Let c(m) be the first derivative of 5*m**9/3024 - m**8/140 + 3*m**7/280 - m**6/180 + 4*m**3/3 + 8. Let n(f) be the third derivative of c(f). Factor n(b).
b**2*(b - 1)**2*(5*b - 2)
Let m(h) be the second derivative of h**7/42 + h**6/120 - h**5/20 - h**4/48 - 22*h. What is p in m(p) = 0?
-1, -1/4, 0, 1
Let i(c) be the third derivative of 0*c - 1/48*c**4 + 1/120*c**5 - 1/6*c**3 + 4*c**2 + 0. Factor i(s).
(s - 2)*(s + 1)/2
Let t(j) be the second derivative of j**7/10 - j**6/20 - 7*j**5/20 + j**4/4 - 3*j**2/2 - 5*j. Let g(d) be the first derivative of t(d). Factor g(p).
3*p*(p - 1)*(p + 1)*(7*p - 2)
Solve 2/7*k**3 + 1944/7*k + 11664/7 + 108/7*k**2 = 0.
-18
Let s(h) be the first derivative of -h**5/45 + h**4/36 + h**3/27 - h**2/18 + 1. Factor s(v).
-v*(v - 1)**2*(v + 1)/9
Let l = 8 - 2. Let h(s) = s - 2. Let m be h(l). Find r, given that 2*r**5 - 4*r**4 + 0*r**m + 2*r**4 = 0.
0, 1
Let v be 40/15 + 2/(-3). Let f be (1 - -1) + -1 - -1. Find m, given that -m**5 + 2*m - 6*m + f*m + 7*m**v + 5*m**4 - 9*m**3 = 0.
0, 1, 2
Factor -3*r**2 + 3*r - 18 + 6*r**2 + 0*r.
3*(r - 2)*(r + 3)
Let k(d) be the first derivative of -d**4 + d**3/3 + 2*d**2 - d - 1. Factor k(j).
-(j - 1)*(j + 1)*(4*j - 1)
Let v be 3/5 - (-162)/30. Let l(i) = -5*i**2 + 4*i + 1. Let y(n) = -n**3 + n**2 + n - 1. Let d(f) = v*y(f) + 2*l(f). Determine k so that d(k) = 0.
-2, 1/3, 1
Let g be (-2)/(-5) - 112/(-20). Suppose 4*d + 3 - 11 = j, -j = 3*d - g. Factor -4*q + 8 - 5*q + q + d*q**2.
2*(q - 2)**2
Let g(l) be the second derivative of l**5/190 - 7*l**4/114 + 30*l. Suppose g(k) = 0. What is k?
0, 7
Let -15*y**3 + 35*y**4 - 7*y - 36*y**2 + y**2 + 0*y**3 + 25*y**5 - 3*y = 0. Calculate y.
-1, -2/5, 0, 1
Let u be (-21)/(-6)*8/14. Find z such that 0*z**u + 1/3*z - 1/3*z**3 + 0 = 0.
-1, 0, 1
Let n(u) be the third derivative of -u**6/30 + u**5/15 + 6*u**2. Find d such that n(d) = 0.
0, 1
Suppose 4*x - 11 = 3*m + 3, 0 = -4*m + x - 10. Let s be (21/m)/((-120)/32). Factor -4/5*g**2 + 4/5 - s*g + 14/5*g**3.
2*(g - 1)*(g + 1)*(7*g - 2)/5
Let o(m) be the first derivative of 3*m**5/5 - 3*m**4/2 + 3*m**2 - 3*m - 5. Factor o(d).
3*(d - 1)**3*(d + 1)
Let p(o) be the third derivative of -o**7/315 - o**6/60 - o**5/30 - o**4/36 + o**2 + 2. Factor p(g).
-2*g*(g + 1)**3/3
Let i(b) be the third derivative of -b**8/168 + 2*b**7/105 - b**5/15 + b**4/12 - 5*b**2. Factor i(f).
-2*f*(f - 1)**3*(f + 1)
Factor 4*s + 859*s**3 - s**4 - 857*s**3 + 5*s**4 - 10*s**2.
2*s*(s - 1)*(s + 2)*(2*s - 1)
Factor 2/3*u**3 - 4/3*u**2 - 2/3*u + 1/3*u**4 + 1.
(u - 1)**2*(u + 1)*(u + 3)/3
Let u(k) be the first derivative of 1 - k**3 + 1/2*k**6 + 3/5*k**5 + 3*k**2 + 0*k - 9/4*k**4. Find g, given that u(g) = 0.
-2, -1, 0, 1
Let v(k) be the third derivative of 0 + 1/10*k**5 + 2/3*k**3 + 5/12*k**4 + 2*k**2 + 0*k. Factor v(r).
2*(r + 1)*(3*r + 2)
Let k = -39/20 - -11/4. Factor 0 - k*l - 14/5*l**2.
-2*l*(7*l + 2)/5
Let b(o) be the first derivative of -o**4/6 + 4*o**3/9 - o**2/3 + 5. Factor b(x).
-2*x*(x - 1)**2/3
Suppose -3*m - 5*i - 4 = 79, -2*m - 3*i = 56. Let c = m - -94/3. Factor c*k - 1/3*k**2 + 0.
-k*(k - 1)/3
Factor 24/7*b**4 - 4/7*b - 52/7*b**3 + 32/7*b**2 + 0.
4*b*(b - 1)**2*(6*b - 1)/7
Let f be ((-2)/(-6)*-2)/((-3)/18). Let p(q) be the second derivative of -3/20*q**5 + 1/2*q**3 + 0 + 0*q**f + 4*q + 0*q**2. Factor p(m).
-3*m*(m - 1)*(m + 1)
Let a(s) be the first derivative of 5*s**4 - 35*s**3/3 - 5*s**2 - 21. Factor a(n).
5*n*(n - 2)*(4*n + 1)
Let -10*v + 6*v**2 + 3 + 4 - 3 = 0. What is v?
2/3, 1
Let k(s) be the first derivative of -s**4/4 + 4*s**3/3 - 5*s**2/2 + 2*s + 8. Factor k(h).
-(h - 2)*(h - 1)**2
Let t = 11 - 6. Suppose 0 = x + 5*j, 3*x + 3*j = t*x. Suppose -2/3*h**2 + 2/3 + x*h = 0. Calculate h.
-1, 1
Factor 0 - 2/15*y**4 - 4/15*y**3 + 0*y**2 + 0*y.
-2*y**3*(y + 2)/15
Let s(g) be the first derivative of -4*g**3/15 - 2*g**2/5 + 16. Suppose s(f) = 0. Calculate f.
-1, 0
Let t be (-56)/(-21)*(-3)/(-2). Suppose -3*p**3 + 17*p**3 + 2*p**2 - 14*p**5 - 6*p**2 + 2*p**t + 2*p**4 = 0. Calculate p.
-1, 0, 2/7, 1
Let q be ((-7)/(-28))/((-6)/(-4)). Let s(o) be the third derivative of 0*o - 1/210*o**7 - q*o**4 + 0 - 1/6*o**3 - 1/30*o**6 + 2*o**2 - 1/10*o**5. Factor s(w).
-(w + 1)**4
Let k(m) be the third derivative of -3*m**2 - 3/8*m**4 + m**3 - 3/5*m**5 + 0*m + 0 - 7/40*m**6. Determine v, given that k(v) = 0.
-1, 2/7
Let j = 436 + -436. Factor -1/3*g**5 + 1/3*g**2 + j + 1/3*g**3 - 1/3*g**4 + 0*g.
-g**2*(g - 1)*(g + 1)**2/3
Let c(s) be the second derivative of s**4/6 - 2*s**3/3 - 7*s. Solve c(g) = 0.
0, 2
Let a(i) be the first derivative of 4*i**7/105 - 7*i**6/60 + i**5/15 + i**4/12 + i**2/2 - 3. Let h(t) be the second derivative of a(t). Factor h(v).
2*v*(v - 1)**2*(4*v + 1)
Let x(y) be the third derivative of y**9/30240 - y**8/25200 - y**7/2520 + y**6/900 + y**5/30 - y**2. Let l(z) be the third derivative of x(z). Factor l(m).
2*(m - 1)*(m + 1)*(5*m - 2)/5
Let g(a) = 3*a**4 - 5*a**3 - 7*a**2 + 5*a + 8. Let z(i) = -i**3 + i**2 + i + 1. Let j(m) = g(m) - 2*z(m). Factor j(v).
3*(v - 2)*(v - 1)*(v + 1)**2
Factor -10/3 + 1/3*m**2 - m.
(m - 5)*(m + 2)/3
Let y(q) = -q**3 - q**2 + q. Let b(t) = -4*t**3 + 14*t**2 + 56*t. Let h(l) = -b(l) + 6*y(l). Factor h(z).
-2*z*(z + 5)**2
Let t(f) be the second derivative of 1/48*f**4 + 0 + 1/30*f**5 - f - 1/2*f**2 + 0*f**3. Let a(r) be the first derivative of t(r). Factor a(o).
o*(4*o + 1)/2
Let g(y) be the third derivative of y**9/60480 - y**8/10080 - y**5/60 + y**2. Let i(l) be the third derivative of g(l). Factor i(h).
h**2*(h - 2)
Let d be 2/(-7) + (-154)/(-196). Factor 1 + 1/2*m - d*m**2.
-(m - 2)*(m + 1)/2
Let o = 27 + -18. Suppose -17*a + o = -14*a. Factor 0*h - 2/5*h**a - 2/5*h**2 + 0.
-2*h**2*(h + 1)/5
Let i(p) be the second derivative of p**4/4 + 3*p. Factor i(m).
3*m**2
Let d(k) be the second derivative of -k**7/84 - k**6/80 + k**5/60 - k**2 - 3*k. Let q(l) be the first derivative of d(l). Suppose q(c) = 0. What is c?
-1, 0, 2/5
Suppose -b - b - 4*w = 10, -8 = 2*w. Let v(z) be the first derivative of 1/5*z**5 + 3 + z**2 - z - 1/2*z**4 + 0*z**b. Solve v(p) = 0 for p.
-1, 1
Let d(a) = -7*a**3 + 5*a**2 + 7*a + 7. Let v(z) = 8*z**3 + 0*z - 8 - 6*z**2 - 12*z + 4*z. Let q(x) = 7*d(x) + 6*v(x). Factor q(s).
-(s - 1)*(s + 1)**2
Let t be (-6)/33 + 4/22. Factor 4 + 2 + t + 9*v + 3*v**2 + 0*v**2.
3*(v + 1)*(v + 2)
Let b = -28 - -22. Let j be 8/b*42/(-28). Suppose 1/4*y - 1/2 + 1/4*y**j = 0. Calculate y.
-2, 1
Let v(n) be the second derivative of n**6/360 - n**5/180 - n**2 + 2*n. Let i(a) be the first derivative of v(a). Factor i(u).
u**2*(u - 1)/3
Let m(t) be the third derivative of -t**8/10080 + t**6/1080 + t**4/12 + 3*t**2. Let h(j) be the second derivative of m(j). Factor h(i).
-2*i*(i - 1)*(i + 1)/3
Suppose -4*h = -v - 1, -2*h + 3*h - 3*v = 3. Factor h + 2/9*b**3 + 0*b**2 + 2/9*b**4 + 0*b.
2*b**3*(b + 1)/9
Let y(a) be the first derivative of -1/3*a**3 - a + 1 + a**2. Factor y(g).
-(g - 1)**2
Let n(j) = -j**2 + 6*j - 6. Let m be n(4). What is d in 3/4*d - 1/4*d**3 + 1/2 + 0*d**m = 0?
-1, 2
Let g(k) be the second derivative of -k**5/30 - k**4/6 + 4*k**3/9 + 10*k. Factor g(i).
-2*i*(i - 1)*(i + 4)/3
Let 6/7*s + 2/7 + 4/7*s**2 = 0. Calculate s.
-1, -1/2
Let u(o) be the first derivative of o**6/15 - 8*o**5/25 + 2*o**4/5 + 4*o**3/15 - o**2 + 4*o/5 - 1. Find c, given that u(c) = 0.
-1, 1, 2
Let p(y) be the third derivative of y**5/80 + y**4/32 + 17*y**2. Find d, given that p(d) = 0.
-1, 0
Let h be ((-28)/18)/(4/(-3)). Let c(x) be the second derivative of -2/3*x**3 - 2*x + 0*x**2 + 0 + h*x**4. Suppose c(q) = 0. What is q?
0, 2/7
Let t(x) = x**3 + 25*x**2 - 29*x - 76. Let z be t(-26). Let y be (-12)/10 - -1 - -1. Find m such that 1/5*m**z + 4/5 - y*m = 0.
2
Suppose -5*m - 3*t + 9 = 0, -2*m + 0*t - 6 = -2*t. Determine w so that m + 0*w**2 + 1/4*w + 0*w**4 - 1/2*w**3 + 1/4*w**5 = 0.
-1, 0, 1
Let z(v) = -v - v**3 - 4 + 0*v**2 + 7*v**2 - 4*v. Let c be z(6). Let u**2 - 4*u**2 + 5*u**c + 8*u**4 + 10*u**3 = 0. Calculate u.
-1, -1/4, 0
Let x(p) be the third derivative of -1/540*p**6 - 1/27*p**3 + 1/270*p**5 + 0 - 4*p**2 + 1/108*p**4 + 0*p. Factor x(u).
-2*(u - 1)**2*(u + 1)/9
Suppose u = -2*j - 10, -4*j - 5*u - 17 - 3 = 0. Let k be 18/210 + (-1)/j. Factor -k*g + 4/7 - 2/7*g**2.
-2*(g - 1)*(g + 2)/7
Let z(h) = -h. Let o(p)