + 2 + 0*r + 15/4*r**4. What is u in n(u) = 0?
-2/3, -2/5, 0
Suppose 25 = 7*f - 2*f, -4*l = 2*f - 22. Let b(p) be the first derivative of -l + 0*p + 1/4*p**3 - 1/8*p**2 - 3/16*p**4 + 1/20*p**5. Factor b(h).
h*(h - 1)**3/4
Suppose 1/5*i**2 + 6/5*i + 9/5 = 0. What is i?
-3
Let w(g) be the first derivative of g**4/20 + 8*g**3/15 + 13*g**2/10 + 6*g/5 + 57. Let w(v) = 0. What is v?
-6, -1
Suppose -2*y - 2*s - 5 = -1, 3*s + 6 = 0. Factor -1/4*k**2 + y - 1/4*k + 5/4*k**3 - 3/4*k**4.
-k*(k - 1)**2*(3*k + 1)/4
Factor 0 + 3/4*z**3 + 3/2*z**4 + 0*z + 3/4*z**5 + 0*z**2.
3*z**3*(z + 1)**2/4
Factor 1/5*d**2 - d - 6/5.
(d - 6)*(d + 1)/5
Let m be -2*5*(-2)/4. Let x = 0 + m. Solve -2*w**5 + 2*w**x + w - 2*w + 2*w**3 - w**5 = 0 for w.
-1, 0, 1
Let z(m) = m**3 - 13*m**2 + 2. Let x be z(13). Factor 2*v**x - 3 - 6 + 3 - 4*v**2 - 8*v.
-2*(v + 1)*(v + 3)
Let k = 520/7 - 74. Factor k + 1/7*u**2 + 3/7*u.
(u + 1)*(u + 2)/7
Let u(s) = -4*s**2 + 4. Let h(p) = -p**2 + 1. Let c(y) = -6*h(y) + u(y). Factor c(g).
2*(g - 1)*(g + 1)
Factor -4/3*o**4 + 0 - 2/3*o**2 + 7/3*o**3 - 1/3*o.
-o*(o - 1)**2*(4*o + 1)/3
Let v = -14 + 9. Let n(y) = -7*y**3 - 4*y**2 - 5*y - 5. Let j(g) = 4*g**3 + 2*g**2 + 3*g + 3. Let q(t) = v*j(t) - 3*n(t). Factor q(p).
p**2*(p + 2)
Let c(y) be the third derivative of 49*y**7/75 + 637*y**6/300 + 63*y**5/25 + 23*y**4/15 + 8*y**3/15 + 7*y**2. Factor c(b).
2*(b + 1)*(7*b + 2)**3/5
Suppose -y + 2*g = -8, 4*g + 16 = 5*y - 0*y. Factor y*c**2 + 1/3*c + 0 - 1/3*c**3.
-c*(c - 1)*(c + 1)/3
Let q(l) be the third derivative of l**8/18144 + l**7/11340 - l**5/30 + 5*l**2. Let r(u) be the third derivative of q(u). Let r(m) = 0. Calculate m.
-2/5, 0
Suppose 19*d + 40 = 39*d. Let d*u + 2 + 9/2*u**4 - 11/2*u**2 - 3*u**3 = 0. Calculate u.
-2/3, 1
Let v be 0/(-1) - 5763/21. Let n = v - -275. Let -2/7*u**5 + 8/7*u**2 - 4/7 + 4/7*u**3 - 2/7*u - n*u**4 = 0. What is u?
-2, -1, 1
Let g(k) be the third derivative of 2*k**7/15 - 8*k**6/15 + 4*k**5/15 - 59*k**2. Solve g(t) = 0.
0, 2/7, 2
Let f be 5/10*(-9)/(-30). Let i(r) be the first derivative of 1/5*r**2 - 1/3*r**3 + 1 + 0*r - f*r**4. What is k in i(k) = 0?
-2, 0, 1/3
Determine k so that -1/6*k**2 + 1/6*k + 1 = 0.
-2, 3
Let c = 4 - 2. Let m(z) = z**2 + 4*z - 2 + c + 0. Let b(q) = q. Let f(d) = 4*b(d) - m(d). Suppose f(o) = 0. Calculate o.
0
Let m be 22/24 + 12/(-18). Suppose 5*i = -2*u + 16, 2*u - 9 = -3*i + 3. Solve -m*d**i + 3/4*d - 1/2 = 0.
1, 2
Let w(z) = 10*z**5 - 11*z**4 + 18*z**3 - 13*z**2 + 2*z + 6. Let f(l) = 9*l**5 - 12*l**4 + 19*l**3 - 13*l**2 + 2*l + 5. Let c(n) = 6*f(n) - 5*w(n). Factor c(x).
x*(x - 2)*(x - 1)**2*(4*x - 1)
Let n(v) be the second derivative of 2*v**7/21 - 2*v**6/15 - v**5/5 + v**4/3 - 4*v. Factor n(c).
4*c**2*(c - 1)**2*(c + 1)
Suppose 2*y + 0*h + 5*h + 6 = 0, 3*y + 2*h = 2. Let t = 0 + 3. Factor -4*q**t - 6*q + 2 + 6*q**2 + y*q**3 + 0*q.
-2*(q - 1)**3
Factor 1/2*l**4 + 5/4*l**3 + l**2 + 1/4*l + 0.
l*(l + 1)**2*(2*l + 1)/4
Let t = -77/3 + 26. Let n(p) be the first derivative of -t*p**2 - 2/9*p - 1/18*p**4 - 2 - 2/9*p**3. Factor n(u).
-2*(u + 1)**3/9
Let s(g) be the first derivative of g**7/1680 - g**6/720 - g**5/240 + g**4/48 - g**3/3 - 1. Let z(u) be the third derivative of s(u). Factor z(d).
(d - 1)**2*(d + 1)/2
Let i(r) be the second derivative of -r**7/420 + r**5/60 - r**3/6 - 2*r. Let d(v) be the second derivative of i(v). Factor d(t).
-2*t*(t - 1)*(t + 1)
Let b be (-10)/(-4 - (0 - 2)). Let v(f) be the third derivative of 0*f**4 + f**2 + 1/30*f**b + 0*f**3 + 0 - 1/60*f**6 + 0*f. Factor v(p).
-2*p**2*(p - 1)
Let f(t) = -t**2 + 6*t + 1. Let d be f(5). Suppose -6*u**2 - d*u + 4*u**2 + 2 + u**3 + 5*u = 0. Calculate u.
-1, 1, 2
Let -2*u + 1/2*u**3 - 4 + u**2 = 0. Calculate u.
-2, 2
Let y(p) = p**4 - p**3 - p**2 - 1. Let i(v) = v**3 + 2