3
Factor 12/5*c + 0 + 3/5*c**2.
3*c*(c + 4)/5
Let b(u) be the first derivative of u**2 + 1/3*u**3 + 0*u - 5 - 1/4*u**4. Suppose b(x) = 0. Calculate x.
-1, 0, 2
Solve -8/3*l**2 + 0 + 8/3*l**3 + 10/3*l**5 + 26/3*l**4 + 0*l = 0.
-2, -1, 0, 2/5
Let f(u) = -2*u**2 + 9*u + 1. Let v be f(4). Determine a, given that 22*a**2 + 25/2*a**4 - 27*a**3 + 0 - 2*a**v - 4*a = 0.
0, 1/4, 2
Let d(b) be the third derivative of 0 + 0*b**6 + 1/35*b**7 - 1/112*b**8 + 0*b**3 + 1/8*b**4 + 10*b**2 + 0*b - 1/10*b**5. Determine r so that d(r) = 0.
-1, 0, 1
Let d(f) be the first derivative of f**6/30 - f**5/10 + f**3/3 - f**2/2 - 8*f + 6. Let j(u) be the first derivative of d(u). Solve j(v) = 0 for v.
-1, 1
Solve -2*a**2 + 9*a**2 - 3*a**2 = 0.
0
Let o(m) be the first derivative of -3*m**5/5 - 3*m**4/2 + 3*m**2 + 3*m + 10. Factor o(g).
-3*(g - 1)*(g + 1)**3
Let f be 468/38 - 4/2. Let u = 1452/95 + f. Factor -u*m**3 - 24/5*m - 2/5 - 96/5*m**2.
-2*(4*m + 1)**3/5
Factor 1919*c + 8*c**2 - 1920*c + 0 + 0.
c*(8*c - 1)
Let o be 2/6 + 64/24. Let p(x) = 2*x - 4. Let g be p(o). Let 2 - 2 + 3*q**g + 3*q**3 = 0. What is q?
-1, 0
Let m(t) be the first derivative of t**4/4 + 2*t**3/3 - 2*t**2 - 8*t - 9. Suppose m(k) = 0. Calculate k.
-2, 2
Let u = -25 - -30. Suppose 0*v + u*v = 0. Factor 1/2*g**4 + v*g - 1/2*g**3 - 1/2*g**2 + 1/2*g**5 + 0.
g**2*(g - 1)*(g + 1)**2/2
Let n be (-83)/(-8) + 6/(-16). Let b be (6/n)/((-12)/(-8)). Factor b*l**2 + 0*l - 2/5.
2*(l - 1)*(l + 1)/5
Let k(b) be the third derivative of b**6/40 - 3*b**4/8 - b**3 + 6*b**2. Determine w so that k(w) = 0.
-1, 2
Let h(m) = m**2 + 2*m - 7. Let u(p) = p**2 + 5*p - 15. Let z be (18/4)/((-9)/(-18)). Let l(t) = z*h(t) - 4*u(t). Factor l(q).
(q - 1)*(5*q + 3)
Let z(l) be the second derivative of l**6/90 - l**5/60 - l**4/18 + l. Factor z(x).
x**2*(x - 2)*(x + 1)/3
Let k(y) be the second derivative of 16*y**6/195 + 28*y**5/65 + 19*y**4/26 + 19*y**3/39 + 2*y**2/13 - 11*y. Suppose k(f) = 0. What is f?
-2, -1, -1/4
Suppose 0*i + 0*i**3 - 1/4*i**4 + 0 + 0*i**2 = 0. Calculate i.
0
Factor 3*z**5 + 9*z**4 + 4*z**3 + 3*z**2 + z**3 + 4*z**3.
3*z**2*(z + 1)**3
Let t(c) be the first derivative of -4*c**3/15 - 3*c**2/5 - 2*c/5 - 4. Let t(p) = 0. Calculate p.
-1, -1/2
Suppose 76 = 4*k - 0*k. Suppose 3*x - k = -7. Solve 0*q**4 + 3*q**5 - 2*q**4 - q**x = 0.
0, 1
Let x(i) be the second derivative of -1/3*i**3 + 1/2*i**2 + 0 + i + 1/15*i**5 + 7/24*i**4. Let l(q) be the first derivative of x(q). Factor l(t).
(t + 2)*(4*t - 1)
Let n(t) be the third derivative of -t**7/3780 + t**6/810 - t**5/540 + t**3 - 6*t**2. Let x(g) be the first derivative of n(g). Factor x(q).
-2*q*(q - 1)**2/9
Suppose 0*l = 2*l - 3*l. Let a(d) be the third derivative of -d**2 + 0 + 1/240*d**6 - 1/120*d**5 + 0*d**3 + 0*d + l*d**4. Factor a(s).
s**2*(s - 1)/2
Determine h, given that -h**2 - 32 - 18*h**4 - h**2 + 5*h**3 + 16*h**4 + 7*h**3 - 48*h = 0.
-1, 4
Let l = 173665834/309 + -562027. Let i = 2/103 - l. Factor -i*a**2 - 2/3 + 7/3*a.
-(a - 1)*(5*a - 2)/3
Let c(r) be the third derivative of 1/720*r**6 + 1/48*r**4 - 1/120*r**5 + 0*r + 1/2*r**3 - 2*r**2 + 0. Let m(o) be the first derivative of c(o). Factor m(w).
(w - 1)**2/2
Factor -4/9*u**2 + 1/3 + 1/9*u**4 + 2/9*u - 2/9*u**3.
(u - 3)*(u - 1)*(u + 1)**2/9
Let a = 635609/68 - 9347. Let m = a - -1/17. Factor 0 + m*d**2 + 1/4*d.
d*(d + 1)/4
Let k = -349/12 - -110/3. Let s = -1/12 + k. Factor -3/4 - 75/4*i**2 - s*i.
-3*(5*i + 1)**2/4
Let i(r) be the first derivative of 0*r**2 + 0*r - 1 - 24/5*r**5 + 8*r**6 - 21/4*r**4 - r**3. Solve i(b) = 0.
-1/4, 0, 1
Factor -4/5*p**2 + 0 - 16/5*p.
-4*p*(p + 4)/5
Let m(k) be the first derivative of 3*k**4/5 - 22*k**3/15 + 4*k**2/5 + 2*k/5 - 2. Let m(j) = 0. Calculate j.
-1/6, 1
Let p(b) = -11*b**2 - b - 11*b**3 - 5 + 3*b - 7*b. Let c(x) = 7*x**3 + 7*x**2 + 3*x + 3. Let h(v) = 8*c(v) + 5*p(v). Determine q, given that h(q) = 0.
-1, 1
Factor 0 + 1/3*a**4 + 0*a**2 + 0*a - 1/3*a**3.
a**3*(a - 1)/3
Let g be (-4)/10 + (-12)/(-5). Find x such that 2*x**2 + 0 - 10*x**2 - 9 + 24*x - 8*x**g = 0.
3/4
Factor 0 - 4/3*r**2 - 8/3*r + 2/3*r**3 + 1/3*r**4.
r*(r - 2)*(r + 2)**2/3
Let p(i) be the second derivative of i**8/5040 - i**6/540 + i**4/72 - i**3/2 - 2*i. Let s(k) be the second derivative of p(k). Solve s(o) = 0 for o.
-1, 1
Let i(o) = -2*o**3 + 2*o**2 + 3*o + 1. Let x be i(-1). Let q(p) be the first derivative of 2*p**2 - x - p - 4/3*p**3. What is u in q(u) = 0?
1/2
Let o be (6/(-10))/((-12)/8). Suppose -v - 4*v - 15 = -5*y, -2*y - 2*v = -2. Determine w, given that 2/5*w**3 - o + 6/5*w - 6/5*w**y = 0.
1
Factor -1/2*y**3 + 1 - y**2 + 1/2*y.
-(y - 1)*(y + 1)*(y + 2)/2
Let n = 9 - 9. Let y(u) be the third derivative of -1/105*u**7 + 0 + 0*u**6 - 1/336*u**8 + 1/24*u**4 - u**2 + n*u + 0*u**3 + 1/30*u**5. Factor y(q).
-q*(q - 1)*(q + 1)**3
Let u(p) be the first derivative of p**3/3 + p**2 - 8. Factor u(b).
b*(b + 2)
Suppose 0 = 2*j + j - 5*f + 14, 2*f - 11 = 3*j. Let q = j + 6. Factor 2*d**2 - 3 - 4*d**2 + 2 + q*d.
-(d - 1)*(2*d - 1)
Let u(r) be the second derivative of -r**6/360 + r**5/30 - r**4/6 - r**3/3 - 6*r. Let i(v) be the second derivative of u(v). Factor i(w).
-(w - 2)**2
Let r(g) be the first derivative of -g**7/189 - 2*g**6/135 + g**5/90 + g**4/27 - g - 5. Let v(z) be the first derivative of r(z). Solve v(x) = 0 for x.
-2, -1, 0, 1
Let s(w) = -w**3 - 2*w**2 - 2*w - 1. Suppose -4*t = -0*m - 2*m - 4, -20 = 5*m. Let o be s(t). Factor 0*h**2 + 1/2*h + 1/2*h**5 + o - h**3 + 0*h**4.
h*(h - 1)**2*(h + 1)**2/2
Let d(g) be the second derivative of -g**5/10 + g**4/2 + g**3/3 - 3*g**2 + 6*g. Factor d(p).
-2*(p - 3)*(p - 1)*(p + 1)
Let m(q) be the third derivative of -3*q**2 + 0 + 1/48*q**6 + 0*q + 1/280*q**7 + 0*q**3 + 1/60*q**5 - 1/12*q**4. Factor m(s).
s*(s + 2)**2*(3*s - 2)/4
Let o(c) be the first derivative of 24*c**5/5 - 75*c**4/4 + 19*c**3 - 3*c**2 + 13. Factor o(i).
3*i*(i - 2)*(i - 1)*(8*i - 1)
Let b(n) be the second derivative of n**7/105 + n**6/75 - n**5/50 - n**4/30 + 21*n. Factor b(g).
2*g**2*(g - 1)*(g + 1)**2/5
Let q(z) be the third derivative of 0 - 1/60*z**5 + 1/24*z**4 + z**2 + 0*z**3 + 0*z. Determine r, given that q(r) = 0.
0, 1
Let q(r) = r**2 - 12*r + 14. Let u(v) = -v + 2. Let g(y) = -2*q(y) + 6*u(y). Factor g(j).
-2*(j - 8)*(j - 1)
Let a(l) = -4*l**3 + 9*l**2 + 4*l - 4. Let i(d) = 2*d**3 - 5*d**2 - 2*d + 2. Let f(s) = -3*a(s) - 5*i(s). Find z, given that f(z) = 0.
-1, 1
Suppose 4*k - 5*c - 29 = 0, -3*k + 26 = k - 2*c. Suppose 4*y + 5*y - y**2 + 4*y**2 + k = 0. Calculate y.
-2, -1
Let r(f) be the second derivative of 7*f**6/540 - f**5/15 - f**4/9 - 5*f**3/6 + 4*f. Let m(n) be the second derivative of r(n). Determine h so that m(h) = 0.
-2/7, 2
Let m(z) be the first derivative of -4*z**2 - 2 + 2/3*z**3 + 8*z. Factor m(n).
2*(n - 2)**2
Factor -2/13*h**2 + 0 + 0*h.
-2*h**2/13
Let m(j) be the first derivative of -j**3/21 - j**2/2 + 8*j/7 + 31. Factor m(p).
-(p - 1)*(p + 8)/7
Let r = -608/39 + 246/13. Factor -r*l**3 + 5/3 + 10/3*l - 5/3*l**2.
-5*(l - 1)*(l + 1)*(2*l + 1)/3
Let u(t) = 4*t + 2. Let w be u(0). Let x be (-6)/1*w/(-4). Determine a so that -5/4*a**x - 7/4*a**2 - 1/2*a + 0 = 0.
-1, -2/5, 0
Suppose b + 21 = 4*v, -3*v + b + 27 = -2*b. Let z(j) be the third derivative of -1/18*j**3 + 1/360*j**6 + 2*j**2 - 1/60*j**5 + 0*j + 0 + 1/24*j**v. Factor z(u).
(u - 1)**3/3
Determine t, given that -18/13*t**3 + 2/13*t**5 - 2/13*t**4 - 22/13*t**2 - 8/13*t + 0 = 0.
-1, 0, 4
Let d(x) be the third derivative of -x**6/160 - x**5/80 + x**4/32 + x**3/8 - 4*x**2. Factor d(c).
-3*(c - 1)*(c + 1)**2/4
Let c(p) be the first derivative of 3*p**5/5 + 3*p**4/4 - 3. Solve c(r) = 0 for r.
-1, 0
Let a = 10 - -26. Suppose 1 + a*i**4 + 38*i**2 - 113/2*i**3 - 21/2*i - 8*i**5 = 0. Calculate i.
1/4, 1, 2
Let z be 6/(-1008)*(-8)/10. Let s(p) be the third derivative of 0*p**5 + z*p**7 + 0 - 1/6*p**3 - 1/60*p**6 + 2*p**2 + 0*p + 1/12*p**4. Factor s(u).
(u - 1)**3*(u + 1)
Factor w - 2/3 - 1/3*w**2.
-(w - 2)*(w - 1)/3
Let r(c) be the second derivative of c**5/80 - 5*c**4/48 + c**3/3 - c**2/2 + c. Solve r(h) = 0.
1, 2
Let k(f) be the second derivative of f**9/15120 + f**8/6720 + f**4/4 - f. Let a(c) be the third derivative of k(c). Factor a(r).
r**3*(r + 1)
Factor 23*h - h**2 - 3 - 15*h + 3.
-h*(h - 8)
Let l = 7 - 1. Let y be 