f) = 3*f**2 + 11*f + 2. Let r(i) = 5*i**2 + 17*i + 3. Let m(t) = -8*b(t) + 5*r(t). Let z be m(4). Factor -2/3*k**z + 0*k**2 + 0*k + 0 + 5/3*k**4.
k**3*(5*k - 2)/3
Let a(n) be the first derivative of -1/21*n**6 + 0*n**2 - 2/35*n**5 + 2 + 0*n + 2/21*n**3 + 1/14*n**4. Solve a(c) = 0 for c.
-1, 0, 1
Suppose 2*f + 3*h = 5*h, 5*f = 4*h. Suppose f = 3*d - 2 - 4. Find t such that 0 - 1/4*t**d + 0*t = 0.
0
Let t = -678/5 + 136. Determine d so that t*d**2 - 4/5*d + 0 + 2/5*d**3 = 0.
-2, 0, 1
Let c(r) = -r + 1. Let m(q) = q + 2. Let p be m(-4). Let f be c(p). Factor -4*k + 3*k - 3*k**f + 5*k**3 + 3*k + 4*k**2.
2*k*(k + 1)**2
Let -2/5*j**2 - 32/5 + 16/5*j = 0. Calculate j.
4
Let a(s) be the first derivative of s**3/12 + s**2/2 + 45. Solve a(j) = 0.
-4, 0
Let v be (-2)/(-7) - 6/21. Suppose v = 5*i - 28 + 3. Solve 6*t + t**3 - 2*t**3 - i*t = 0.
-1, 0, 1
Let y(r) be the first derivative of -r**6/810 + r**5/216 - r**4/216 + r**3 - 4. Let v(w) be the third derivative of y(w). Factor v(p).
-(p - 1)*(4*p - 1)/9
Let h(l) = 3*l**5 + 20*l**4 + 7*l**3 + 14*l**2 + 8. Let s(v) = v**5 + 7*v**4 + 2*v**3 + 5*v**2 + 3. Let y(b) = 3*h(b) - 8*s(b). Let y(g) = 0. What is g?
-2, -1, 0
Let q(i) be the third derivative of i**8/24 + 4*i**7/35 + i**6/20 - i**5/15 - 5*i**2. Factor q(t).
2*t**2*(t + 1)**2*(7*t - 2)
Let i be ((-1)/(-2))/(4/48). Suppose -4*o + i = -o. Factor -12/7*q**3 + 8/7 + 2/7*q**4 - 24/7*q + 26/7*q**o.
2*(q - 2)**2*(q - 1)**2/7
Let z(y) = -y**2 - 6*y + 9. Let l be z(-7). Suppose -20 = 5*s, 4*u - 12 = s - 0*s. Factor l*q**2 - q - q**2 + 2*q**u.
q*(3*q - 1)
Let x be (2/(-8))/(5/(-40)). Factor -3*t**3 + t**3 - t**2 + t**4 - 2*t**2 + 4*t**x.
t**2*(t - 1)**2
Let z(v) = -7*v**4 - 11*v**3 + 3*v**2 + 11*v + 4. Let w(q) = -36*q**4 - 56*q**3 + 16*q**2 + 56*q + 20. Let p(f) = -3*w(f) + 14*z(f). Factor p(o).
2*(o - 1)*(o + 1)**2*(5*o + 2)
Let j(p) be the first derivative of -3*p**5/35 + 3*p**4/14 - 3*p**2/7 + 3*p/7 + 13. Factor j(z).
-3*(z - 1)**3*(z + 1)/7
Let f(k) be the third derivative of k**6/480 + k**5/240 - k**4/96 - k**3/24 + 2*k**2. Determine h, given that f(h) = 0.
-1, 1
Let w be (-2)/(-3) - 730/1100. Let j(g) be the third derivative of -g**2 + 0 + 0*g + w*g**5 + 2/33*g**3 + 1/44*g**4. Let j(n) = 0. What is n?
-2, -1
Let f(m) be the second derivative of m**4/8 + 3*m**3/2 - 27*m. Suppose f(u) = 0. Calculate u.
-6, 0
Let l(a) be the third derivative of 1/270*a**5 - 1/945*a**7 - 1/540*a**6 + 0*a + 4*a**2 + 0 + 0*a**3 + 1/108*a**4. Factor l(p).
-2*p*(p - 1)*(p + 1)**2/9
Let u be 2/(6/5) + (-1)/3. Determine a, given that -1/3*a**2 - 4/3*a - u = 0.
-2
Let b(i) be the third derivative of -i**6/180 - i**5/30 - i**4/12 - i**3/9 + 64*i**2. Find j, given that b(j) = 0.
-1
Let g(k) be the second derivative of 3*k + 1/18*k**3 - k**2 - 1/45*k**5 - 1/24*k**4 + 0. Let l(r) be the first derivative of g(r). Factor l(v).
-(v + 1)*(4*v - 1)/3
Let l(u) be the second derivative of u**6/60 + u**5/5 + 3*u**4/4 - u**2 + u. Let a(p) be the first derivative of l(p). Factor a(c).
2*c*(c + 3)**2
Suppose -4*q = -5*l + 8, 2*l = -q + 3*q + 4. Let g(h) be the first derivative of 0*h + 0*h**3 + h**2 + 1/3*h**6 + l*h**5 - h**4 + 2. Let g(k) = 0. Calculate k.
-1, 0, 1
Let d(c) = -19*c**3 - 8*c**2 - 11*c - 14. Let f be d(-6). Let p = -34700/9 + f. Find t, given that -38/9*t**2 - p*t**4 + 0 + 4/9*t + 38/3*t**3 + 32/9*t**5 = 0.
0, 1/4, 1, 2
Factor 0*r**2 + 8*r**4 + 8/7*r**3 + 14*r**5 + 0 + 0*r.
2*r**3*(7*r + 2)**2/7
Let c(b) be the second derivative of 5*b**7/42 - b**6 + 7*b**5/2 - 20*b**4/3 + 15*b**3/2 - 5*b**2 - 23*b. Determine q, given that c(q) = 0.
1, 2
Let z(l) = 6*l**3 - 42*l**2 - 63*l - 15. Let u(y) = y**3 - 6*y**2 - 9*y - 2. Let h(x) = 15*u(x) - 2*z(x). Determine k so that h(k) = 0.
-1, 0, 3
Let l(t) be the first derivative of -t**5/45 + t**4/18 + 4*t**3/9 - t**2 + 4. Let w(p) be the second derivative of l(p). Factor w(z).
-4*(z - 2)*(z + 1)/3
Let z = -6 - -11. Let y = z + -3. Factor y - 7*k + k**2 - 2*k + 8*k**2.
(3*k - 2)*(3*k - 1)
Let o be 21/18*54/1092. Let k = o + 141/260. Determine i, given that -3/5*i**5 - 6/5*i**2 + 0 + 6/5*i**4 + k*i + 0*i**3 = 0.
-1, 0, 1
Let b be (-3)/10*10/(-12). Let v be (-10)/12 + (-25)/(-30). Factor 0 + v*t - 1/4*t**4 + b*t**2 + 1/4*t**3 - 1/4*t**5.
-t**2*(t - 1)*(t + 1)**2/4
Let h(t) = 15*t**3 - 15*t**2 - 10*t + 10. Let c(o) = -23*o**3 + 23*o**2 + 15*o - 15. Let q(j) = -5*c(j) - 8*h(j). What is l in q(l) = 0?
-1, 1
Let f(q) = q - 6. Let l be f(5). Let p(b) = -2*b**2 - 9*b - 4. Let a(h) = h. Let v(g) = l*p(g) - 3*a(g). Find r such that v(r) = 0.
-2, -1
Let j = 22/67 + 113/268. Solve 0*i**3 + 0*i + 0 + 3/4*i**2 - j*i**4 = 0.
-1, 0, 1
Let m(p) be the third derivative of p**8/294 + p**7/735 + 8*p**2. Factor m(i).
2*i**4*(4*i + 1)/7
Solve -14*u**2 - u + 21*u**2 + u**4 + 2 + u**3 - 10*u**2 = 0 for u.
-2, -1, 1
Let j = -799 - -11989/15. Let 2/15*y + j - 2/15*y**2 = 0. What is y?
-1, 2
Let j(q) be the second derivative of 5*q**4/12 - 25*q**3/3 + 125*q**2/2 + 12*q. Solve j(v) = 0 for v.
5
Let s = 53 + -33. Let z be (s/16 - 0) + -1. Let -z*d**3 + 1/2*d**2 + 0 + 0*d = 0. Calculate d.
0, 2
Let b(d) be the third derivative of -d**5/55 + 5*d**4/44 - 2*d**3/11 - 29*d**2. Factor b(m).
-6*(m - 2)*(2*m - 1)/11
Let k(a) be the third derivative of a**5/330 - a**4/33 + 4*a**3/33 - 10*a**2. Factor k(f).
2*(f - 2)**2/11
Let s be (-1)/(-3) - 53/(-53). Let u(w) = w + 4. Let n be u(-4). Factor 10/3*v**2 + n - 14/3*v**3 + s*v.
-2*v*(v - 1)*(7*v + 2)/3
Factor 4*b**2 + 10/3*b + 2*b**3 + 1/3*b**4 + 1.
(b + 1)**3*(b + 3)/3
Let b(f) = -6*f**2 - f - 7. Let w(l) = -120*l**2 + 0*l - l + 115*l**2 - 6. Let p(m) = -6*b(m) + 7*w(m). Find y, given that p(y) = 0.
0, 1
Let k(i) be the first derivative of i**4/12 + i**3/9 - i**2/6 - i/3 + 2. Factor k(t).
(t - 1)*(t + 1)**2/3
Let u(p) be the second derivative of -p**6/40 + 3*p**5/20 - p**4/4 - 3*p. Factor u(y).
-3*y**2*(y - 2)**2/4
Let s(b) be the first derivative of 8/21*b**3 + 2/7*b - 5/7*b**2 + 1. Factor s(c).
2*(c - 1)*(4*c - 1)/7
Let a be 10/6 - 4/(-12). Let w(v) be the first derivative of 2*v**a + 2*v + 1 + 2/3*v**3. Find m such that w(m) = 0.
-1
Let 14 - 6*l - 3*l**2 - 7 - 7 = 0. What is l?
-2, 0
Let w be (-4)/(-6) + 14/6. Let i(o) = 9*o**3 - o**2 - o + 1. Let f be i(1). Let 2 - 6*d**3 + 0*d**2 - 2*d**w - f*d + 2*d**4 + 12*d**2 = 0. Calculate d.
1
Let j be -1*(-15)/(-20)*(-5)/15. Determine w so that -3/4*w**3 - 1/2*w**2 - j*w**4 + 0*w + 0 = 0.
-2, -1, 0
Let y(g) be the third derivative of -g**6/420 - g**5/210 + g**4/42 - 56*g**2. Factor y(t).
-2*t*(t - 1)*(t + 2)/7
Let p be (5 - (0 - -3)) + 2. Factor 6*t**3 + t - 3 + 0*t**3 - t**p - 7*t + 4*t**4.
3*(t - 1)*(t + 1)**3
Let k(a) = 10*a**2 - 4*a - 7. Let s(g) be the first derivative of 7*g**3/3 - 3*g**2/2 - 5*g - 3. Let b(x) = 5*k(x) - 7*s(x). Factor b(o).
o*(o + 1)
Let s = -3 + 7. Suppose -5*o = -m - 16, -2*o + 28 = 4*m + s. Factor 0*y + y**2 + 0 + 1/2*y**3 - 1/2*y**o.
-y**2*(y - 2)*(y + 1)/2
Let v(f) be the third derivative of 0 + 0*f**4 + 1/60*f**6 - 1/112*f**8 + 0*f - 1/210*f**7 + 0*f**3 + 4*f**2 + 0*f**5. Factor v(m).
-m**3*(m + 1)*(3*m - 2)
Suppose -2*q = -6*q. Suppose -4 + q*v**4 - 5*v**4 + 1 + 6*v**2 + 2*v**4 = 0. What is v?
-1, 1
Let t(w) be the first derivative of 9*w**6/4 + 27*w**5/10 - 9*w**4/4 - 5*w**3/3 + 7*w**2/4 - w/2 + 3. Factor t(x).
(x + 1)**2*(3*x - 1)**3/2
Let h = -2/95 + 289/190. Factor 2*t**2 + h*t - 1/2.
(t + 1)*(4*t - 1)/2
Find d, given that 1/3*d**2 + 0*d - 4/3 = 0.
-2, 2
Suppose -2*w = -k - 6, 0 = 5*k + 6*w - w - 30. Factor -1/4*y**5 + 1/4*y + 0 + 0*y**3 + 1/2*y**k - 1/2*y**4.
-y*(y - 1)*(y + 1)**3/4
Let s(h) be the first derivative of -3*h**5/5 - 9*h**4/4 - h**3 + 9*h**2/2 + 6*h + 5. Factor s(a).
-3*(a - 1)*(a + 1)**2*(a + 2)
Let f(i) = i**4 + 3*i**3 + 8*i**2 - 4*i + 5. Let v(g) = g**2 - g + 1. Suppose -5*x - 37 = -4*k, -3*k = 3 - 12. Let a(s) = x*v(s) + f(s). Factor a(l).
l*(l + 1)**3
Let v = -140 + 143. Factor -16/7*w + 18/7*w**v - 8/7 + 6/7*w**2.
2*(w - 1)*(3*w + 2)**2/7
Let c(v) be the second derivative of -v**5/20 - v**4/2 - v. Let f be c(-6). Let 0*x**3 + 1/4*x**4 + 1/4*x**5 + f + 0*x**2 + 0*x = 0. Calculate x.
-1, 0
Factor 7/2*v**3 - 4/3 + 10*v - 61/3*v**2 + 49/6*v**4.
(v - 1)*(v + 2)*(7*v - 2)**2/6
Let n(q) be the first derivative of 4*q**5/5 - 2*q**4 - 4*q**3 