*f**2 + 0*f + 1/60*f**6 + 0 + 1/1008*f**8. Factor w(l).
l*(l - 1)**4/3
Find j such that -2/13 + 0*j + 2/13*j**2 = 0.
-1, 1
Suppose 6*t - 6 - 24 = 0. Let a(z) be the second derivative of -1/9*z**4 + 7/9*z**3 - 5*z + 0 - 7/30*z**t + 2/3*z**2. Let a(g) = 0. What is g?
-1, -2/7, 1
Suppose 4/11*x**2 + 2/11*x**5 - 4/11*x**4 + 0 + 0*x**3 - 2/11*x = 0. Calculate x.
-1, 0, 1
Suppose -5*f + 2 = -3. Factor f + 3 - 1 - 15*p - 9 + 21*p**2.
3*(p - 1)*(7*p + 2)
Let x(k) be the second derivative of k**5/70 + k**4/14 + k**3/7 + k**2/7 - 5*k. Factor x(j).
2*(j + 1)**3/7
Let a(h) be the second derivative of h**7/315 + 4*h**6/225 + h**5/30 + h**4/45 - 13*h. Factor a(k).
2*k**2*(k + 1)**2*(k + 2)/15
Let r(y) be the third derivative of y**8/70560 - y**7/5880 - y**5/30 + 4*y**2. Let f(s) be the third derivative of r(s). Factor f(w).
2*w*(w - 3)/7
Solve 2/7*b**2 + 0 - 6/7*b = 0 for b.
0, 3
Let p(d) be the third derivative of 0*d + 0 + 1/72*d**4 + 0*d**3 - 1/630*d**7 + 7*d**2 - 1/360*d**6 + 1/180*d**5. Factor p(w).
-w*(w - 1)*(w + 1)**2/3
Let d be (-8)/36 - 58/(-18). Let a(m) be the third derivative of m**2 + 1/5*m**4 + 1/300*m**6 + 1/25*m**5 + 0*m + 0 + 8/15*m**d. Factor a(n).
2*(n + 2)**3/5
Let h(p) = -p**2 + p. Let a(y) = 8*y**2 + 43*y + 192. Let b(f) = a(f) + 5*h(f). Solve b(w) = 0 for w.
-8
Suppose 8*g - 11*g = -9. Factor 0*o**3 + 2*o - 12*o**2 + 6*o**2 - g*o**3 - 5*o.
-3*o*(o + 1)**2
Let i(z) be the second derivative of -7*z**4/3 + 2*z**3 - 3*z - 2. Let i(s) = 0. Calculate s.
0, 3/7
Let j(q) be the third derivative of -1/2352*q**8 + 0*q - 1/168*q**4 + 1/42*q**3 - 3*q**2 + 0 + 1/1470*q**7 + 1/420*q**6 - 1/210*q**5. Factor j(s).
-(s - 1)**3*(s + 1)**2/7
Let m(v) be the second derivative of -v**3/6 - 9*v**2/2 - 5*v. Let k be m(-11). Factor -k*g**3 + 1/3*g**4 + 4/3 - 4*g + 13/3*g**2.
(g - 2)**2*(g - 1)**2/3
Let c(s) be the third derivative of s**8/10080 + s**7/1260 + s**6/360 + s**5/180 - s**4/24 - s**2. Let r(w) be the second derivative of c(w). Factor r(b).
2*(b + 1)**3/3
Factor -4*b**2 + b**5 + 0*b**3 + 5*b**5 + 14*b**3 + 7*b**4 - 23*b**4.
2*b**2*(b - 1)**2*(3*b - 2)
Let p = -1143 - -1147. Determine q, given that 8/9*q**5 + 2/9*q + 0 + 2/3*q**p - 10/9*q**3 - 2/3*q**2 = 0.
-1, 0, 1/4, 1
Let j(y) = y**3 + 5*y**2 - 5*y + 7. Let o be j(-6). Solve -o - 3*q**2 - 3*q + 2*q**3 + 3*q**2 - 2*q**2 + q**5 + 3*q**4 = 0 for q.
-1, 1
Suppose -2*s - 5*l = -18, 2*s + 3*l - 10 = s. Find c such that 5*c**4 - 5*c**4 + 6*c**3 - 2*c**4 - s*c**2 = 0.
0, 1, 2
Let x(z) = 8*z**2 - 20*z - 3. Let n(y) = 9*y**2 - 20*y - 4. Let w(r) = 3*n(r) - 4*x(r). Factor w(p).
-5*p*(p - 4)
Let x = 4229/9 + -469. Factor 0 - 2/3*w - x*w**2.
-2*w*(4*w + 3)/9
Find y such that 36/5*y - 12/5 - 27/5*y**2 + 6/5*y**3 = 0.
1/2, 2
Factor 0 + 3/5*o**3 - 1/5*o**2 + 0*o + 1/5*o**5 - 3/5*o**4.
o**2*(o - 1)**3/5
Let o be 6*(4/(-8))/((-6)/4). Let 0*v**4 + 0*v**o + 1/3*v**5 + 0*v + 0 - 1/3*v**3 = 0. Calculate v.
-1, 0, 1
Let y(t) be the first derivative of 1/10*t**4 + 1/25*t**5 + 2 + 0*t**3 - 1/5*t**2 - 1/5*t. Find h such that y(h) = 0.
-1, 1
Let t be (-4)/(-1) + 3/(-3). Suppose 0 = -2*r - t*r + 25. What is p in -2*p**4 + p**4 - 2*p**4 + 3*p**r = 0?
0, 1
Let t(v) = 39*v**2 - 150*v + 159. Let j(m) = 8*m**2 - 30*m + 32. Let l(q) = 24*j(q) - 5*t(q). Factor l(g).
-3*(g - 9)*(g - 1)
Let s = -408 + 411. Let -1 - 3*p**4 - 1/2*p**5 - 8*p**2 - 9/2*p - 7*p**s = 0. What is p?
-2, -1
Let d(o) be the second derivative of 5*o + 2/9*o**4 + 0*o**3 + 0*o**2 + 1/126*o**7 + 0 + 1/15*o**6 + 1/5*o**5. Factor d(h).
h**2*(h + 2)**3/3
Let g be 3/(-2)*(-20)/(-15). Let p be g*(-3 + (-26)/(-9)). Find x, given that 0 - 2/9*x**2 - p*x**3 + 0*x = 0.
-1, 0
Let v(l) be the second derivative of -l**4/36 - l**3/9 - l**2/6 - 13*l. Factor v(t).
-(t + 1)**2/3
Factor 4/7*z**3 - 8/7*z**2 + 0 + 4/7*z.
4*z*(z - 1)**2/7
Let a = -235 + 237. Factor -3/4*o**a - 3/4*o**3 + 3/4 + 3/4*o.
-3*(o - 1)*(o + 1)**2/4
Let i(m) = 3*m**2 + 2*m - 2. Let t be i(-2). Suppose l - 3*l + t = 0. Determine g, given that -4*g + 6*g**2 + 0*g**2 - 5*g**l + 4*g**2 - 3*g**3 + 2*g**4 = 0.
0, 1, 2
Let n(t) be the first derivative of t**6/180 + t**5/180 - t**4/36 - t**3/18 - t**2 - 3. Let z(b) be the second derivative of n(b). Factor z(u).
(u - 1)*(u + 1)*(2*u + 1)/3
Let g(z) be the third derivative of 1/288*z**6 + 1/6*z**3 + 7/480*z**5 + 0*z + 2*z**2 + 0 + 1/48*z**4. Let s(f) be the first derivative of g(f). Factor s(r).
(r + 1)*(5*r + 2)/4
Let a(b) be the third derivative of 0 + 0*b + 5*b**2 + 1/168*b**7 + 1/48*b**4 + 7/240*b**5 + 3/160*b**6 + 1/1344*b**8 + 0*b**3. Factor a(c).
c*(c + 1)**3*(c + 2)/4
Let p(v) be the second derivative of -v**5/20 + v**4/4 - v**3/3 - 3*v. Factor p(a).
-a*(a - 2)*(a - 1)
Suppose -7*i**4 + 6*i**4 - 3*i**2 - 14*i**4 + 9*i**3 + 3*i**5 + 6*i**4 = 0. What is i?
0, 1
Let p be (-24)/(-3)*18/108. Suppose 5/3*a**2 + p + 16/3*a - 7/3*a**3 = 0. What is a?
-1, -2/7, 2
Let a(d) be the third derivative of d**8/5040 + d**7/630 + d**6/180 + d**5/90 - 5*d**4/12 + 2*d**2. Let h(y) be the second derivative of a(y). Factor h(v).
4*(v + 1)**3/3
Find y such that -41*y**2 + 363*y + y**3 - 816 - 515 + 8*y**2 = 0.
11
Suppose 20 = 31*x - 26*x. Let c(g) be the third derivative of -1/40*g**6 + 0 + 0*g + 0*g**5 + 0*g**3 - 2*g**2 + 1/8*g**x. Factor c(m).
-3*m*(m - 1)*(m + 1)
Let z = -3 + 6. Let c be (21/(-9) + z)*12. Factor -37*u**4 - c*u**2 + 2*u + 43*u**3 - 9*u**2 + 9*u**4.
-u*(u - 1)*(4*u - 1)*(7*u - 2)
Suppose 2*d + 10 = -s, -36 = 4*s - 2*s - 4*d. Let y be ((-6)/(-21))/((-2)/s). Factor -18*n**3 + 6*n**y - 3*n**2 + n**2.
-2*n**2*(9*n - 2)
Factor -6*k - 10*k + 17 - 17 + 4*k**3 - 12*k**2.
4*k*(k - 4)*(k + 1)
Let p(w) be the third derivative of -w**8/84 - 3*w**7/70 - w**6/60 + 2*w**5/15 + w**4/4 + w**3/6 - 11*w**2. Suppose p(j) = 0. What is j?
-1, -1/4, 1
Let p be -3 + 11 - 1/3. Let u = -11/21 - -6/7. Solve 7*w**5 - p*w**3 + 1/3*w**4 + 0 + 2/3*w - u*w**2 = 0 for w.
-1, -1/3, 0, 2/7, 1
Let q(c) be the second derivative of c**5/5 - c**4/3 - 10*c**3/3 - 6*c**2 - 19*c. Find b such that q(b) = 0.
-1, 3
Factor -1/6*l**5 + 0*l**3 + 1/3*l**4 - 1/3*l**2 + 1/6*l + 0.
-l*(l - 1)**3*(l + 1)/6
Let a(t) be the first derivative of -t**4/10 + t**2/5 - 4. Find d such that a(d) = 0.
-1, 0, 1
Suppose 2*i = -2*h + 8, 5*i + 0*i = -2*h + 14. Factor -8/13*x + 8/13 + 2/13*x**h.
2*(x - 2)**2/13
Let f be (-6040)/(-16)*1/245. Let k = f - 2/49. Determine b so that 3/2*b**4 + k*b - 3/2*b**3 - 3/2*b**2 + 0 = 0.
-1, 0, 1
Let u(a) be the second derivative of 1/3*a**3 + 0 + a + 1/30*a**5 + 1/3*a**2 + 1/6*a**4. Factor u(m).
2*(m + 1)**3/3
Let i(w) = w**2 - w + 2. Suppose 2*o = o. Let b be i(o). Factor d**2 - b*d + 3*d + 0*d.
d*(d + 1)
Let k be (-1*6)/(-2) + -1. Factor h**2 - 3*h + 2 - 2*h**3 + 2*h**k - 5 + 5*h**3.
3*(h - 1)*(h + 1)**2
Suppose -g**3 + 0*g**4 - 49*g**3 - 8 - 43*g**2 - 27*g**2 - 12*g**4 - 40*g = 0. Calculate g.
-2, -1, -2/3, -1/2
Let n(z) be the second derivative of z**7/84 - z**6/60 - z**5/20 + z**4/12 + z**3/12 - z**2/4 - 2*z + 7. Factor n(b).
(b - 1)**3*(b + 1)**2/2
Let o(n) be the third derivative of n**7/315 - n**6/60 + n**5/30 - n**4/36 + 3*n**2 + 2*n. Let o(u) = 0. Calculate u.
0, 1
Let q(c) = 8*c**2 - 5*c + 5. Let t(h) = -12*h**2 + 8*h - 8. Let z(g) = -8*q(g) - 5*t(g). Factor z(b).
-4*b**2
Factor 7*k - 28*k**3 - 12*k**3 - 27*k + 4 + 20*k**4 - 4*k**5 + 40*k**2.
-4*(k - 1)**5
Let r(z) = -6*z**3 + 4*z**2 - 10 + 8*z + 3*z**3 + z**3. Let q(u) be the first derivative of -u**2/2 + u + 2. Let f(k) = -10*q(k) - r(k). Factor f(l).
2*l*(l - 1)**2
Suppose -4*x = -149 + 17. Let d be 25/(-10)*(-24)/20. Find g such that -60*g**4 - 31*g**3 - x*g - 80*g**2 - 4 - 69*g**d - 14*g**5 + 3*g = 0.
-1, -2/7
Suppose -4*i + 13 = m, 0*i - 1 = -4*i - 5*m. Suppose -i*k = -5*v - 37, k + v = -v - 7. Suppose -2/5 - 2/5*q**k + 2/5*q**2 + 2/5*q = 0. What is q?
-1, 1
Let c(p) be the second derivative of -p**7/189 - p**6/135 + p**5/90 + p**4/54 + 8*p. Find z such that c(z) = 0.
-1, 0, 1
Let c(j) be the second derivative of 0 + 1/2*j**2 - 1/3*j**3 + 1/24*j**4 + j + 1/60*j**5. Let p(z) be the first derivative of c(z). Let p(v) = 0. Calculate v.
-2, 1
Let d = -18 - -12. Let l be d*(-1 + (-75)/(-81)). Suppose l - 2/3*i + 2/9*i**2 = 0. What is i?
1, 2
Factor -i**2 - 10*i + 0*i**2 + 8*i + 2*i**3 + 7*i**2 - 6*i**4.
-2*i*(i - 1)*(i + 1)*(3*i 