2/7*k**4 - 4/7*k**3 + 0 + 2/7*k**2.
2*k**2*(k - 1)**2/7
Let f(p) be the first derivative of 7*p**6/18 + p**5 + 3*p**4/4 + p**3/9 + 6. Solve f(o) = 0.
-1, -1/7, 0
Let q(x) = 6*x**2 - 4*x + 3. Let v be q(2). Let w = 39/2 - v. Solve w*m - 1/4*m**2 - 1/4 = 0.
1
Let -5*f - 30 - f**2 + 0*f**2 + 6*f**2 = 0. Calculate f.
-2, 3
Let x be (4/(-18))/(5/(-45)). Determine a, given that a + 1/2*a**x + 1/2 = 0.
-1
Suppose 6/13*z + 4/13 + 2/13*z**2 = 0. Calculate z.
-2, -1
Let h be 46/253 - -6*14/22. Let k be (-2)/(-2) + 28/(-36). Solve 2/9*c**5 + 4/9*c**2 + 0*c**3 - k*c + 0 - 4/9*c**h = 0 for c.
-1, 0, 1
Let p = 4272/7 + -610. Factor -8/7 - p*h**3 + 0*h + 6/7*h**2.
-2*(h - 2)**2*(h + 1)/7
Let j be 4 + -2 + (2 - 0). Let z(k) = -k**5 + 5*k**3 - 3*k**2 - k - 3. Let y(x) = 4*x**3 - 4*x**2 - 4. Let i(p) = j*z(p) - 3*y(p). Find l such that i(l) = 0.
-1, 0, 1
Let u(x) = -x**3 + 3*x**2 + 4*x + 2. Let g be u(4). Let 2*n - 2 + g*n**2 + 0 + 2 = 0. What is n?
-1, 0
Suppose -18 = -5*p - 3. Let a be (((-4)/4)/(-1))/p. Factor 0 + 0*i + a*i**2.
i**2/3
Let s(o) be the third derivative of -o**6/450 - o**5/25 - 3*o**4/10 + o**3 + 9*o**2. Let q(v) be the first derivative of s(v). Factor q(d).
-4*(d + 3)**2/5
Suppose -4*p - 93 = -3*a + 16, 5*p = 25. Find v such that 4*v**3 - v**4 - a + 43 + v**2 - 4*v**5 = 0.
-1, -1/4, 0, 1
Let z(t) be the third derivative of 0 - 1/70*t**7 + 1/336*t**8 + 1/30*t**5 + 1/6*t**3 - 1/8*t**4 + 0*t + 1/60*t**6 - 7*t**2. Factor z(i).
(i - 1)**4*(i + 1)
Factor 4*j - 2/3*j**2 - 6.
-2*(j - 3)**2/3
Let p = 327 + -3267/10. Let z(s) be the first derivative of 1/12*s**6 + 2 + 0*s**2 + p*s**5 + 3/8*s**4 + 0*s + 1/6*s**3. Find m, given that z(m) = 0.
-1, 0
Let x(s) = 2*s - 22. Let c be x(11). Let q(r) be the first derivative of 0*r**2 + 2 + c*r + 2/3*r**3. Suppose q(m) = 0. What is m?
0
Factor 0*l + 0 - 4/5*l**3 - 2/5*l**4 - 2/5*l**2.
-2*l**2*(l + 1)**2/5
Suppose 0 = p + 2*u - 3, -p + 5*p - 9 = -5*u. Let b be p/2 - (-5)/2. Find w, given that 0*w**4 - w**4 - 4*w**b - 2*w**2 - w**4 = 0.
-1, 0
Let y(b) be the first derivative of 2*b**4 - 2*b**3 - 9*b**2 - 4*b + 14. Determine x, given that y(x) = 0.
-1, -1/4, 2
Factor -3/2*l**2 + 4*l - 8/3.
-(3*l - 4)**2/6
Let y(f) = f - 2. Let j be y(12). Let x = j - 8. What is p in p**x + p**2 - 6*p**2 - 2*p + 3*p**2 = 0?
-2, 0
Let x(c) be the third derivative of -7*c**5/90 + 5*c**4/18 - c**3/3 - 7*c**2. Find w such that x(w) = 0.
3/7, 1
Let f(c) = c**2 - 2. Let u be f(0). Let t be u + 2 - (-1 - 4). Factor 0 - 1/2*o + 1/4*o**4 - 3/4*o**3 + 1/4*o**t - 5/4*o**2.
o*(o - 2)*(o + 1)**3/4
Let j(b) be the second derivative of b**6/105 + b**5/70 - b**4/42 - b**3/21 - 8*b. Factor j(n).
2*n*(n - 1)*(n + 1)**2/7
Suppose 0 = 2*z + 5*x - 16, -3*x + 0 = -z - 3. Let u(v) = v**2 - 4*v - 2. Let f be u(5). Let 1 - z*l - 2*l**f + l**3 + 0*l + 0*l + 3*l**2 = 0. What is l?
1
Let a(d) = d**3 - 10*d**2 - 13*d + 22. Let k be a(11). Let o(j) be the third derivative of 1/2*j**4 - 2*j**2 + k + 0*j - 3*j**3 - 1/30*j**5. Factor o(f).
-2*(f - 3)**2
Let -2*n**2 - n**2 + 4*n**2 + 3*n**3 + 3*n + 5*n**2 = 0. What is n?
-1, 0
Let o be 1/(-4) - ((-85)/20 + 4). Let q(s) be the second derivative of 0*s**2 - 3*s + 1/24*s**4 + o + 1/12*s**3. Factor q(l).
l*(l + 1)/2
Let q(c) = 3. Let u(f) = f + 1. Let l(g) = q(g) - u(g). Let p be l(2). Factor 1/5*r**3 + p*r + 0 + 0*r**2 + 1/5*r**4.
r**3*(r + 1)/5
Let -25/7*w + 0 - 1/7*w**3 - 10/7*w**2 = 0. Calculate w.
-5, 0
Let p(a) be the third derivative of -a**8/5040 + a**7/1260 - a**6/1080 - 2*a**3/3 + 4*a**2. Let z(v) be the first derivative of p(v). Let z(k) = 0. Calculate k.
0, 1
Let b(l) be the third derivative of -1/200*l**6 - 6/5*l**4 + l**2 - 3/25*l**5 + 0 + 0*l - 32/5*l**3. Let b(d) = 0. Calculate d.
-4
Factor 0 + 2/5*y - 2/5*y**3 + 0*y**2.
-2*y*(y - 1)*(y + 1)/5
Suppose 6 = 2*l + 2. Let z(d) be the second derivative of -1/5*d**5 + 0 - l*d + 2/3*d**3 - 1/15*d**6 + d**2 + 0*d**4. Find y such that z(y) = 0.
-1, 1
Suppose 5 + 11 = 4*o. Let f(r) be the first derivative of 1/2*r**3 - 3/4*r**2 - 1/8*r**o + 2 + 1/2*r. Find x, given that f(x) = 0.
1
Let s(w) = -3*w**3 - w**2 - w. Let j be s(-1). Factor q**3 + 0*q**3 + 2*q**4 + q**j.
2*q**3*(q + 1)
Let j = -8 - -14. Suppose -j*x = -x. Factor 0 - u**4 + 0*u**2 + 1/2*u**5 + 1/2*u**3 + x*u.
u**3*(u - 1)**2/2
Let o(d) = -2*d**3 - 3*d**2 + d + 2. Let z(x) = -x - 8. Let j be z(-6). Let g be o(j). Let 8/3*b**3 + 0 + 0*b - 8/3*b**2 - 2/3*b**g = 0. What is b?
0, 2
Suppose -b = 2*b - 42. Let n = b - 11. Factor 2/3*t**n + 2/3*t + 4/3*t**2 + 0.
2*t*(t + 1)**2/3
Factor -17*v + 8 - v**2 - 2*v**3 - 2*v**4 - 5*v + 19*v**2.
-2*(v - 1)**3*(v + 4)
Let i(g) = -3*g**2 - 36*g - 109. Let k(u) = -1. Let o(f) = -i(f) + k(f). Determine m, given that o(m) = 0.
-6
Let b(q) = -7*q**4 + 4*q**3 + 3*q**2 + 4*q + 4. Let i(g) = -g**4 + g**3 + g + 1. Let s(a) = -b(a) + 4*i(a). Find y, given that s(y) = 0.
-1, 0, 1
Suppose -m + 4*m + 4*h - 38 = 0, -m = -5*h. Factor 8*i + 4*i**3 - 6*i**2 + 13*i - m*i**2 - 9*i.
4*i*(i - 3)*(i - 1)
Let f(l) = l**3 - 5*l**2 + 4*l + 1. Let y be f(4). Let z be (8/50)/(y/5). Determine s, given that 2/5*s**2 + z*s + 2/5 = 0.
-1
Let o(x) be the third derivative of -1/3*x**3 + 0*x**4 - 1/1800*x**6 + 0*x + 2*x**2 + 0 - 1/600*x**5. Let s(y) be the first derivative of o(y). Factor s(d).
-d*(d + 1)/5
Solve -4/15*i**2 + 0 + 2/15*i + 2/15*i**3 = 0 for i.
0, 1
Let l = 11 + -11. Let 0*z + 0*z**2 + 0 + l*z**3 + 2/9*z**4 = 0. What is z?
0
Let c(o) be the second derivative of 0 + 1/360*o**6 + 0*o**2 + 0*o**5 - o - 1/24*o**4 - 1/6*o**3. Let g(y) be the second derivative of c(y). Factor g(q).
(q - 1)*(q + 1)
Let y(p) be the second derivative of -p**5/42 + p**4/28 + 2*p**3/21 - 2*p**2 - 5*p. Let j(q) be the first derivative of y(q). Suppose j(f) = 0. What is f?
-2/5, 1
Let m = 4 + -2. Factor -4 + 2 + 3 - x**m.
-(x - 1)*(x + 1)
Let w(o) be the first derivative of -o**6/120 - o**5/20 - o**4/8 - o**3/6 - o**2/2 - 6. Let f(i) be the second derivative of w(i). Factor f(s).
-(s + 1)**3
Let x be (1 + -1 + 1)*2. Factor 5*j**2 + j**2 + 2*j**3 + 1 + 1 + 6*j + 0*j**x.
2*(j + 1)**3
Suppose 9 = 3*g - 0. Let o(y) be the first derivative of -7/12*y**3 - 3/16*y**4 - 5/8*y**2 - 1/4*y + g. Suppose o(h) = 0. What is h?
-1, -1/3
Let x(h) be the second derivative of 0*h**2 + 1/50*h**6 - 8*h + 1/5*h**4 - 3/25*h**5 + 0*h**3 + 0. Factor x(d).
3*d**2*(d - 2)**2/5
Let k be (-20)/(-9) - 10/45. Let s(u) be the first derivative of 2 + 0*u**3 - 2/5*u + 2/25*u**5 - 2/5*u**k + 1/5*u**4. Solve s(m) = 0.
-1, 1
Let t = 41 + -39. Let n = 1264/7 - 180. Factor 6/7*i - n*i**t - 2/7.
-2*(i - 1)*(2*i - 1)/7
Solve 2/3 + 1/6*v**2 - 2/3*v = 0 for v.
2
Factor 0*u - 3*u + 2*u**2 + 13*u + 0*u**2.
2*u*(u + 5)
Let g(i) = -2*i + 6. Let x be g(11). Let u be -4*4/x*0. Factor -4/5*z**3 + 2/5*z**4 + 4/5*z + u*z**2 - 2/5.
2*(z - 1)**3*(z + 1)/5
Find x, given that -2*x**2 - 5*x**3 + 5*x**3 - 2*x**3 = 0.
-1, 0
Let z(h) = -h**2. Let s(n) = -n**2. Let w be (-1)/(39/18 - 2). Suppose -5*t = -16 - 9. Let a(o) = t*z(o) + w*s(o). Factor a(k).
k**2
Let z(n) be the second derivative of -n**9/60480 + n**8/13440 - n**7/10080 - n**4/3 - 3*n. Let r(u) be the third derivative of z(u). Factor r(x).
-x**2*(x - 1)**2/4
Let l(z) be the first derivative of 2 + 1/25*z**5 + 16/5*z + 2/5*z**4 + 16/5*z**2 + 8/5*z**3. Find j, given that l(j) = 0.
-2
Let x(u) be the first derivative of -u**9/6048 + u**7/560 + u**6/360 + 2*u**3/3 - 3. Let o(i) be the third derivative of x(i). Let o(t) = 0. What is t?
-1, 0, 2
Let m(s) = -6*s**5 - 28*s**4 - 28*s**3 - 6*s**2 + 10. Let o(p) = -2*p**5 - 9*p**4 - 9*p**3 - 2*p**2 + 3. Let t(x) = -6*m(x) + 20*o(x). Let t(q) = 0. What is q?
-1, 0
Let w be 11/(11/(-3)) - -7. Determine x, given that 0*x - 4/7*x**5 + 6/7*x**w - 2/7*x**2 + 0 + 0*x**3 = 0.
-1/2, 0, 1
Let h(k) = -k**3 - 6*k**2 - k - 3. Let j be h(-6). Factor 4*f**3 - 6*f**j - 3*f**3 + 3*f**3.
-2*f**3
Let i be 5 + (2 - 3 - -3). Factor -w**3 + 3*w**2 - w**2 + 2*w + i*w**2 + 8*w**3.
w*(w + 1)*(7*w + 2)
Let k(g) be the third derivative of g**6/280 - g**4/8 - 3*g**3/7 - 34*g**2. Factor k(s).
3*(s - 3)*(s + 1)*(s + 2)/7
Let b(x) be the second derivative of -x**7/840 + x**6/240 - x**4/4 - x. Let d(g) be the third derivative of b(g). Factor d(c).
-3*c*(c - 1)
Suppose -788 + 786 + 5*t**2 + 3*t**2 + 4*t**2 - 