be the third derivative of 0*m + 0*m**4 + m**2 + 1/80*m**6 + 1/120*m**5 + 0*m**3 + 0 + 1/140*m**o + 1/672*m**8. Factor v(l).
l**2*(l + 1)**3/2
Let g(s) be the second derivative of 0*s**2 + 1/3*s**3 + s + 1/10*s**5 + 0 - 1/3*s**4. Suppose g(a) = 0. Calculate a.
0, 1
Suppose 3*q - 6 = -0*q. Factor -3 + 0*p**2 + 2*p**2 + 5*p**q - 4*p**2.
3*(p - 1)*(p + 1)
Determine k so that -8 - 226*k**3 + 147*k**5 + 87*k**4 + 49*k**5 - 82*k**2 + 3*k**4 + 64*k - 34*k**5 = 0.
-1, 2/9, 1
Let i(g) = -g + 5. Let f be i(4). Let h be 3/f + 0/5. What is k in -5*k**2 - 8 - h*k**2 + 0*k**2 - 32*k - 34*k**2 - 18*k**3 = 0?
-1, -2/3
Let i = -65/2 + 34. Let u(n) be the first derivative of 3 + 1/3*n**3 + 2*n - i*n**2. Factor u(q).
(q - 2)*(q - 1)
Let w = -509/6 - -85. Let d(p) be the second derivative of 0 - p - w*p**3 - 1/24*p**4 - 1/4*p**2. Factor d(c).
-(c + 1)**2/2
Let r(t) be the first derivative of -t**4/2 - 2*t**3/3 + 2*t**2 - 31. Solve r(o) = 0.
-2, 0, 1
Let w = 142/175 + -2/175. Solve -8/5*v + v**2 - 1/5*v**3 + w = 0 for v.
1, 2
Let h(g) be the first derivative of g**6/18 + 4*g**5/15 + g**4/2 + 4*g**3/9 + g**2/6 - 9. Factor h(o).
o*(o + 1)**4/3
Find g such that 24*g**2 - 128 - 9*g + 41*g - 8*g**3 - 8*g**3 + g**4 + 6*g**3 = 0.
-2, 4
Let l(v) be the third derivative of v**5/45 + 5*v**4/18 + 8*v**3/9 + 8*v**2. Determine z, given that l(z) = 0.
-4, -1
Let f be (-20)/6*18/(-15). Find w such that -w + 4*w**3 - w**5 - 2*w**3 + 85*w**4 - 85*w**f = 0.
-1, 0, 1
Let g(u) be the third derivative of u**9/9072 - u**8/2520 - u**7/2520 + u**6/540 + 4*u**3/3 + 2*u**2. Let q(w) be the first derivative of g(w). Factor q(k).
k**2*(k - 2)*(k - 1)*(k + 1)/3
Let p(d) be the first derivative of -1/4*d - 1/4*d**3 + 1 + 3/8*d**2 + 1/16*d**4. Factor p(m).
(m - 1)**3/4
Let k(i) be the first derivative of 0*i - 2/15*i**3 - 2/5*i**2 + 7. Factor k(t).
-2*t*(t + 2)/5
Suppose 4*r = -q, q - 11 = r + 4*q. Let y = r - -1. Suppose 4/3*n**3 + 2/3 - 2/3*n**5 - 4/3*n**y - 2/3*n + 2/3*n**4 = 0. Calculate n.
-1, 1
Solve -2/5*w + 0 - 22/5*w**3 + 2*w**4 + 14/5*w**2 = 0 for w.
0, 1/5, 1
Let j(b) be the third derivative of 0*b**3 + b**2 - 1/24*b**4 + 0*b + 0 - 1/60*b**5. Factor j(y).
-y*(y + 1)
Suppose 5*a - 5*b + 5 = 0, -3*a + 0*b = b - 9. Factor -2 + 2*d - 2*d**3 + 0*d**a + d**2 + d**2 + 0*d.
-2*(d - 1)**2*(d + 1)
Let x(b) be the third derivative of b**7/105 - b**6/30 - 23*b**2. Determine u, given that x(u) = 0.
0, 2
Let o(v) = v**3 - 9*v**2 - 2*v - 4. Let p be o(9). Let i = -19 - p. Factor -1/5*z**i + 0*z + 0 - 1/5*z**2.
-z**2*(z + 1)/5
Let j be ((-3)/3)/((-1)/(-1)). Let x be j - ((-11)/(-9))/(-1). Suppose 2/3*w**3 + 10/9*w**2 - x + 2/9*w = 0. Calculate w.
-1, 1/3
Let a(s) = -s**5 + s**3 - s**2 + s. Let q(o) = -7*o**5 + 3*o**4 + 3*o**3 - 5*o**2 + 6*o. Let j(r) = -6*a(r) + q(r). Find t such that j(t) = 0.
0, 1
Suppose 3*j + 4 = -5. Let q(g) = 3*g**3 - 3*g**2 - 3*g - 3. Let p(y) = -y**4 - 6*y**3 + 6*y**2 + 6*y + 5. Let h(k) = j*p(k) - 5*q(k). Factor h(t).
3*t*(t - 1)*(t + 1)**2
Let t(g) be the second derivative of -1/4*g**4 - 3*g - g**2 + 1/30*g**6 - 1/20*g**5 + 5/6*g**3 + 0. Factor t(a).
(a - 1)**3*(a + 2)
What is n in 0 + 1/3*n**2 + 4/3*n = 0?
-4, 0
Suppose -14 + 23 = 3*h. Solve 4/3*r**h + 0 - 10/3*r**2 + 10/3*r**4 - 4/3*r = 0.
-1, -2/5, 0, 1
Let u(p) = -p**2 + p + 6. Let t be u(-2). Find c, given that -2/7*c**3 - 2/7*c**4 + 2/7*c**2 + 2/7*c**5 + t + 0*c = 0.
-1, 0, 1
Let u(w) be the third derivative of w**7/315 + w**6/45 + w**5/45 - w**4/9 - w**3/3 - 22*w**2. Factor u(j).
2*(j - 1)*(j + 1)**2*(j + 3)/3
Let k(m) be the first derivative of -m**4/36 - m**3/9 - m**2/9 + 1. Factor k(p).
-p*(p + 1)*(p + 2)/9
Let w(y) be the third derivative of 0*y**3 + 1/200*y**6 - 1/350*y**7 + 1/100*y**5 + 2*y**2 + 0*y - 1/40*y**4 + 0. What is j in w(j) = 0?
-1, 0, 1
Suppose a + 2 = 5*g, 0*a - 11 = -3*a - 2*g. Factor 1/2*h**2 - 1/4*h + 1/4*h**a - 1/2.
(h - 1)*(h + 1)*(h + 2)/4
Let c(b) = b**3 - 10*b**2 + b - 4. Let n be c(10). Find k, given that 3*k**3 + 3*k - k**3 - n*k**2 + k**3 = 0.
0, 1
Factor 19/4*o + 3/2 - 19/4*o**2 + o**3.
(o - 3)*(o - 2)*(4*o + 1)/4
Suppose -24*u + 118 - 22 = 0. Let 2/7*p**2 + 0*p**3 - 2/7*p**u + 0 + 0*p = 0. Calculate p.
-1, 0, 1
Let c = 30 - 30. Let z(w) be the second derivative of 1/60*w**4 + c - 3*w - 1/30*w**3 - 1/5*w**2. Factor z(u).
(u - 2)*(u + 1)/5
Let g(x) be the third derivative of -2*x**2 - 1/30*x**4 - 1/300*x**6 + 0*x**3 + 1/50*x**5 + 0 + 0*x. Factor g(f).
-2*f*(f - 2)*(f - 1)/5
Let a(i) be the second derivative of -2*i**6/5 + i**5 - i**4/3 - 2*i**3/3 + 56*i. Factor a(q).
-4*q*(q - 1)**2*(3*q + 1)
Let w(y) = -4*y + 3*y - y**3 + 2*y**3. Let o(r) = -6*r**3 + 4*r**2 + 2*r. Suppose 7 = -i + 3. Let z(s) = i*w(s) - o(s). Factor z(f).
2*f*(f - 1)**2
Let a(d) be the third derivative of d**6/60 + 7*d**5/90 - 4*d**3/9 - 6*d**2. Factor a(p).
2*(p + 1)*(p + 2)*(3*p - 2)/3
Solve 27*s**3 - 106*s + 3*s**5 + 6*s**4 - 24*s**4 + 106*s = 0 for s.
0, 3
Let d(n) = -n**2 + 2*n + 2. Let c be d(0). Let j be ((-3)/c)/(27/(-12)). Determine f, given that -j + 1/3*f**2 + 1/3*f = 0.
-2, 1
Let d(b) = -45*b + 5. Let x be d(0). Suppose -9*o**x - 15/4*o**3 + 15/4*o - 45/4*o**2 + 75/4*o**4 + 3/2 = 0. What is o?
-2/3, -1/4, 1
Factor 2*v**2 + v**2 - 4*v**2 + 2 + 3*v**2 + 4*v.
2*(v + 1)**2
Let j be (-1)/(-3) + 3 + (-1 - 2). Let n(z) be the first derivative of -1/6*z**2 - 3 + 1/9*z**3 - j*z + 1/12*z**4. Solve n(v) = 0.
-1, 1
Factor -2*y**2 + 2/5*y + 2 - 2/5*y**3.
-2*(y - 1)*(y + 1)*(y + 5)/5
Determine u so that 0 + 8/9*u**2 + 0*u - 10/9*u**3 + 2/9*u**4 = 0.
0, 1, 4
Solve 8/5 + 16/5*c - 18/5*c**2 - 16/5*c**3 + 2*c**4 = 0 for c.
-1, -2/5, 1, 2
Let f(v) be the second derivative of v**8/840 + v**7/140 - v**5/15 + v**3/2 - 3*v. Let o(q) be the second derivative of f(q). Determine h, given that o(h) = 0.
-2, 0, 1
Let n(r) = 2*r + 21. Let j be n(-18). Let x = 49/3 + j. Factor x + 14*k**2 - 26/3*k.
2*(3*k - 1)*(7*k - 2)/3
Let n(c) be the first derivative of -9*c**4/13 - 46*c**3/39 - 3*c**2/13 + 4*c/13 + 28. Find v such that n(v) = 0.
-1, -1/2, 2/9
Suppose 5*g + 4 = -3*m + g, -5*m - 1 = g. Let r(q) be the second derivative of 1/6*q**3 - 2/15*q**6 + 0*q**2 - 1/2*q**4 - 2*q + m + 9/20*q**5. Factor r(j).
-j*(j - 1)**2*(4*j - 1)
Let a = 132 + -93/2. Let g = a - 84. Determine d so that -1/2*d**3 + 1/2*d + 0 + 3/2*d**4 - g*d**2 = 0.
-1, 0, 1/3, 1
Let g be (4 + -5)/(1/(-3)). Let -2*k**g + 4*k**3 - 3*k - k**5 + 2*k = 0. What is k?
-1, 0, 1
Let m(d) = -d**4 + d**3 - 1. Let y = -4 - -6. Let p(k) = -2*k**5 - 16*k**4 + 8*k**3 + 6*k**2 + 4*k - 10. Let i(v) = y*p(v) - 20*m(v). Solve i(a) = 0.
-2, -1, 0, 1
Let t(z) be the first derivative of -z**3/3 + 2*z**2 - 4*z - 7. Determine i so that t(i) = 0.
2
Suppose 0 = 4*k - 5*b - 102, -3*b + 84 = 4*k + b. Suppose 4*f + 7 = k. Find s such that s**f - s**3 - s**4 + s**4 = 0.
0, 1
Let y be (-10)/(-4) - (-4)/8. Solve b**3 + b**3 + b**2 - 4*b**y + b**2 = 0 for b.
0, 1
Let w be (4 - 3) + (-6)/10. Suppose 6*x - 2*x - 12 = 0. Factor -1/5*j - w*j**4 + 0 + 0*j**x + 2/5*j**2 + 1/5*j**5.
j*(j - 1)**3*(j + 1)/5
Find x, given that 4/3*x - 2/3*x**2 + 0 = 0.
0, 2
Let o(v) be the second derivative of 0*v**2 + 0*v**4 - 2*v + 0*v**5 + 0 + 1/6*v**3 - 1/540*v**6. Let p(q) be the second derivative of o(q). Factor p(r).
-2*r**2/3
Let u(a) be the second derivative of -a**6/12 + a**5/10 + a**4/24 - 27*a. Let u(w) = 0. What is w?
-1/5, 0, 1
Let k(l) be the first derivative of -1/240*l**6 + 0*l - 1/40*l**5 - 2 + 2*l**2 + 1/3*l**3 + 0*l**4. Let z(m) be the second derivative of k(m). Factor z(s).
-(s - 1)*(s + 2)**2/2
Let l = 22 + -17. Let a(m) be the second derivative of -128/25*m**l - 256/75*m**6 - 16/15*m**3 + 2*m + 0 - 1/5*m**2 - 16/5*m**4. Factor a(r).
-2*(4*r + 1)**4/5
Suppose 4 + 0 = -4*t - 4*j, 3*j = 2*t - 8. Let z = 3 - t. Factor 4*a**3 - 27*a**2 - 6 - 5*a**3 - z*a**3 + 27*a + 9*a**4.
3*(a - 1)**2*(a + 2)*(3*a - 1)
Factor -z + 2 + 0*z + 0*z**2 + z**2 - 4.
(z - 2)*(z + 1)
Let d be (4 + (-1632)/405)/(4/(-10)). Let i(x) be the first derivative of 0*x**2 + 1/27*x**6 + 0*x - 1 + d*x**3 - 1/18*x**4 - 2/45*x**5. Solve i(z) = 0.
-1, 0, 1
Let y(x) be the first derivative of x**4/4 + 5*x**3/3 + 2*x**2 - 21. Factor y(s).
s*(s + 1)*(s + 4)
Let n(i) be the third derivative of 0*i**3 + 0*i + 1/336*i**8 - 1/315*i**7 + 0 + 0*i**4 - 3*i**2 