 o(k) be the first derivative of f(k). Find p such that o(p) = 0.
2/3, 1
Let l = 67/3 - 22. Suppose 3*a = -0*a + 12, 3*a = 2*x + 4. Suppose 0 + 0*d**2 - l*d**x - 1/3*d**3 + 0*d = 0. What is d?
-1, 0
Let b be ((-12)/(-18))/((-2)/(-6)). Factor 48*s**3 + 24*s**2 + 22*s**2 + 6*s + 21*s**4 - 13*s**b.
3*s*(s + 1)**2*(7*s + 2)
Let p(m) = -m**2 + 13*m - 16. Let q(t) = -t + 1. Let j(w) = -3*p(w) - 21*q(w). Solve j(z) = 0 for z.
3
Determine x, given that -3/8*x**5 + 0*x**2 + 0 + 0*x**4 + 3/4*x**3 - 3/8*x = 0.
-1, 0, 1
Solve -9/4*v + 7/2 + 1/4*v**2 = 0 for v.
2, 7
Let h(j) be the second derivative of -3*j**5/40 + 4*j. Determine n so that h(n) = 0.
0
Suppose -3*u = 3*h - 15, 10 = 2*h - 3*u + 6*u. Suppose h + 3 = n. Solve -4*k**4 + 8*k**3 - 2*k**4 + k - k**5 - n*k**5 + 6*k**2 = 0 for k.
-1, -1/3, 0, 1
Let i(l) = l**4 + l**3 + 6*l + 6. Let g(u) = -u**3 - u - 1. Let v(y) = -30*g(y) - 5*i(y). Solve v(o) = 0.
0, 5
Suppose 0 = -2*n - n - 18. Let k be 4/n - 164/(-12). Let 18*x**5 - 21*x**4 - 16*x**4 + k*x**4 + 8*x**2 - 4*x**3 + 2*x = 0. What is x?
-1/3, 0, 1
Let m(s) be the first derivative of -2/3*s**3 + 3 + 5/3*s**2 - 1/6*s**4 - 4/3*s + 2/15*s**5. Factor m(c).
2*(c - 1)**3*(c + 2)/3
Factor 0*p + 0 + 1/5*p**4 + 1/5*p**3 - 1/5*p**5 - 1/5*p**2.
-p**2*(p - 1)**2*(p + 1)/5
Suppose -5*t - 1 + 21 = 0. Let 2*n**5 - 10*n**4 + n**t + 6*n**3 + n**5 = 0. What is n?
0, 1, 2
Let u(x) be the second derivative of x**8/20160 + x**7/3780 + x**4/6 + 5*x. Let n(c) be the third derivative of u(c). Suppose n(t) = 0. Calculate t.
-2, 0
Let z(a) = -a**2 + 5. Let d be z(0). Suppose -4 = 4*h - d*h. Factor 0*g**h - 1/3*g**3 + 0*g**2 + 0 + 0*g + 1/3*g**5.
g**3*(g - 1)*(g + 1)/3
Let h(j) = 18*j**5 + 20*j**4 + 4*j**3 + 2*j**2. Let z(y) = -18*y**5 - 19*y**4 - 4*y**3 - 3*y**2. Let k(f) = 6*h(f) + 4*z(f). Factor k(v).
4*v**3*(v + 1)*(9*v + 2)
Factor 0 + 9/2*g**3 - 3/2*g**5 + 15/2*g**2 + 3*g - 3/2*g**4.
-3*g*(g - 2)*(g + 1)**3/2
Let g(t) be the first derivative of t**5/30 + 5*t**4/18 + 7*t**3/9 + t**2 - 2*t - 5. Let p(j) be the first derivative of g(j). Factor p(k).
2*(k + 1)**2*(k + 3)/3
Let k(i) be the first derivative of -i**4/2 - 2*i**3 - 1. Factor k(o).
-2*o**2*(o + 3)
Let p(q) be the third derivative of -q**5/210 + q**4/42 - q**3/21 + 4*q**2. Suppose p(j) = 0. Calculate j.
1
Let c(l) be the first derivative of 0*l - 2 + 0*l**2 + 1/14*l**4 - 4/21*l**3. Solve c(j) = 0.
0, 2
Let v(x) be the second derivative of x**7/1260 - x**6/180 + x**5/60 - x**4/4 + 3*x. Let l(f) be the third derivative of v(f). Factor l(q).
2*(q - 1)**2
Let b(a) be the third derivative of -7/20*a**5 - 2*a**2 + 0 + 0*a**3 + 0*a - 1/4*a**4. Factor b(g).
-3*g*(7*g + 2)
Factor -1/4*w**4 + 0*w**2 + 0*w**3 + 0 + 1/4*w**5 + 0*w.
w**4*(w - 1)/4
Let b be (-24)/(-15) - (-4)/10. Suppose i = 4*m + b + 12, -2*i = 2*m + 2. Find p such that 5*p + p**3 + 4*p**i + 0*p**2 + 2 + 0*p**3 = 0.
-2, -1
Let i(s) = -s + 4. Let u be i(4). Suppose u*z - 8 = -2*z. Factor 4*g**3 + 9*g**z - 2*g - 2*g**5 - 9*g**4.
-2*g*(g - 1)**2*(g + 1)**2
Let v(y) be the third derivative of y**7/70 - y**6/20 + 3*y**2. Factor v(t).
3*t**3*(t - 2)
Let d(l) be the second derivative of l**9/15120 - l**8/3360 + l**7/2520 - l**4/6 + l. Let z(i) be the third derivative of d(i). Factor z(t).
t**2*(t - 1)**2
Let f(s) be the first derivative of 4*s**3/9 - 11*s**2/6 - s - 15. Factor f(z).
(z - 3)*(4*z + 1)/3
Factor 0 + 0*f**3 + 0*f - 1/7*f**4 + 0*f**2.
-f**4/7
Let l(q) be the third derivative of 0*q + q**2 + 1/140*q**7 - 2/3*q**3 + 1/20*q**5 - 1/4*q**4 + 11/240*q**6 + 0. Factor l(x).
(x - 1)*(x + 2)**2*(3*x + 2)/2
Let n be (-3)/7 + (-48)/(-14). Suppose -n*r + 6*r = 15. Factor -q - r*q**3 + 4*q + 3*q**5 - q**3.
3*q*(q - 1)**2*(q + 1)**2
Let t(v) be the first derivative of -v**2 - v**4 - 1 + 0*v - 1/5*v**5 - 5/3*v**3. Let t(c) = 0. What is c?
-2, -1, 0
Let y(x) be the third derivative of -x**8/4704 + x**7/735 - x**6/280 + x**5/210 - x**4/3 - 4*x**2. Let a(q) be the second derivative of y(q). Factor a(l).
-2*(l - 1)**2*(5*l - 2)/7
Let x(c) be the third derivative of 1/200*c**6 + 0*c**3 + 0 + 0*c + 1/100*c**5 - 1/20*c**4 + 8*c**2. Factor x(b).
3*b*(b - 1)*(b + 2)/5
Let h(t) = -t**2 - 1. Let a(y) = 6*y - 5 - 11*y**2 + 2*y**2 - 5*y. Let b = 17 - 7. Let k(n) = b*h(n) - 2*a(n). Solve k(z) = 0.
0, 1/4
Let r(c) be the third derivative of -c**7/1680 + c**6/480 + c**5/480 - c**4/96 - 43*c**2. Factor r(t).
-t*(t - 2)*(t - 1)*(t + 1)/8
Let n(w) = w**3 - 3*w**2 + 2. Let l be n(3). Factor 12 - 12*h - 2*h**2 + 5*h**l + 0*h**2.
3*(h - 2)**2
Suppose -29*s**4 + 128*s**2 - 111*s**4 + 12*s**5 + 16*s**2 + 384*s**3 = 0. Calculate s.
-1/3, 0, 6
Factor 3*d**2 + 2/3 + 1/3*d**4 + 7/3*d + 5/3*d**3.
(d + 1)**3*(d + 2)/3
Suppose -d - 4*s = -s + 3, -4*d + s + 14 = 0. Suppose -c = d*c - 12. Factor 4*m**5 - m**2 - 23 - 9*m**4 + 6*m**c + 23.
m**2*(m - 1)**2*(4*m - 1)
Let n(p) = 17 + 3*p + p**3 - 20 + 4*p**3 - 2*p**4. Let q(z) = -2*z**4 + 4*z**3 + 2*z - 2. Let s(h) = -4*n(h) + 6*q(h). Solve s(v) = 0 for v.
0, 1
Suppose 2*t + 0*t = 6. Suppose -4*f + r + 37 = -4*r, -6 = 3*f + t*r. Factor 2*a**3 + a**2 - a**f - 2*a**2.
a**2*(a - 1)
Let -z - 2/3 - 1/3*z**2 = 0. What is z?
-2, -1
Let p(g) be the second derivative of g**6/90 + g**5/12 - 7*g**4/12 + 23*g**3/18 - 4*g**2/3 + 47*g. Let p(x) = 0. What is x?
-8, 1
Let r be (0 - 6)/(3 - 51/3). Factor 1/7*g**2 + 4/7*g + r.
(g + 1)*(g + 3)/7
Find l, given that -3*l - 4*l**2 - 12*l + 20 - l**2 = 0.
-4, 1
Let l(f) be the first derivative of -f**4/4 - f**3/2 + f + 3. Let n(i) be the first derivative of l(i). Determine a, given that n(a) = 0.
-1, 0
Factor 3*a**2 - 2*a**2 + 9*a**3 + 2*a - 3*a - 1 - 8*a**3.
(a - 1)*(a + 1)**2
Suppose 0*x = 2*x - 3*q - 27, 2*x = -3*q - 3. Solve 2*j - 2*j**4 - 6*j**2 + x*j**3 + 2 + 3 - 5 = 0.
0, 1
Suppose -4*y + 142 = -194. Let u be (-4)/7 - (-104)/y. Solve 2*g - u + 2/3*g**3 - 2*g**2 = 0.
1
Suppose 5 = 3*d + 5*y, -5*d + 0 = -5*y + 5. Let l(u) be the second derivative of 2*u + d - 1/3*u**3 + 0*u**2 - 1/6*u**4. Find a, given that l(a) = 0.
-1, 0
Let s(c) = -3*c**3 + c**2 + c - 1. Let h(k) = -4*k**3 - 6 + 1 + 5*k**2 + 3*k**3 - 15*k**3 + 5*k. Let j(m) = -4*h(m) + 22*s(m). Factor j(u).
-2*(u - 1)**2*(u + 1)
Suppose 5*f - 3*z + 206 = -z, f + 28 = -4*z. Let y = f - -121/3. Find l such that 0*l**2 - 1/3*l**5 + 0*l + 0 - 2/3*l**4 - y*l**3 = 0.
-1, 0
Let r(v) = -2*v**2 + 8*v + 5. Let b(k) = -k**2 - 1. Let h(c) = 3*b(c) - r(c). Let u be h(-6). Let -1 + 0 - 2*j**2 + u*j - 1 = 0. Calculate j.
1
Let s(j) be the second derivative of -1/36*j**4 - j + 1/90*j**6 + 0 + 0*j**2 - 1/60*j**5 + 1/18*j**3. Find h such that s(h) = 0.
-1, 0, 1
Suppose 0 - 2/3*o**2 + 0*o - 2/3*o**3 = 0. Calculate o.
-1, 0
Let l(k) = -75*k**3 - 340*k**2 + 520*k - 125. Let t(i) = -37*i**3 - 169*i**2 + 260*i - 62. Let d(x) = 2*l(x) - 5*t(x). Find c, given that d(c) = 0.
-6, 2/7, 1
Let v(g) be the third derivative of g**7/70 + g**6/40 - g**5/20 - g**4/8 - 6*g**2. Factor v(w).
3*w*(w - 1)*(w + 1)**2
What is v in -2/7*v**3 + 2/7*v**4 + 1/7*v - 4/7*v**2 + 1/7*v**5 + 2/7 = 0?
-2, -1, 1
Let r = -43 + 43. Factor 2/5*l**2 + r - 2/5*l**4 + 2/5*l - 2/5*l**3.
-2*l*(l - 1)*(l + 1)**2/5
Let d(z) be the second derivative of -z**9/7560 + z**8/1680 - z**6/180 + z**5/60 - z**4/12 + 3*z. Let u(o) be the third derivative of d(o). Factor u(i).
-2*(i - 1)**3*(i + 1)
Solve 3/2*u**4 + 9/2 + 3*u**3 - 3*u - 6*u**2 = 0.
-3, -1, 1
Factor 0*c - 6/13*c**2 + 8/13 - 2/13*c**3.
-2*(c - 1)*(c + 2)**2/13
Let m = -8471/15 - -565. Factor -2/15*i**4 - 4/15*i**3 + 2/15 + 0*i**2 + m*i.
-2*(i - 1)*(i + 1)**3/15
Solve 2/5*p**4 + 0 - 8/5*p**3 - 4/5*p + 2*p**2 = 0 for p.
0, 1, 2
Let u(a) be the second derivative of a**4/72 - a**3/12 + a**2/6 - 16*a. Factor u(d).
(d - 2)*(d - 1)/6
Let k(b) be the third derivative of -3*b**6/40 - b**5/5 + 5*b**4/8 + b**3 + 16*b**2. Factor k(y).
-3*(y - 1)*(y + 2)*(3*y + 1)
Find p such that 5/2*p - 1 + 7/2*p**2 = 0.
-1, 2/7
Let i(r) be the third derivative of r**6/24 - 5*r**4/8 - 5*r**3/3 - 13*r**2. Factor i(b).
5*(b - 2)*(b + 1)**2
Factor -1/3*z**2 - 2/3 - z.
-(z + 1)*(z + 2)/3
Let l(h) be the first derivative of -h**4 + 4*h**3/3 + 4*h**2 + 5. Suppose l(d) = 0. Calculate d.
-1, 0, 2
Let n be (-63)/14*4/(-15). Factor -4/5*q + n*q**2 + 24/5*q**3 + 14/5*q**4 + 0.
2*q*(q + 1)**2*(7*q - 2)/5
Let b(g) be the 