0
Let r(s) be the third derivative of -1/30*s**5 + 0*s**3 + 0 + 1/105*s**7 - 1/24*s**4 + s**2 + 0*s + 1/336*s**8 + 0*s**6. Let r(m) = 0. What is m?
-1, 0, 1
Let l(f) = -16*f**2 + 176*f - 148. Let s(j) = -32*j + 21 + 8 - 2 + 3*j**2. Let d(a) = 5*l(a) + 28*s(a). Factor d(g).
4*(g - 2)**2
Let 3/2*f - 1 - 1/2*f**2 = 0. Calculate f.
1, 2
Let x(o) be the third derivative of 0*o**3 + 0*o**7 + 0*o**5 - 1/540*o**6 + 0*o**4 + 1/1512*o**8 + 0*o - o**2 + 0. Factor x(t).
2*t**3*(t - 1)*(t + 1)/9
Let y be (-1)/(0 - (-2)/(-4)). Suppose 2*c + y*f = 4*f + 6, c - 3 = -4*f. Factor 6*q**2 - 4*q**2 + 2*q + 0 - 2*q**c - 2.
-2*(q - 1)**2*(q + 1)
Suppose 5*r - 2 = 3. Suppose 2*b = -k + 4*k - 16, b = -3*k + r. Factor u**4 + u - 3*u + 4 + k*u**3 - 5.
(u - 1)*(u + 1)**3
Let b(a) be the third derivative of a**8/84 + 2*a**7/15 + 3*a**6/5 + 22*a**5/15 + 13*a**4/6 + 2*a**3 + 20*a**2. Find h such that b(h) = 0.
-3, -1
Let 3*w**3 - 9*w**2 + 0*w**3 + 11 + 0*w**3 - 14 + 9*w = 0. Calculate w.
1
Suppose 7*s**2 + 8*s + 4*s**2 + 5*s**2 + 6 - 14*s**2 = 0. Calculate s.
-3, -1
Let s(d) be the third derivative of -1/150*d**6 + 0*d + 0*d**3 - 2/75*d**5 + 1/10*d**4 + 0 + 9*d**2. Determine w so that s(w) = 0.
-3, 0, 1
Let h(s) be the first derivative of s**6/9 + 4*s**5/15 - s**4/2 + 61. Factor h(d).
2*d**3*(d - 1)*(d + 3)/3
Let -9*q - 1966*q**2 + 28*q**3 - 7*q - 8*q**4 + 1950*q**2 = 0. What is q?
-1/2, 0, 2
Let j(k) be the second derivative of -k**5/10 - k**4/3 - k**3/3 - 7*k. Find r, given that j(r) = 0.
-1, 0
Let p(w) be the first derivative of w**6/420 - w**5/105 + w**4/84 + 3*w**2/2 - 2. Let y(s) be the second derivative of p(s). Factor y(j).
2*j*(j - 1)**2/7
Suppose -10*b - 10 = -11*b. Let p be b/4*(-16)/(-10). Solve 5*s**3 + 2*s**2 + 5*s - 5*s + s**5 + p*s**4 = 0.
-2, -1, 0
Let m(y) = -4*y**5 - y**3 + 3*y**2 + 5*y + 3. Let p(x) = -3*x**5 - x**4 - x**3 + 3*x**2 + 4*x + 2. Let d(h) = -2*m(h) + 3*p(h). Factor d(c).
-c*(c - 1)*(c + 1)**2*(c + 2)
Let z(f) be the second derivative of -f**5/120 - f**4/48 + f**3/6 + f**2/2 + f. Let x(g) be the first derivative of z(g). Solve x(c) = 0.
-2, 1
Let x(z) = z - 1. Let s(a) = -6*a + 9. Let u(l) = -s(l) - 5*x(l). Let j be u(4). Factor 2*c - 8*c**2 + 5/2*c**3 + 25/2*c**4 + j.
c*(c + 1)*(5*c - 2)**2/2
Factor -4/3*r**2 + 5/6*r**3 - 19/6*r - 1.
(r - 3)*(r + 1)*(5*r + 2)/6
Let n be (54/(-4))/(-3)*1. Let t = n + -4. Factor -t*i**2 + 1/2*i**3 + 0*i + 0.
i**2*(i - 1)/2
Factor -2*p - 2*p**2 + p**2 + 5*p**2 - 2*p.
4*p*(p - 1)
Suppose -2*s - 2*q = -4, 0*q = 4*s - 2*q - 8. Suppose -s*k = -7*k + 15. Find n, given that 0 - 2/7*n**k + 2/7*n**2 - 2/7*n**4 + 2/7*n**5 + 0*n = 0.
-1, 0, 1
Let f be (0/(3/3))/1. Suppose f*a + 11 = a. Let 686*g**5 + 40*g**2 + 0*g + 5*g - 252*g**3 + a*g - 490*g**4 = 0. What is g?
-2/7, 0, 2/7, 1
Let n(u) be the second derivative of -1/6*u**2 + 0 + 1/36*u**4 + 1/60*u**5 + 2*u - 1/18*u**3. Factor n(s).
(s - 1)*(s + 1)**2/3
Let o be 294/35 - (-3)/5. Suppose -3*v - o = 4*c - 3*c, 4*v = -5*c - 1. Determine l so that -5/2*l**2 + 3/2*l**4 + 1/2*l**c - 1/2*l + 1 = 0.
-1, 2/3, 1
Suppose -3*o + 18 = n, o - 10 - 10 = -5*n. Suppose 11 = n*c + 5. Suppose -c - 3*s**3 + 2 - 6*s**2 + 3*s**2 = 0. Calculate s.
-1, 0
Suppose -7*o + 30 = -2*o. Solve -35*d**3 + 2*d**2 - o*d**2 + 37*d**3 + 2*d = 0 for d.
0, 1
Let r be 4/(-22) + (1587/198)/23. Let i(n) be the first derivative of 0*n**2 + 0*n + 3 - 3/16*n**4 + r*n**3. Suppose i(h) = 0. Calculate h.
0, 2/3
Let x(q) be the third derivative of -q**8/560 + q**6/100 - q**4/40 - 3*q**2. Solve x(a) = 0 for a.
-1, 0, 1
Let x(b) = 2*b**3 - 5*b**2 - 3*b + 12. Let l(v) = -v**3 - 1. Let u(t) = -3*l(t) - x(t). Determine y so that u(y) = 0.
-3, 1
Let l(j) be the first derivative of j**3/3 - 2*j**2 - 5*j - 4. Let i be l(5). Determine o so that -2/7*o**2 + 0*o**3 + i + 2/7*o**4 + 0*o = 0.
-1, 0, 1
Suppose -13*x**2 - 8*x - 67*x**2 + 56*x**4 - 8*x - 68*x**3 = 0. Calculate x.
-1/2, -2/7, 0, 2
Let s(u) be the second derivative of -u**5/4 - 5*u**4/3 + 5*u**3/6 + 10*u**2 + 3*u - 5. Factor s(z).
-5*(z - 1)*(z + 1)*(z + 4)
Let f(c) = -c**3 - 8*c**2 - 8*c. Let t be f(-7). Let p = -7 + t. Factor -q**3 - 2 - 3*q - q**3 + p*q + 2*q**2 + 5*q.
-2*(q - 1)**2*(q + 1)
Let v(k) be the first derivative of k**3 - 3*k**2 + 3*k - 1. Factor v(g).
3*(g - 1)**2
Let s(c) be the second derivative of -c**6/75 + c**5/25 + c**4/30 - 2*c**3/15 + 6*c. Let s(o) = 0. What is o?
-1, 0, 1, 2
Let s be (-3)/(-1) - 3 - (-1)/2. Let h(r) be the first derivative of -r**2 - s*r**4 - 2 + 0*r - 4/3*r**3. Let h(y) = 0. What is y?
-1, 0
Let l(r) be the second derivative of r**7/6300 + r**6/450 + r**5/75 - r**4/6 + 2*r. Let b(t) be the third derivative of l(t). Suppose b(c) = 0. Calculate c.
-2
Suppose -6/7*b + 3/7*b**4 + 6/7*b**3 - 3/7 + 0*b**2 = 0. What is b?
-1, 1
Suppose -5*u = -c - 0*c - 3, 5*u - 5*c = -5. Suppose -u + 13 = 2*l. Factor -2*v**5 + 6*v**4 + 2*v**3 - l*v**4.
-2*v**3*(v - 1)*(v + 1)
Let p(d) be the first derivative of -3*d**4/16 - d**3/4 + 3*d**2/4 + 15. Factor p(k).
-3*k*(k - 1)*(k + 2)/4
Let x(j) = j - 1. Let c be x(5). Suppose -3*l - 4*k - 1 - 1 = 0, -4 = -c*l - 2*k. Factor 4 - d**2 - d**2 + 2*d + d**2 - 2*d**3 - 3*d**l.
-2*(d - 1)*(d + 1)*(d + 2)
Let s be (-6)/(-21) - (-38)/14. Let 2*x**2 - 2*x**5 + x**3 - 1 + x**s - 2*x**4 + 1 = 0. What is x?
-1, 0, 1
Let m(z) be the first derivative of 3*z**5/5 - 15*z**4/4 + 9*z**3 - 21*z**2/2 + 6*z - 7. What is n in m(n) = 0?
1, 2
Let c(f) be the first derivative of -f**6/5 + f**5/10 + f**4/2 - f**3/3 + 5*f - 2. Let l(t) be the first derivative of c(t). Factor l(x).
-2*x*(x - 1)*(x + 1)*(3*x - 1)
Let r(d) be the first derivative of d**6/24 - d**5/10 - d**4/16 + d**3/6 - 1. Factor r(k).
k**2*(k - 2)*(k - 1)*(k + 1)/4
Let l(h) = h - 3. Let s be l(-4). Let m = 11 + s. Factor 4*p - m*p - 2*p**3 + 2*p.
-2*p*(p - 1)*(p + 1)
Suppose -6*u + 38 = 14. Let s(o) be the first derivative of 1/2*o**2 - 1 + 0*o + 0*o**3 - 1/4*o**u. Factor s(m).
-m*(m - 1)*(m + 1)
Let f(q) = 3*q**5 - 3*q**4 - 11*q**3 + q**2 + 8*q. Let s(h) = h**3 + h**2 - h. Let w(x) = f(x) + 2*s(x). Factor w(a).
3*a*(a - 2)*(a - 1)*(a + 1)**2
Factor -j**3 + 0 + 1/4*j**4 + 5/4*j**2 - 1/2*j.
j*(j - 2)*(j - 1)**2/4
Let w(o) be the second derivative of o**4/60 - o**3/15 - 18*o. Factor w(k).
k*(k - 2)/5
Let w be (-12)/(-5) - 6/15. Suppose -2*p + 2 = -2*n - 2*n, 0 = -2*n + w. Factor s**p - s + 1/2 + 0*s**2 - 1/2*s**4.
-(s - 1)**3*(s + 1)/2
Let k(p) be the second derivative of p**7/1680 - p**6/240 - 3*p**5/80 + p**4/6 + p. Let a(w) be the third derivative of k(w). Find b such that a(b) = 0.
-1, 3
Let l(x) = 30*x**5 - 105*x**4 + 56*x**3 - 11*x. Let j(h) = -10*h**5 + 35*h**4 - 19*h**3 + 4*h. Let v(w) = 11*j(w) + 4*l(w). Factor v(b).
5*b**3*(b - 3)*(2*b - 1)
Factor 0*d**2 - 5 + 4*d**2 + 4*d - 3.
4*(d - 1)*(d + 2)
Let h(k) be the first derivative of -k**6/2 + 9*k**4/4 - 2*k**3 + 4. Factor h(v).
-3*v**2*(v - 1)**2*(v + 2)
Let q be 4/(-30) + 4 + 76/(-20). Let c(j) be the third derivative of 0*j**4 + j**2 + 0 + 0*j**3 - 1/20*j**6 - q*j**5 + 0*j. Factor c(w).
-2*w**2*(3*w + 2)
Suppose -1/3*i**2 + 4*i + 13/3 = 0. What is i?
-1, 13
Solve 3/4*h**2 + 0*h - 3 = 0 for h.
-2, 2
Let p(x) = -2*x**3 + 7*x**2 - 19*x + 5. Let u(j) = -2*j**3 + 6*j**2 - 20*j + 4. Let h(a) = -4*p(a) + 3*u(a). Determine v so that h(v) = 0.
1, 2
Let h(v) be the second derivative of -1/4*v**2 + 1/3*v**3 + 1/10*v**5 - 1/4*v**4 - 4*v + 0 - 1/60*v**6. Solve h(o) = 0 for o.
1
Suppose 8*g - 5 = 3*g. Let l(k) = 2*k - 2. Let d be l(g). Factor 0*s**2 + d + 1/5*s**3 + 1/5*s**5 - 2/5*s**4 + 0*s.
s**3*(s - 1)**2/5
Let x(a) = 3*a - 4. Let q be x(-4). Let b be (-6)/(-9) - q/(-33). Let 6/11*s**4 - 14/11*s**2 - 2/11*s**3 + b*s**5 + 8/11 + 0*s = 0. What is s?
-2, -1, 1
Let v(s) be the third derivative of 0*s + 0*s**4 + 1/735*s**7 + 1/210*s**5 + 1/210*s**6 + 0 + 4*s**2 + 0*s**3. Solve v(m) = 0.
-1, 0
Let v = 5 - 2. Let q = -128 - -130. Suppose 0 + 0*c + 2/3*c**v - 8/9*c**4 + 2/9*c**q = 0. What is c?
-1/4, 0, 1
Let t(h) be the second derivative of -h**7/10080 - h**6/480 - 3*h**5/160 + 5*h**4/12 - h. Let q(y) be the third derivative of t(y). Suppose q(d) = 0. What is d?
-3
Factor 29 + 2*m**2 - 12 - 19 - 8*m + 8*m**3.
2*(m - 1)*(m + 1)*(4*m + 1)
Let s(g) be the second derivative of -g**9/15120 + g**7/840 - g**6/360 - g**4/6 + 4*g