e second derivative of -4/5*n**2 + 4/15*n**3 - 1/30*n**4 + i + 3*n. Suppose l(r) = 0. What is r?
2
What is b in -2/3*b - 3/2*b**4 + 8/3*b**2 + 0 + 11/6*b**3 = 0?
-1, 0, 2/9, 2
Let v(n) be the second derivative of 2*n**4/3 + 2*n**3/3 + n**2/4 + 5*n. Determine o so that v(o) = 0.
-1/4
Let h(o) be the second derivative of 0*o**5 + 1/60*o**6 + 1/168*o**7 - 1/24*o**4 - 1/24*o**3 + 0 - 5*o + 0*o**2. Find p, given that h(p) = 0.
-1, 0, 1
Let c(z) be the third derivative of 0*z - 5*z**2 + 0*z**3 - 1/40*z**6 + 1/8*z**4 + 1/20*z**5 - 1/70*z**7 + 0. Factor c(l).
-3*l*(l - 1)*(l + 1)**2
Suppose 28*z**3 - 4*z**2 + 20*z**3 - 44*z**3 = 0. What is z?
0, 1
Factor 0*r - r**3 - 1/2*r**4 + 0 - 1/2*r**2.
-r**2*(r + 1)**2/2
Let g be 1/(3/(-2))*(-6)/96. Let y(f) be the third derivative of 0 - 1/3*f**3 - f**2 + g*f**4 + 0*f + 1/60*f**5. Solve y(u) = 0.
-2, 1
Let u(m) be the third derivative of -m**8/336 - m**7/105 + m**6/40 - 13*m**2. Find w, given that u(w) = 0.
-3, 0, 1
Let w(v) = v**3 - 8*v**2 + 6. Let p be w(8). Suppose 4*z = z + p. Let 2/7*l**3 - 2/7*l - 4/7 + 4/7*l**z = 0. What is l?
-2, -1, 1
Let a(c) be the first derivative of 5*c**4/4 - 10*c**3/3 - 5*c**2/2 + 10*c - 14. Solve a(w) = 0.
-1, 1, 2
Let h(q) be the second derivative of 0*q**4 - 1/27*q**3 - 3*q + 3/2*q**2 + 1/270*q**5 + 0. Let n(w) be the first derivative of h(w). Factor n(j).
2*(j - 1)*(j + 1)/9
Factor -7*k**3 - 3*k**5 + 3*k - 2*k + 0*k**3 - 8*k**4 + k**3.
-k*(k + 1)**3*(3*k - 1)
Factor 3/2*i**3 + 3/2 - 3/2*i - 3/2*i**2.
3*(i - 1)**2*(i + 1)/2
Let x(b) = b**2 - 13*b + 39. Let m be x(9). Let v(r) be the third derivative of 0*r - 1/90*r**5 - 7/144*r**4 - 3*r**2 + 1/18*r**m + 0. Let v(j) = 0. What is j?
-2, 1/4
Suppose -3*a = 3*a. Let d(n) be the second derivative of a*n**2 + n - 1/5*n**6 - 1/10*n**5 + 1/3*n**4 + 0*n**3 + 0. Factor d(x).
-2*x**2*(x + 1)*(3*x - 2)
Let z = -23 + 29. Let x(g) be the third derivative of 0 - 3/80*g**z - 1/12*g**4 + 0*g + 0*g**3 + g**2 - 1/10*g**5. Solve x(c) = 0.
-2/3, 0
Let y(p) be the second derivative of p**7/840 - p**5/40 + p**4/4 + p. Let j(l) be the third derivative of y(l). Factor j(c).
3*(c - 1)*(c + 1)
Suppose 8 = 4*c - 2*c. Let y(p) = -p**4 - p**3 + p. Let i(q) = 5*q**4 + 7*q**3 - 8*q. Let f(l) = c*y(l) + i(l). Find m such that f(m) = 0.
-2, 0, 1
Let j(a) = -3*a + 18. Let z be j(6). Let q(p) be the first derivative of 2/21*p**3 - 2/7*p + z*p**2 + 3. Factor q(h).
2*(h - 1)*(h + 1)/7
Let y(u) be the second derivative of 0*u**3 + 1/105*u**7 - 1/50*u**5 + 0*u**2 + 0 + 1/75*u**6 - 1/30*u**4 + 5*u. Find r such that y(r) = 0.
-1, 0, 1
Let s be (-4)/(2 + -4 + 3). Let k be 7 + (-5)/((-10)/s). Factor 8*i + 1 + 4*i**2 - 4*i**3 + 0 - 6*i**4 + 1 - 2*i**k - 2*i.
-2*(i - 1)*(i + 1)**4
Let q(a) = a**3 - 2*a**2 - 8*a. Let f be q(4). Let n(w) be the first derivative of 0*w**3 - 2/45*w**5 + f*w**2 + 0*w**4 - 2 + 0*w. Determine c so that n(c) = 0.
0
Let l be 8/(-20) - (4/(-10) - 0). Let s(q) be the third derivative of 1/210*q**5 + l*q + 0 + 1/21*q**3 + 1/42*q**4 + q**2. Factor s(u).
2*(u + 1)**2/7
Let v(p) be the second derivative of 1/6*p**4 - p**2 + 1/10*p**5 + 0 - 3*p - 1/3*p**3. Factor v(q).
2*(q - 1)*(q + 1)**2
Let p(i) be the third derivative of -i**6/480 + i**5/160 - i**3/3 + 6*i**2. Let c(d) be the first derivative of p(d). Factor c(u).
-3*u*(u - 1)/4
Solve 2*i**2 + i**2 + 6*i - i**2 - 2 - 2*i**3 - 4*i = 0.
-1, 1
Let 4*t - 7*t - t - 5*t + 6 + 3*t**2 = 0. What is t?
1, 2
Let t be 8/(-32) - (-26)/8. Let j(v) be the second derivative of 1/10*v**t - 1/5*v**2 - 1/60*v**4 + 0 + v. Factor j(d).
-(d - 2)*(d - 1)/5
Let j(x) be the first derivative of 0*x**5 + 0*x**3 + 3/4*x**4 + 0*x**2 + 0*x - 4 - 1/2*x**6. Factor j(r).
-3*r**3*(r - 1)*(r + 1)
Let d(n) be the first derivative of -7/4*n**4 - 1 - 1/5*n**5 - 9/2*n**2 - 5*n**3 + 0*n. Factor d(b).
-b*(b + 1)*(b + 3)**2
Let h(f) be the third derivative of f**5/3 + 7*f**4/3 - 2*f**3 + 35*f**2. Factor h(b).
4*(b + 3)*(5*b - 1)
Let j(g) be the first derivative of -1/120*g**6 + 3 - 1/24*g**3 + 1/80*g**5 + 2*g + 0*g**2 + 1/48*g**4. Let y(p) be the first derivative of j(p). Factor y(q).
-q*(q - 1)**2*(q + 1)/4
Find b such that 4*b**3 - 3*b - b + 0*b + 2*b**4 - 2 = 0.
-1, 1
Suppose -27 - 13 = -4*k. Let r = -6 + k. Let 0*d**2 - r*d**2 + 2*d + 3*d**2 = 0. What is d?
0, 2
Let u(i) be the first derivative of -2/15*i**3 + 2 + 0*i**2 + 0*i. Factor u(r).
-2*r**2/5
Let -3/7*n**2 - 2/7 - 5/7*n = 0. What is n?
-1, -2/3
Let v(s) = -27*s**2 + 205*s - 53. Let o(w) = 14*w**2 - 102*w + 26. Let z(t) = 5*o(t) + 2*v(t). Factor z(y).
4*(y - 6)*(4*y - 1)
Let h(v) be the first derivative of -v**6/180 - v**5/60 + 2*v**3 - 2. Let a(z) be the third derivative of h(z). Factor a(b).
-2*b*(b + 1)
Let c(a) = -6*a**3 - 13*a**2 + 7. Let w = 7 - 4. Let b = w - 10. Let g(x) = 4*x**3 + 9*x**2 - 5. Let o(l) = b*g(l) - 5*c(l). Factor o(t).
2*t**2*(t + 1)
Let a(t) be the third derivative of 1/2*t**3 + 0 + 0*t - 1/84*t**4 + 2*t**2 - 1/1260*t**6 + 1/210*t**5. Let c(q) be the first derivative of a(q). Factor c(f).
-2*(f - 1)**2/7
Factor 8/3*f**2 + f**3 - 2/3 + f.
(f + 1)*(f + 2)*(3*f - 1)/3
Let a be (10/6)/((40/16)/1). Factor -4/3*t**2 + 0*t - a*t**3 + 0.
-2*t**2*(t + 2)/3
Let u(d) be the third derivative of -d**5/160 - 5*d**4/32 - 38*d**2. Factor u(l).
-3*l*(l + 10)/8
Let u(s) be the third derivative of 0*s**3 + 2*s**2 + 0*s - 1/30*s**4 + 1/25*s**5 + 11/600*s**6 - 2/175*s**7 - 1/240*s**8 + 0. Suppose u(t) = 0. What is t?
-2, -1, 0, 2/7, 1
Let i(q) be the third derivative of -q**6/180 - 23*q**5/90 - 143*q**4/36 - 121*q**3/9 - 40*q**2 + q. Factor i(u).
-2*(u + 1)*(u + 11)**2/3
Let o(a) be the third derivative of 4*a**7/1365 - 3*a**6/260 + a**5/65 - a**4/156 - 4*a**2. Factor o(x).
2*x*(x - 1)**2*(4*x - 1)/13
Let z(r) = 2*r**2 - 4*r - 2. Let k be z(3). Let w(f) be the second derivative of -1/40*f**5 - f + 1/4*f**2 - 1/4*f**3 + 0 + 1/8*f**k. Factor w(g).
-(g - 1)**3/2
Let l(b) be the second derivative of b**7/12600 + b**6/1800 + b**5/600 + b**4/3 + 4*b. Let p(a) be the third derivative of l(a). Factor p(v).
(v + 1)**2/5
Let k be (4/(-54))/(8/(-24)). Factor 2/9*s**4 + 0 + 0*s + 0*s**3 - k*s**2.
2*s**2*(s - 1)*(s + 1)/9
Let d(q) = -5*q**3 + 4*q**2 + 3*q - 2. Let b = 6 + -6. Let j(r) = -5*r**2 + r**3 + 5*r**3 - 3*r + 2 + b*r. Let w(f) = 5*d(f) + 4*j(f). Factor w(h).
-(h - 1)**2*(h + 2)
Suppose -4*n = -2*n - 18. Determine q, given that 9*q**5 - 2*q**3 + 11*q**4 - n*q**2 - 2*q - 5*q**3 - 2*q**4 = 0.
-1, -2/3, -1/3, 0, 1
Let v(d) be the first derivative of d**7/84 - d**6/60 - d**5/40 + d**4/24 - 2*d - 3. Let y(l) be the first derivative of v(l). Solve y(k) = 0 for k.
-1, 0, 1
Let y(r) be the third derivative of 2*r**7/105 - r**6/15 - r**5/20 + 7*r**4/24 - r**3/3 - 7*r**2. Factor y(t).
(t - 2)*(t + 1)*(2*t - 1)**2
Let f be (-2)/(-8) + 0/(-4). Let p(r) be the first derivative of 1/6*r**3 - f*r**2 - 1 - 1/2*r + 1/8*r**4. Factor p(h).
(h - 1)*(h + 1)**2/2
Suppose 2 = o - 0*o. Factor -4*x + 0*x + 0*x - 2*x**o - 2*x - 4.
-2*(x + 1)*(x + 2)
Let s(h) be the third derivative of -1/18*h**3 + 0 + 1/180*h**5 + h**2 - 1/120*h**6 + 0*h + 1/24*h**4. Factor s(t).
-(t - 1)*(t + 1)*(3*t - 1)/3
Let a(u) be the first derivative of 55*u**3/3 - 50*u**2 - 20*u + 10. Factor a(b).
5*(b - 2)*(11*b + 2)
Let i(r) = -10*r**2 - 6*r + 6. Let n(o) = 20*o**2 + 12*o - 13. Suppose 3*q - 2*c = 7, 2*q - 1 = 3*c - 3. Let g(u) = q*i(u) + 2*n(u). Let g(d) = 0. What is d?
-1, 2/5
Let n = -4 - -4. Suppose n = -3*c - j - 3*j - 20, -4*j = 20. Factor c - 2/5*d + 2/5*d**2.
2*d*(d - 1)/5
Let r(h) = -20*h**3 + 10*h**2 - 81*h + 98. Let g be 34/((-3 - -2) + 3). Let j(o) = -7*o**3 + 3*o**2 - 27*o + 33. Let y(p) = g*j(p) - 6*r(p). Factor y(k).
(k - 3)**3
Suppose -r - 2 = -q, r - 16 = 2*q - 4*q. Solve 2*z - q*z - 8*z**2 - 4*z - 2*z**3 = 0 for z.
-2, 0
Factor 0 + 8/5*k**3 + 0*k + 4/5*k**2 + 4/5*k**4.
4*k**2*(k + 1)**2/5
Suppose 3*f = -b - 1, 3*f - 2*b - 2*b = 4. Let s = 4/15 + 1/15. Factor s*p**2 + f - 1/3*p.
p*(p - 1)/3
Let i(p) be the first derivative of 0*p + 3 - 1/15*p**6 + 0*p**2 + 0*p**3 - 1/10*p**4 - 4/25*p**5. Factor i(o).
-2*o**3*(o + 1)**2/5
Suppose 6*i - 25 = -1. Let j(p) be the first derivative of 1/2*p + 1/4*p**2 - 1/6*p**3 - 1/8*p**i + 1. Find a such that j(a) = 0.
-1, 1
Let n(q) be the first derivative of 2*q**3/33 + 3*q**2/1