4*f**2 + 5*f - 3. Let m(a) = 9*a**3 - 8*a**2 + 9*a - 5. Let x(p) = z*m(p) - 5*g(p). Factor x(q).
2*q*(q - 1)**2
Let -4*f**2 - f - 3*f - 4*f**3 - 4 - 8*f**2 - 8*f = 0. Calculate f.
-1
Determine a, given that 9/4*a**3 - 3/2*a**2 + 0*a + 0 - 3/4*a**4 = 0.
0, 1, 2
Let 8/5*v - 2/5*v**3 + 16/5 - 4/5*v**2 = 0. Calculate v.
-2, 2
Factor 2/9 - 1/3*m**2 - 1/9*m + 1/9*m**3 + 1/9*m**4.
(m - 1)**2*(m + 1)*(m + 2)/9
Let c be 38/30 - 35/(-105). Factor -c - 2/5*s**2 + 8/5*s.
-2*(s - 2)**2/5
Let d(l) be the second derivative of 8*l**5/5 + 4*l**4 + 4*l**3 + 2*l**2 - l. Let d(k) = 0. What is k?
-1/2
Solve -n + 1/2*n**2 - 3/2 = 0 for n.
-1, 3
Let n(r) be the second derivative of -2*r**6/25 + 11*r**5/25 - r**4 + 6*r**3/5 - 4*r**2/5 + 6*r. Let n(o) = 0. What is o?
2/3, 1
Let r(n) be the first derivative of -n**5/210 + n**4/42 - n**3/21 - n**2/2 - 5. Let x(q) be the second derivative of r(q). Factor x(p).
-2*(p - 1)**2/7
Suppose 2*o - 9 = 3*x, 4*x - 2*x = -4*o - 22. Let c be (o + 3)*(-2)/(-6). Factor 0*b**4 - 1/2*b**5 + 0 + c*b**2 - 1/2*b + b**3.
-b*(b - 1)**2*(b + 1)**2/2
Let r(k) be the third derivative of 0*k + 0*k**3 + 0 + 1/180*k**5 - 1/72*k**4 + k**2. Find z such that r(z) = 0.
0, 1
Factor -16/9*g**2 + 4/9*g**3 + 16/9*g + 0.
4*g*(g - 2)**2/9
Let h(u) be the second derivative of -u**5/5 + 6*u**4 - 72*u**3 + 432*u**2 + 12*u. Factor h(s).
-4*(s - 6)**3
Let m(p) = 17*p**3 + 31*p**2 - 113*p + 47. Let v(i) = 8*i**3 + 16*i**2 - 56*i + 24. Let k(x) = 4*m(x) - 9*v(x). Suppose k(z) = 0. Calculate z.
-7, 1
Let u(z) be the second derivative of -2*z**6/5 + 66*z**5/25 - 57*z**4/20 - 23*z**3/2 + 15*z**2 + z + 2. Find i, given that u(i) = 0.
-1, 2/5, 5/2
Let v(h) = -h**2 - h + 1. Let p(j) = -3*j**2 - 3*j - 12. Let s(w) = p(w) - 6*v(w). Factor s(i).
3*(i - 2)*(i + 3)
Factor -17*y - 26*y**2 - 9 + 23*y**2 + 5*y - 3.
-3*(y + 2)**2
Let i(m) be the first derivative of -m**6/900 - m**5/150 - m**4/60 - m**3 - 2. Let h(f) be the third derivative of i(f). Find l such that h(l) = 0.
-1
Let a(w) = 2*w**2 + 2*w - 4. Suppose -n - 5 = 2*x, 0 = -x - 2*n + 1 + 1. Let m(s) = s**2 + 3*s - 5. Let h(z) = x*m(z) + 5*a(z). What is c in h(c) = 0?
0, 1/3
Let f be (-1)/(-2)*(-6)/3. Let p be 0 + ((-15)/21 - f). Factor -8/7*w**3 + 12/7*w**2 + p - 8/7*w + 2/7*w**4.
2*(w - 1)**4/7
Suppose 6 + y - 3*y**2 - y + 3*y - 6*y = 0. What is y?
-2, 1
Let m(b) = 11*b**2 + b - 1. Let w be m(1). Suppose -4*r = 3 - w. Solve -5*n**3 - n**r + 2*n + 2 - n**2 + 3*n**3 = 0 for n.
-1, 1
Let g(p) be the first derivative of -3/4*p**4 + 2*p**3 + 1 - 3/2*p**2 + 0*p. Factor g(r).
-3*r*(r - 1)**2
Let g be 30/7 + (-2)/7. Suppose -q - 2 + g = 0. Solve -2*k**3 + 12*k**q - 12*k**2 = 0 for k.
0
Let f(y) = -y**2. Let t = -9 + 10. Let a(g) be the second derivative of -2*g**4 - 2*g**3/3 + 2*g. Let i(b) = t*a(b) - 10*f(b). Factor i(o).
-2*o*(7*o + 2)
Suppose -3*o + 2 = 5*d, 5*o - 5*d - 29 - 1 = 0. Suppose r**3 + 8*r**4 - 2*r**2 - r**5 + 0*r**4 - 6*r**o = 0. Calculate r.
-1, 0, 1, 2
Let q(y) be the second derivative of y**7/42 - y**6/10 + 3*y**5/20 - y**4/12 + 17*y. Let q(r) = 0. What is r?
0, 1
Let v(h) be the second derivative of -h**6/30 + h**5/4 - 2*h**4/3 + 2*h**3/3 - 48*h. Factor v(l).
-l*(l - 2)**2*(l - 1)
Factor -3*k - 4*k + 3*k**2 + 2*k**3 + 5*k.
k*(k + 2)*(2*k - 1)
Let p(y) be the third derivative of -y**7/420 + y**6/120 + y**5/30 - y**4/24 - y**3/4 - 9*y**2. Solve p(x) = 0 for x.
-1, 1, 3
Suppose -2*a + 5*n - 1 = 0, n + 2*n + 1 = 2*a. Let -4*g**a - 10*g**2 + 8*g**3 + 8*g + 2*g**2 - 2*g**4 - 2 = 0. Calculate g.
1
Let o = 1/10 + -1/60. Let f(b) be the first derivative of -2 - 1/4*b + 0*b**2 + o*b**3. Solve f(a) = 0.
-1, 1
Let 28/3*n + 1/3*n**2 + 196/3 = 0. Calculate n.
-14
Factor 3*k**4 - 16*k**2 + 8*k**2 + 10*k**3 - 5*k**4.
-2*k**2*(k - 4)*(k - 1)
Let u(d) = 5*d**2 + 5*d - 7. Let y(g) = -1. Let m(c) = -u(c) - 3*y(c). Factor m(p).
-5*(p - 1)*(p + 2)
Solve -2*u**5 - 6*u**4 + 4*u + 6*u**2 + 0*u**5 + 0*u**5 - 2*u**3 = 0 for u.
-2, -1, 0, 1
Factor -4/3*l + 0 - 2/3*l**3 + 2*l**2.
-2*l*(l - 2)*(l - 1)/3
Find z, given that 2*z - 3/4*z**2 + 1/4*z**4 - 1/2*z**3 - 1 = 0.
-2, 1, 2
Let c(f) = 2*f**2 - f - 2. Let s be c(2). Let l be 5/(-2)*s/(-25). Let -2/5*w**5 - 4/5*w**2 + 4/5*w**4 + 0 + l*w + 0*w**3 = 0. Calculate w.
-1, 0, 1
Find i such that -1/3*i**2 + 13/3*i - 4 = 0.
1, 12
Let l = -148/3 + 50. Let y(q) be the second derivative of -1/36*q**4 - 2*q - 2/9*q**3 - l*q**2 + 0. Factor y(p).
-(p + 2)**2/3
Let g(t) be the third derivative of t**6/120 - t**5/240 + 14*t**2. Determine s, given that g(s) = 0.
0, 1/4
Solve 6/17*w**2 + 0 + 0*w - 2/17*w**3 = 0 for w.
0, 3
Suppose 7*s = -13*s + 2*s. Let i(d) be the third derivative of -1/150*d**5 - d**2 + s + 0*d + 1/15*d**3 + 0*d**4. Factor i(r).
-2*(r - 1)*(r + 1)/5
Let u(i) = -12*i**4 + 72*i**3 - 20*i**2 - 296*i - 192. Let h(c) = -8*c**4 + 48*c**3 - 13*c**2 - 197*c - 128. Let w(r) = 8*h(r) - 5*u(r). Factor w(d).
-4*(d - 4)**2*(d + 1)**2
Suppose -7*c + 17 = 3. Factor 25/4*n**4 + 9/4*n**5 + 21/4*n**3 + 3/4*n**c - 1/2*n + 0.
n*(n + 1)**3*(9*n - 2)/4
Let c be 10/24 - 7/(-21)*1. Determine k, given that -15/8*k**5 - 27/8*k**3 + 39/8*k**4 + 0 - 3/8*k**2 + c*k = 0.
-2/5, 0, 1
Let o(y) = -5*y**2 + 10*y. Let i(f) = 36*f**2 - 69*f. Let t(r) = 2*i(r) + 15*o(r). Factor t(v).
-3*v*(v - 4)
Let a(j) be the third derivative of 0*j**3 + 1/12*j**4 + 0 + 0*j - 4*j**2 + 1/60*j**5. Factor a(i).
i*(i + 2)
Let j(r) be the third derivative of 3*r**2 + 0*r - 2/135*r**5 + 0 + 1/36*r**4 + 1/27*r**3. Factor j(m).
-2*(m - 1)*(4*m + 1)/9
Let j(a) = 13*a**4 - 8*a**3 - 5*a**2 + 9*a + 9. Let l = -10 + 1. Let q(u) = 3*u**4 - 2*u**3 - u**2 + 2*u + 2. Let p(h) = l*q(h) + 2*j(h). Factor p(o).
-o**2*(o - 1)**2
Suppose -j + 4*s = 8, 3 = -5*j - 3*s + 9. Find w such that 3/2*w**4 + 3/2*w**5 + j*w**3 + 0*w + 0 + 0*w**2 = 0.
-1, 0
Suppose -19 - 1 = -4*q + 2*m, 5*m - 28 = -3*q. Let p be (1 - 3/q) + 1. Factor -1/2*o**2 + 3/2*o**3 - 1/2*o**4 - p*o + 1.
-(o - 2)*(o - 1)**2*(o + 1)/2
Let k(s) be the first derivative of 0*s - 1/6*s**3 + 1/4*s**2 - 1. Factor k(h).
-h*(h - 1)/2
Let 3*f**3 - 2*f - 3*f + 0*f + 2*f**3 + 20*f**2 - 20 = 0. Calculate f.
-4, -1, 1
Let i(t) be the third derivative of -1/180*t**6 + 2*t**2 + 0*t + 0 + 1/18*t**5 + 1/3*t**3 - 7/36*t**4. Let i(q) = 0. What is q?
1, 3
Let k(d) = 17*d**4 - 17*d**3 - 4*d**2 + 17*d + 13. Let y(p) = 8*p**4 - 8*p**3 - 2*p**2 + 8*p + 6. Let g(q) = -6*k(q) + 13*y(q). Factor g(o).
2*o*(o - 1)**2*(o + 1)
Let v(p) = p**3 - 2*p**2 - 9*p + 20. Let k be v(3). Suppose -2*d - 4 = -6*o + o, -5*o + 5*d = -10. Factor 6/5*s - 4/5 - 2/5*s**3 + o*s**k.
-2*(s - 1)**2*(s + 2)/5
Suppose -3*i - 15 = 0, 5*i = -t - 7 - 16. Let -1/4*y**5 + 1/2*y**3 + 0*y**t + 1/4*y**4 + 0 + 0*y = 0. What is y?
-1, 0, 2
Let k(z) be the first derivative of -18*z**5/115 - 39*z**4/46 - 110*z**3/69 - 25*z**2/23 + 2. Determine l so that k(l) = 0.
-5/3, -1, 0
Let d(z) be the first derivative of -3*z**4/8 - 7*z**3/12 + z**2/2 - 7*z + 7. Let v(a) be the first derivative of d(a). Let v(m) = 0. Calculate m.
-1, 2/9
Factor -4*y**2 - 16*y - 64/3 - 1/3*y**3.
-(y + 4)**3/3
Let w(p) = p**3 - p + 5. Let t be w(0). Suppose -t*f = -b + 40, 0 = -2*b + f + 4*f + 55. Factor 4 + 0*v**4 + 16*v**4 - 22*v**3 + 12*v - b*v**2 + 5*v**4.
(v - 1)**2*(3*v + 2)*(7*v + 2)
Let m be (3/2)/((-2)/(-4)). Let 10*r - r**2 - 3 - 7*r**2 + 1 + 2*r**m - 2 = 0. What is r?
1, 2
Let i = 74/45 - 4/9. Factor 0 - i*t**2 + 2/5*t**3 + 4/5*t.
2*t*(t - 2)*(t - 1)/5
Let h(z) = -z**3 - 2*z**2 + z - 3. Suppose -4*j - 2 = 10. Let s be h(j). Factor -4/5 - 2/5*k**s - 8/5*k**2 - 2*k.
-2*(k + 1)**2*(k + 2)/5
Let h(k) be the second derivative of 1/80*k**5 - 8*k + 0 - 1/24*k**3 + 1/8*k**2 - 1/48*k**4. Factor h(t).
(t - 1)**2*(t + 1)/4
Suppose 0 = -0*d - 2*d + 6. Suppose 2*y - 3*y = 3*h - 13, d*y + 5*h - 35 = 0. Solve -2*v**3 - 5 - 4*v**3 - 14*v**2 + 3 - y*v = 0.
-1, -1/3
Let q(c) be the first derivative of 4*c**6/3 + 12*c**5/5 - 4*c**3/3 - 10. Solve q(j) = 0.
-1, 0, 1/2
Let q(l) be the first derivative of -1/3*l**3 + 3 - 2/5*l**5 + 0*l**2 + 0*l + 5/8*l**4 + 1/12*l**6. Factor q(v).
v**2*(v - 2)*(v - 1)**2/2
Let t(r) be the third derivative of -r**8/168 - 2*r**7/105 - r**6/60 - 2*r**2. Factor t(i).
-2*i**3*(i + 1)**2
Let k(y) be the first derivative of 0*y + 3/2*y**2 - 3/4*y**4 + 0*y**3 + 6. Find u, given