30307/210 - -4355/7. Let f(g) be the second derivative of -1/3*g**4 + z*g**6 + 0*g**3 + 0*g**5 + 0*g**2 + g + 0. Solve f(v) = 0 for v.
-2/7, 0, 2/7
Let q(p) be the second derivative of -3*p**8/2240 + p**7/420 + p**6/80 - p**5/20 - p**4/6 + 5*p. Let r(a) be the third derivative of q(a). Factor r(j).
-3*(j - 1)*(j + 1)*(3*j - 2)
Let m(u) be the first derivative of 2*u**6/3 + 24*u**5/5 + 14*u**4 + 64*u**3/3 + 18*u**2 + 8*u - 5. Factor m(r).
4*(r + 1)**4*(r + 2)
Let k(q) be the first derivative of -2*q**6/3 + 7*q**5/5 + q**4/8 - 13*q**3/6 + 7*q**2/4 - q/2 - 3. Find j, given that k(j) = 0.
-1, 1/4, 1/2, 1
Let n(i) be the second derivative of -i**6/165 + 3*i**5/110 - i**4/33 - 12*i. Factor n(l).
-2*l**2*(l - 2)*(l - 1)/11
Let k = -162 - -814/5. Factor 2/5*g**4 - 2/5*g + 2/5 - 4/5*g**2 + k*g**3 - 2/5*g**5.
-2*(g - 1)**3*(g + 1)**2/5
Let h be (4/(-6))/((-1)/(-3)). Let p be 5/2 + 1/h. Factor u**3 + 3*u**3 - 4*u + 0*u**3 + p - 2*u**4 + 0.
-2*(u - 1)**3*(u + 1)
Let b(x) be the third derivative of -x**7/1050 + x**6/150 + 11*x**5/300 + x**4/20 + 4*x**2 + 5. Factor b(o).
-o*(o - 6)*(o + 1)**2/5
Suppose 10*g - g**5 + 14*g**3 + 5*g**5 + 38*g**3 + 6*g + 48*g**2 + 24*g**4 = 0. What is g?
-2, -1, 0
Suppose c - 6*c = -4*j + 24, -5*j = -5. Let k be (-18)/4*c/6. Solve 0 + 4/5*z**k - 2/5*z**4 + 0*z - 2/5*z**2 = 0.
0, 1
Factor 0*d**3 + 0 + 6/5*d - 3/5*d**4 + 9/5*d**2.
-3*d*(d - 2)*(d + 1)**2/5
Solve -14*h**2 - 14*h - 106*h - 1200 + 8*h**2 + 3*h**2 = 0.
-20
Let t be (-26)/(-36) - 140/630. Factor -h + 1/2 + t*h**2.
(h - 1)**2/2
Factor 5/4*h**4 + 0*h**3 - 15/4*h**2 + 5/2*h + 0.
5*h*(h - 1)**2*(h + 2)/4
Find y such that -21*y**3 - 36*y**2 - 24*y + 3*y**3 + 0 - 3*y**4 + 0 = 0.
-2, 0
Let w(v) be the first derivative of 2*v**3/21 - 2*v**2/7 - 6*v/7 - 10. Let w(f) = 0. Calculate f.
-1, 3
Let v = 647/2 + -323. Factor -v*x**2 - 1/2*x + 0.
-x*(x + 1)/2
Suppose 2*l = f + 10, 3*l + f + 9 = 24. Factor 1/4*i**l - 1/4 - 1/4*i**4 + 1/4*i + 1/2*i**2 - 1/2*i**3.
(i - 1)**3*(i + 1)**2/4
Find h such that 2/19 + 16/19*h**2 + 32/19*h**3 - 14/19*h = 0.
-1, 1/4
Let z = -1139/5 - -228. Suppose z - 1/5*g - 1/5*g**2 + 1/5*g**3 = 0. Calculate g.
-1, 1
Let a = -3/53 + 271/106. Factor 0 - c**3 - a*c**4 + c + 5/2*c**2.
-c*(c - 1)*(c + 1)*(5*c + 2)/2
Suppose y + p - 8 = 0, y - 3*p - 16 = -y. Factor 6*t**4 - 2*t + 2*t**5 + y*t**3 + 2*t + 2*t**2 - 2*t**3.
2*t**2*(t + 1)**3
Let g(b) be the second derivative of 3*b**5/140 + 3*b**4/28 + b**3/7 + 2*b + 6. Find q, given that g(q) = 0.
-2, -1, 0
Let x(q) be the second derivative of 1/15*q**6 + 0 + q + 0*q**4 + 0*q**3 + 1/27*q**7 + 1/45*q**5 + 0*q**2. Solve x(f) = 0 for f.
-1, -2/7, 0
Let k(p) = p**5 + 7*p**4 + 3*p**3 - 9*p**2 - 6*p. Let a(y) = 3*y**5 + 27*y**4 + 12*y**3 - 36*y**2 - 24*y. Let b(x) = 2*a(x) - 9*k(x). Let b(u) = 0. Calculate u.
-2, -1, 0, 1
Let y(k) = -k**3 + k**2 + 1. Let m(o) = 2*o**2 + 10. Let d(z) = m(z) - 4*y(z). Let h(u) = -u**3 - 1. Let a(w) = -d(w) - 6*h(w). Find j, given that a(j) = 0.
-1, 0
Find m, given that 1/5*m**2 + 1/5 - 2/5*m = 0.
1
Let u = 4 + -1. Let y(w) be the third derivative of 0*w + 0 + 1/30*w**5 + 3*w**2 + 1/60*w**6 - 1/12*w**4 - 1/3*w**u. Factor y(p).
2*(p - 1)*(p + 1)**2
Let d(w) = w**3 - 6*w**2 + w - 4. Let f be d(6). Factor -6*r**f - 4*r**3 - 7*r**2 + 5*r**2.
-4*r**2*(r + 2)
Let v(p) be the first derivative of 1/2*p**2 + 3/5*p**5 - p**3 - 2 - 1/4*p**4 + 0*p. Factor v(m).
m*(m - 1)*(m + 1)*(3*m - 1)
Let s(o) be the first derivative of o**4/24 + o**3/6 + o**2/4 - 3*o + 6. Let d(r) be the first derivative of s(r). Suppose d(n) = 0. What is n?
-1
Let f(i) be the second derivative of i**6/40 - i**5/10 - i**4/8 + i**3 + 3*i**2 + 4*i. Let n(b) be the first derivative of f(b). Factor n(k).
3*(k - 2)*(k - 1)*(k + 1)
Let n(o) be the first derivative of o**6/15 - 2*o**5/25 - 3*o**4/10 + 2*o**3/3 - 2*o**2/5 - 8. Determine d, given that n(d) = 0.
-2, 0, 1
Determine q so that 8 - 14*q**2 - 11 - 6 + 21*q + 3*q**3 - q**2 = 0.
1, 3
Let x(g) be the first derivative of -g + 3 - 1/12*g**3 + 1/2*g**2. Factor x(f).
-(f - 2)**2/4
Let c be (-17 + 5)/(0 + -2 - 8). Factor -6/5*i + c*i**2 - 2/5*i**3 + 2/5.
-2*(i - 1)**3/5
Let x(o) be the second derivative of 0*o**3 - 1/3*o**2 + 4*o + 0 + 1/18*o**4. Factor x(l).
2*(l - 1)*(l + 1)/3
Let z(q) = q**2 - 5*q + 3. Let x(k) = -1 + 0 + 4*k - 3*k. Suppose -2*c + 2 = 6. Let s(r) = c*z(r) - 6*x(r). Factor s(t).
-2*t*(t - 2)
Let n(o) be the first derivative of -16/9*o - 1/18*o**4 + 2 - 4/9*o**3 - 4/3*o**2. Factor n(i).
-2*(i + 2)**3/9
Suppose 2*j - 8 - 3 = -3*f, 5*f + 2*j = 25. Let l(u) = u**2 - 5*u - 10. Let n be l(f). Factor -d**4 + 7*d**n - 4*d**5 - d**4 - d**3.
-d**3*(d - 1)*(4*d - 1)
Let u be 1 - (-60)/13 - (-135)/(-27). Solve 2/13*h + 10/13*h**3 + 0 + u*h**2 + 4/13*h**4 = 0 for h.
-1, -1/2, 0
Factor -157*i**3 + 20*i**2 + 308*i**3 - 147*i**3.
4*i**2*(i + 5)
Let q(d) be the third derivative of -d**8/112 + d**7/70 + d**6/20 - d**5/10 - d**4/8 + d**3/2 - 11*d**2. Solve q(f) = 0 for f.
-1, 1
Let n(a) be the second derivative of a**5/60 - a**3/18 + 40*a. Factor n(d).
d*(d - 1)*(d + 1)/3
Suppose 0 = 2*d + 4*r - r - 96, -5*d + 190 = -5*r. Let q be (4/(-7))/((-12)/d). Let -4/5*x + 2/5*x**q + 2/5*x**3 + 0 = 0. Calculate x.
-2, 0, 1
Factor 61*a - 21*a - 80 - 5*a**2 + 0*a**2.
-5*(a - 4)**2
Let q(b) = b**2 + 2*b - 7. Let h be q(-5). Let a be (h/(-6))/((-12)/18). Factor 0*y**5 - y**5 - y + 2*y**2 + a*y**3 - 5 - 8*y**4 + 4 + 7*y**4.
-(y - 1)**2*(y + 1)**3
Suppose 3*r + 27 = 5*z, -5*z + 3*r - r = -23. Let 6/11*d**2 - 4/11*d + 0 - 2/11*d**z = 0. What is d?
0, 1, 2
Let d(j) = -13*j**2 - 5. Let q(n) = -7*n**2 - 3. Let u(z) = z**2 - 8*z + 12. Let h be u(7). Let a(i) = h*q(i) - 3*d(i). Find c such that a(c) = 0.
0
Suppose -6 - 18 = 3*t. Let c = 13 + t. Factor -2*j**4 - j**c + 8*j**4 + 2*j**5 + 8*j**2 + 12*j**3.
j**2*(j + 2)**3
Let q(j) = j**3 + 11*j**2 - j - 9. Let f be q(-11). Factor 3*i**2 - 3*i**3 - 2*i**f + 2*i**2 + 0*i**2.
-3*i**2*(i - 1)
Let o(j) be the second derivative of 14*j**6/15 + j**5 - 2*j**4/3 - 6*j. Solve o(x) = 0.
-1, 0, 2/7
Let h(k) be the second derivative of 9*k**5/140 - 4*k**4/21 + 5*k**3/42 + k**2/7 + 18*k. Let h(v) = 0. Calculate v.
-2/9, 1
Let o be ((-28)/70)/(-1*2). Let n(k) be the first derivative of -2/15*k**3 - o*k**2 + 2/25*k**5 + 1/10*k**4 + 2 + 0*k. Let n(w) = 0. Calculate w.
-1, 0, 1
Let o(u) be the first derivative of -u**8/420 + u**6/18 - 2*u**4/3 - 8*u**3/3 - 3. Let z(r) be the third derivative of o(r). What is g in z(g) = 0?
-2, -1, 1, 2
Let d(a) be the first derivative of -a**5/10 + a**3/3 + 5*a - 2. Let l(r) be the first derivative of d(r). Let l(z) = 0. Calculate z.
-1, 0, 1
Let t(b) = -1. Let y(k) = -k**2 + k + 3. Let p(w) = -3*t(w) - y(w). Solve p(g) = 0.
0, 1
Let u(x) = -6*x**5 - 15*x**4 - 12*x**3 + 2*x**2 + 5. Let w(n) = 6*n**5 + 15*n**4 + 12*n**3 - n**2 - 4. Let z(p) = 4*u(p) + 5*w(p). What is f in z(f) = 0?
-1, -1/2, 0
Suppose 5*p - 2*v - 34 + 20 = 0, -2*v = 4. Factor -3/5*x - 1/5*x**p - 2/5.
-(x + 1)*(x + 2)/5
Let z be (-95)/(-600) - 1/8. Let c(m) be the second derivative of 5/9*m**3 + 0 + z*m**5 - m + 2/3*m**2 + 2/9*m**4. Factor c(d).
2*(d + 1)**2*(d + 2)/3
Let y(m) be the third derivative of -2/3*m**3 - 1/4*m**4 + 2*m**2 + 0 - 1/240*m**6 - 1/20*m**5 + 0*m. Factor y(p).
-(p + 2)**3/2
Determine b, given that -2/3*b**4 - 1/3*b + 2/3*b**2 + 1/3*b**5 + 0 + 0*b**3 = 0.
-1, 0, 1
Determine k so that 0*k**4 - 6*k**3 - 7*k**2 + 7*k**4 + 4*k**5 + 2*k + 0*k**3 = 0.
-2, -1, 0, 1/4, 1
Suppose -2*o - 16*o + 54 = 0. Factor 0*x + 0 + 2/3*x**4 + 0*x**o + 0*x**2 - 2/3*x**5.
-2*x**4*(x - 1)/3
Let i be (22 - 24) + 1 + 1. Let r(j) be the second derivative of 1/18*j**4 + 1/63*j**7 + j - 1/45*j**6 + i + 0*j**3 - 1/30*j**5 + 0*j**2. Factor r(c).
2*c**2*(c - 1)**2*(c + 1)/3
Let b = 33 + -33. Suppose -4*o + 11 = 3. Factor 2/3*n + b - 2/3*n**o.
-2*n*(n - 1)/3
Let i(y) = 4*y**5 + 17*y**4 + 13*y**3 - 5*y**2 + 5*y - 5. Let w(a) = 2*a**5 + 9*a**4 + 7*a**3 - 3*a**2 + 3*a - 3. Let f(g) = -3*i(g) + 5*w(g). Factor f(j).
-2*j**3*(j + 1)*(j + 2)
Let j be -1*(2 - 3 - 3). What is w in 0*w**3 + 0*w**5 + 15*w**5 - 21*w**j + 6*w**3 = 0?
0, 2/5, 1
Let c(a) be the second derivative of -a**5/15 - a**4/18 - 3*a. Find u, given that c(u) = 0.
-1/2, 0
Let y(f) be the third derivative of -f**7/42 - f**6/24 + f**5/12 +