et f(v) = 0. What is v?
0, 2/3
Let o(a) be the third derivative of -a**7/4620 - a**6/990 - a**5/660 + a**3/6 - a**2. Let s(v) be the first derivative of o(v). Factor s(i).
-2*i*(i + 1)**2/11
Let w(h) be the second derivative of -h**9/4536 + h**7/1260 - h**3/6 + h. Let k(x) be the second derivative of w(x). What is d in k(d) = 0?
-1, 0, 1
Let z(h) be the first derivative of -h**8/168 + 3*h**2/2 - 2. Let u(r) be the second derivative of z(r). Determine n so that u(n) = 0.
0
Suppose 0 = 2*v + v - 63. Let -24*k**4 + 0*k - 3 - 97*k**3 - v*k - 54*k**2 + 37*k**3 = 0. What is k?
-1, -1/2
Let r(q) be the second derivative of q**5/100 - q**4/15 - 7*q. Let r(u) = 0. Calculate u.
0, 4
Let z be (8/(-12)*-1)/(4/10). Solve 0 + z*n**2 + 2/3*n = 0 for n.
-2/5, 0
Let c be (-28)/16*(-496)/6. Let s = 146 - c. Solve -s*f + 2/3 + 2/3*f**2 = 0.
1
Let w(m) = -3*m**3 + 55*m**2 - 244*m + 188. Let t(i) = 21*i**3 - 384*i**2 + 1707*i - 1317. Let o(q) = -4*t(q) - 27*w(q). What is f in o(f) = 0?
1, 8
Suppose 0 = 5*r - 25, -4*r = 4*p - 29 - 3. Factor 2/7*l**4 + 0*l**p - 2/7*l**2 + 0*l + 0.
2*l**2*(l - 1)*(l + 1)/7
Let t = 2/9 - -5/18. Let v be -1*7/((-7)/2). Suppose s + 0 + t*s**v = 0. Calculate s.
-2, 0
Suppose 3*w + o - 25 = -0*w, -4*w - o = -35. Let h = w - 10. Suppose h*g**2 + 0*g + 0 + 1/4*g**3 - 1/4*g**4 = 0. What is g?
0, 1
Let f(d) = d + 14. Let a be f(-7). Let k = -2 + a. Let 4/3 - 5*w**2 + 0*w + 3*w**5 + k*w**4 - 5/3*w**3 = 0. What is w?
-1, 2/3
Let m(l) be the first derivative of -l**3/18 - l**2/4 + 2*l/3 + 4. Find d such that m(d) = 0.
-4, 1
Suppose -17*q + 3 = -48. Suppose -21*s - 63/2*s**q + 183/4*s**2 + 3 + 27/4*s**4 = 0. What is s?
1/3, 2
Suppose -9*n = -14*n. Factor -2/3*j + 2/3*j**3 + 1/3 + n*j**2 - 1/3*j**4.
-(j - 1)**3*(j + 1)/3
Let r(g) be the third derivative of -2*g**2 + 1/96*g**4 - 1/240*g**5 + 0*g**3 + 0 + 0*g. Factor r(f).
-f*(f - 1)/4
Factor q**5 + 11*q**2 + 4*q**5 - 20*q**4 - 25*q + 10 - q**2 + 0*q**5 + 20*q**3.
5*(q - 2)*(q - 1)**3*(q + 1)
Let n(b) be the second derivative of b**5/80 - b**4/24 - b**3/8 + 2*b. Find o such that n(o) = 0.
-1, 0, 3
Let x(i) be the third derivative of 0*i**3 - 1/48*i**4 + 0 - 5*i**2 + 0*i - 1/240*i**5. Factor x(y).
-y*(y + 2)/4
Let x(h) be the second derivative of -h**6/720 + h**5/90 - 5*h**4/144 + h**3/18 + 3*h**2/2 - 2*h. Let q(b) be the first derivative of x(b). Factor q(l).
-(l - 2)*(l - 1)**2/6
Let m(n) be the second derivative of -n**6/80 + 39*n**5/160 - 3*n**4/2 + 9*n**3/4 - 35*n. Suppose m(z) = 0. Calculate z.
0, 1, 6
Suppose 21*x - 6 + 6 = 0. Factor -8/3*d**3 + 5/3*d**4 + 2/3*d + 1/3*d**2 + x.
d*(d - 1)**2*(5*d + 2)/3
Suppose -3*q + 20 = -2*g, -5*q - 6*g + 8 = -3*g. Let -2*n + 1/4*n**2 + q = 0. What is n?
4
Let h(w) be the third derivative of w**7/1260 - w**6/360 - w**5/360 + w**4/72 - 28*w**2. Factor h(s).
s*(s - 2)*(s - 1)*(s + 1)/6
Suppose 5/2*a**2 + 10*a + 15/2 = 0. Calculate a.
-3, -1
Let u(c) be the second derivative of 7/3*c**4 + 0*c**2 - 4*c + 4/3*c**3 + 4/15*c**6 + 0 + 7/5*c**5. Find k, given that u(k) = 0.
-2, -1, -1/2, 0
Solve 225/2*m + 3/2*m**3 + 45/2*m**2 + 375/2 = 0 for m.
-5
Suppose 4*l + 29 = 3*g, g - 1 - 7 = l. Let j(y) be the second derivative of 1/6*y**3 - 1/12*y**4 + g*y + y**2 + 0. Let j(f) = 0. Calculate f.
-1, 2
Let n(a) = -6*a**3 + 5*a**2 + a + 2. Let l(p) = -p**2 + p - 1. Let z(d) = d. Let g be z(-1). Let b(w) = g*n(w) - 2*l(w). Factor b(r).
3*r*(r - 1)*(2*r + 1)
Let q(z) = z**2 + 4*z + 2. Let i be q(-4). Factor 3/4*u**3 - 3/4*u**i - 3/4*u + 3/4.
3*(u - 1)**2*(u + 1)/4
Let v(n) = -n**3 - n**2 - n + 1. Let a(h) = 2*h**3. Let t(c) = 5*a(c) + 5*v(c). Factor t(i).
5*(i - 1)**2*(i + 1)
Let m(h) be the third derivative of -h**7/2940 - h**6/630 - h**3/3 - 4*h**2. Let f(z) be the first derivative of m(z). Determine b so that f(b) = 0.
-2, 0
Let b(l) be the second derivative of -l**5/20 + l**4/12 + l**3/6 - l**2/2 + 3*l. Factor b(g).
-(g - 1)**2*(g + 1)
Factor -7*z**2 + 5*z**2 - 2 + 0 + 4*z.
-2*(z - 1)**2
Find p, given that 75 + 10*p + 1/3*p**2 = 0.
-15
Solve -21*j + 9/4*j**4 + 51/2*j**2 + 6 - 51/4*j**3 = 0 for j.
2/3, 1, 2
Let z(p) be the first derivative of -7*p**4 - 16*p**3 + 120*p**2 - 64*p + 60. Find m such that z(m) = 0.
-4, 2/7, 2
Let m(f) be the third derivative of 0 + 0*f - 1/24*f**4 - 1/180*f**5 - 6*f**2 - 1/9*f**3. Suppose m(o) = 0. Calculate o.
-2, -1
Let u = -10 - -41/4. Let n(d) be the first derivative of -u*d**4 - 6*d**2 + 2*d**3 + 8*d + 3. Factor n(r).
-(r - 2)**3
Let m(t) be the first derivative of -5*t**3/12 + 10*t**2 - 80*t - 32. Factor m(p).
-5*(p - 8)**2/4
Determine m so that 2*m**2 + 7 - 7 + m**3 + m = 0.
-1, 0
Let u = -152 - -1066/7. Factor -u*f - 2/7*f**4 + 2/7*f**2 + 2/7*f**3 + 0.
-2*f*(f - 1)**2*(f + 1)/7
Suppose -32 - o**3 + o + o**4 - o**2 + 32 = 0. Calculate o.
-1, 0, 1
Let i(s) be the second derivative of s**4/42 - s**2/7 + 8*s. Let i(c) = 0. Calculate c.
-1, 1
Let u(z) be the first derivative of -3*z**5/5 - 3*z**4 - 6*z**3 - 6*z**2 - 3*z - 4. Suppose u(x) = 0. What is x?
-1
Let c(o) be the second derivative of 1/30*o**5 + 1/90*o**6 + 0*o**3 + 1/36*o**4 + 0*o**2 + 0 - o. Factor c(v).
v**2*(v + 1)**2/3
Suppose 5 = w, -c + 3*w = -0 + 13. Determine g, given that -c - 3*g**5 - 11*g - 6*g**4 - 24*g**2 - 14*g**4 + 0 - 26*g**3 + 6*g**4 = 0.
-1, -2/3
Let u(m) be the third derivative of -m**7/840 + m**6/240 - m**5/240 + 16*m**2. Determine a, given that u(a) = 0.
0, 1
Let z = 10042/27 - 372. Let a = z - -35/108. Determine s so that a*s**2 - 1/4*s**3 + 0 + 0*s = 0.
0, 1
Let k(h) = -h**4 + h**3 - h**2 + 2*h - 1. Let s(o) = -2*o**4 - 3*o**3 + 6*o - 1. Let a(g) = k(g) - s(g). Suppose a(p) = 0. Calculate p.
-4, -1, 0, 1
Let g(r) be the third derivative of r**7/42 - r**6/6 - 11*r**5/12 - 5*r**4/4 + r**2 + 2. Factor g(c).
5*c*(c - 6)*(c + 1)**2
Let p(b) be the first derivative of 3/4*b**2 + 3/8*b**4 - 4/3*b**3 + b - 5. Let p(i) = 0. What is i?
-1/3, 1, 2
Let i(a) = -9*a**3 + 11*a**2 - 4*a. Let x(c) = 17*c**3 - 23*c**2 + 7*c. Let l(h) = -7*i(h) - 4*x(h). Factor l(z).
-5*z**2*(z - 3)
Let x be (-5 - -13)/((-2)/(-3)). Suppose c + 5*c - x = 0. Solve 4/13*p - 2/13*p**c - 2/13 = 0.
1
Let l(s) be the first derivative of 0*s**2 - 3/10*s**4 + 1 - 3/25*s**5 + 0*s - 1/5*s**3. Find r such that l(r) = 0.
-1, 0
Let t be (-13)/(-5) + 6 + (-33)/5. Let a(s) be the second derivative of 7/48*s**4 - s + 1/4*s**t + 3/8*s**3 + 0. Factor a(c).
(c + 1)*(7*c + 2)/4
Let l(d) be the first derivative of d**8/4200 + d**7/2100 - d**6/900 - d**5/300 - 4*d**3/3 + 1. Let i(t) be the third derivative of l(t). Factor i(y).
2*y*(y - 1)*(y + 1)**2/5
Let v(h) be the third derivative of -h**6/200 - 3*h**5/100 - 3*h**4/40 - h**3/10 - 44*h**2. Factor v(d).
-3*(d + 1)**3/5
Suppose -r + 3*r - 1 - 4*r - r**2 = 0. What is r?
-1
Let u(p) be the first derivative of -4*p**5/5 - 6*p**4 - 12*p**3 - 36. Determine j, given that u(j) = 0.
-3, 0
Suppose 0*z + 4*z = 0. Let w(r) = -r**2 + r + 2. Let f be w(z). Factor -3*a + a**5 + 2*a - 3*a**4 + 2*a**f + a**4.
a*(a - 1)**3*(a + 1)
Suppose -16 = -11*n + 7*n. Let p(u) be the first derivative of 0*u**2 + 0*u + 0*u**3 - 2 - 1/10*u**n. What is g in p(g) = 0?
0
Let v(k) be the first derivative of k**5/120 - k**4/16 + k**3/6 + 5*k**2/2 - 1. Let f(r) be the second derivative of v(r). Factor f(p).
(p - 2)*(p - 1)/2
Factor -1/3*s**2 + 1/9*s**4 + 4/9*s**3 - 10/9*s + 8/9.
(s - 1)**2*(s + 2)*(s + 4)/9
Let a(t) be the second derivative of -t**7/10080 - t**6/960 - t**5/240 - t**4/12 + 7*t. Let z(l) be the third derivative of a(l). Find q, given that z(q) = 0.
-2, -1
Let s be (4/5)/(-18*(-5)/75). Suppose 4*m**2 + 0 + 6*m + s*m**3 = 0. What is m?
-3, 0
Let t be 18/(-27) - (2 + 24/(-9)). Determine q so that 3/2*q**2 + t + q**3 - q - 3/2*q**4 = 0.
-1, 0, 2/3, 1
Let s(m) be the third derivative of -m**7/105 + m**5/15 - m**3/3 - 33*m**2. Factor s(q).
-2*(q - 1)**2*(q + 1)**2
Suppose -3/8*c**3 - 27/8*c + 9/4*c**2 + 0 = 0. Calculate c.
0, 3
Let l(u) be the first derivative of -4*u + 2*u**4 - 4*u**2 + 6 + 0*u**3 + 4/5*u**5. Find g such that l(g) = 0.
-1, 1
Let f(v) = 4*v**2 + 176*v - 800. Let l(m) = -m**2 - 59*m + 266. Let j(k) = -5*f(k) - 16*l(k). Determine a so that j(a) = 0.
8
Let i(n) be the first derivative of n**5/5 - n**4/2 - n**3 + 36. Factor i(c).
c**2*(c - 3)*(c + 1)
Let c(n) = 3*n**2 - 4*n + 5.