Let n(u) = 5*q(u) - 6*z(u). Factor n(p).
-3*p*(p + 5)
Let a(c) be the third derivative of -c**5/12 + 5*c**4/2 - 55*c**3/6 + 2*c**2 - 14*c. Factor a(p).
-5*(p - 11)*(p - 1)
Let s = -77 - -110. Let i = s - 197/6. Solve -2/3*h**3 + i*h**5 + 1/3 - 1/3*h**2 + 0*h**4 + 1/2*h = 0.
-1, 1, 2
Let z be (-20)/(-25) + 0 + -7*(-16)/(-840). Let p be (0 - 2/(-3))*3. Suppose -2/3 + 0*q + z*q**p = 0. Calculate q.
-1, 1
Let w(k) be the third derivative of -k**8/336 - k**7/14 - 37*k**6/60 - 11*k**5/5 - 3*k**4 - 442*k**2 - 1. Find m such that w(m) = 0.
-6, -2, -1, 0
Let p = 280/13 + -1387/65. Suppose -4/5*l + p*l**3 - 2/5*l**2 + 8/5 = 0. What is l?
-2, 2
Let j(w) be the first derivative of 2*w**3/21 - 25*w**2/7 - 266. Find q, given that j(q) = 0.
0, 25
Suppose -3*f = -i - 49, -4*f - 3*i + 2*i = -77. Determine r so that r**5 - 6*r**5 + 15*r**4 + 5*r**2 - f*r**3 + 3*r**3 = 0.
0, 1
Let w(x) be the first derivative of -1/4*x - 1/12*x**3 - 1/4*x**2 - 23. Factor w(l).
-(l + 1)**2/4
Let j(t) be the first derivative of -2*t**3/15 - t**2/5 + 79. Factor j(o).
-2*o*(o + 1)/5
Let d = 796 + -791. Let p(q) be the first derivative of 1/4*q**4 + 1/10*q**d + 0*q**2 + 1/6*q**3 + 8 + 0*q. What is w in p(w) = 0?
-1, 0
Let r(o) be the second derivative of o**6/120 - o**5/80 - 15*o**4/16 + 25*o**3/24 + 125*o**2/2 + 9*o + 12. Factor r(l).
(l - 5)**2*(l + 4)*(l + 5)/4
Factor -215/3*m - 200 - 14/3*m**2 + 1/3*m**3.
(m - 24)*(m + 5)**2/3
Let k(y) = 357*y - 2494. Let x be k(7). Factor 0*r + 0 - 15/8*r**4 + 3/8*r**2 + 9/8*r**x + 3/8*r**3.
3*r**2*(r - 1)**2*(3*r + 1)/8
Factor 8*x**3 - 135*x - 165*x**2 - 40*x**3 + 9*x**3 - 2*x**3 + 5*x**4.
5*x*(x - 9)*(x + 1)*(x + 3)
Let m(o) be the first derivative of 0*o**3 + 0*o + 9/20*o**4 - 6/5*o**2 - 30 + 3/25*o**5. Factor m(c).
3*c*(c - 1)*(c + 2)**2/5
Suppose 0 = -4*p + 3*c + 1 + 16, 5*p - 21 = 4*c. Determine m, given that 18/7*m - 16/7*m**3 + 0 - 12/7*m**4 - 2/7*m**p + 12/7*m**2 = 0.
-3, -1, 0, 1
Let f(n) = -30*n**2 + 37*n - 36. Let t(w) = 14*w**2 - 18*w + 18. Let o(u) = -6*f(u) - 13*t(u). Factor o(v).
-2*(v - 3)**2
Let i(q) = -q**3 + 7*q**2 - 3*q + 3. Let k be i(7). Let l be (-66)/k - (-2)/6. Factor s**5 - 5*s**5 - s**5 + 4*s**5 - s**l + s**2 + s**3.
-s**2*(s - 1)*(s + 1)**2
Let m(q) be the first derivative of 0*q - 6 - 1/480*q**6 + 1/120*q**5 + 0*q**3 - 1/96*q**4 - q**2. Let n(i) be the second derivative of m(i). Factor n(b).
-b*(b - 1)**2/4
Let c(z) be the second derivative of z**6/900 - z**5/100 + z**4/30 - 2*z**3/3 - 6*z. Let j(f) be the second derivative of c(f). Suppose j(b) = 0. Calculate b.
1, 2
Let l(o) be the first derivative of o**4 + 7/15*o**5 + o**2 + 0*o + 8 - 25/9*o**3. Find g, given that l(g) = 0.
-3, 0, 2/7, 1
Let 48*a - 19/2*a**3 + 144 - 35*a**2 + 2*a**4 + 1/2*a**5 = 0. What is a?
-4, -2, 3
Let v(w) be the second derivative of -w**4/60 + 101*w**3/15 - 10201*w**2/10 + 444*w. What is h in v(h) = 0?
101
Let w(s) = -15*s + 5. Let g be w(-2). Let f be 12/(g/10 - 0). Determine c so that -4/7 + 16/7*c**3 + 16/7*c - 4/7*c**4 - f*c**2 = 0.
1
Let t(u) = -3*u - 22. Let a be t(-9). Let f be 4/2 - a*6/(-30). Factor 6/7*x**2 - 3*x + f*x**3 - 6/7.
3*(x - 1)*(x + 1)*(7*x + 2)/7
Let v be (-9 - (2 - 0))/1. Let k = 16 + v. Factor -2*y + k - 8 - y**2 + 2.
-(y + 1)**2
Let b = 22 + -30. Let i(h) = h**2 + 9*h + 10. Let o be i(b). Factor 5*g - 2*g**3 - 20*g - 17*g - o*g**3 - 20*g**2 - 16.
-4*(g + 1)*(g + 2)**2
Let b(r) be the second derivative of 7*r + r**3 + 9/2*r**2 + 1/12*r**4 + 0. Factor b(i).
(i + 3)**2
Let q = 1129 + -1123. Determine h, given that -1/3*h**4 - 8/3 - 7/3*h**3 - q*h**2 - 20/3*h = 0.
-2, -1
Let t be 4/12*-6 + 2. Let u(a) be the first derivative of t*a + 1/8*a**4 - 2 - 1/6*a**3 + 0*a**2. Factor u(s).
s**2*(s - 1)/2
Let o(d) be the third derivative of d**8/1008 - d**7/70 + 13*d**6/180 - 17*d**5/90 + 7*d**4/24 - 5*d**3/18 - 2*d**2 + 48*d. Suppose o(z) = 0. What is z?
1, 5
Suppose 7*s - 2*s - 2*b - 25 = 0, 3*b + 25 = 5*s. Factor 5*q**3 - 136 - s*q + 136.
5*q*(q - 1)*(q + 1)
Let n(g) be the third derivative of 1/24*g**6 + 0*g + 55/6*g**3 + 19*g**2 + 0 + 13/12*g**5 + 115/24*g**4. Let n(y) = 0. What is y?
-11, -1
Let z = -17 + 19. Suppose -z*r - 11 = -15. What is x in -8*x - 6*x**r + 3*x**2 + 2*x + 3*x**4 + 6*x**3 = 0?
-2, -1, 0, 1
Let x(k) = 2*k**2 - 43*k + 65. Let r be x(20). Let s(n) be the second derivative of 0*n**4 + 1/20*n**r + 0 + 0*n**2 + 2*n + 0*n**3. Factor s(o).
o**3
Factor -9*p**4 + 18*p - 1 - 51*p**2 + 30*p**3 + 17*p**3 + 1 - 5*p**3.
-3*p*(p - 3)*(p - 1)*(3*p - 2)
What is z in 45/7 - 24/7*z + 3/7*z**2 = 0?
3, 5
Suppose 5*w - 2*m = -0 - 2, -3*w + 3*m - 3 = 0. Let d(j) be the second derivative of 0*j**2 + w - 1/18*j**3 - 3*j + 1/36*j**4. Suppose d(n) = 0. What is n?
0, 1
Let w(i) be the second derivative of 3/20*i**5 + 0*i**3 + 0*i**2 - 17*i + 0 + 1/8*i**4. Find a such that w(a) = 0.
-1/2, 0
Let a(y) = -2*y**2 - 2*y + 17. Let q be a(-3). Let t(u) be the first derivative of 0*u + 2/9*u**3 + q + 2/15*u**5 + 1/3*u**4 + 0*u**2. Factor t(o).
2*o**2*(o + 1)**2/3
Let n = 384 + -1142/3. Factor 1 - n*k + 11/3*k**2 - 4/3*k**3.
-(k - 1)**2*(4*k - 3)/3
Let b(k) be the second derivative of k**7/63 - k**6/9 + 2*k**5/15 + 8*k**4/9 - 32*k**3/9 + 16*k**2/3 - 60*k. Factor b(j).
2*(j - 2)**3*(j - 1)*(j + 2)/3
Let s = 18151 + -381169/21. Factor 0 + 2/7*a**2 + 10/21*a**4 - s*a**5 - 2/3*a**3 + 0*a.
-2*a**2*(a - 3)*(a - 1)**2/21
Determine m, given that -274/13*m + 2/13*m**2 + 0 = 0.
0, 137
Let y(k) be the third derivative of k**8/420 + k**7/210 - k**3 - k**2. Let s(t) be the first derivative of y(t). Solve s(m) = 0.
-1, 0
Let a(x) = 47*x + 282. Let b be a(-6). Factor 2/7*f**2 + b + 4/7*f.
2*f*(f + 2)/7
Let w(r) be the third derivative of r**5/60 + r**4/8 + r**3/3 - 2*r**2 - 15*r. Suppose w(j) = 0. What is j?
-2, -1
Let s = -12649/10 - -1265. Let v(u) be the second derivative of 0 + s*u**2 - 11*u - 1/15*u**3 + 1/60*u**4. Let v(a) = 0. What is a?
1
Let n(t) be the third derivative of 0*t**3 - 1/20*t**5 - 1/64*t**6 - 1/560*t**7 - 4*t**2 - 1/16*t**4 + 0*t - 1. Factor n(b).
-3*b*(b + 1)*(b + 2)**2/8
Let j(u) be the third derivative of -1/3*u**4 - 1/15*u**5 - 2/3*u**3 + 0 - 14*u**2 + 0*u. Solve j(m) = 0.
-1
Let r(u) be the third derivative of -u**7/210 - 178*u**2. Factor r(t).
-t**4
Suppose -18*x + 5423 - 5351 = 0. Factor -x*c + 13/6*c**2 - 2/3.
(c - 2)*(13*c + 2)/6
Suppose -o + 3*b = 5 - 17, -o - 12 = 3*b. Factor 6/7*i**4 + 0*i**2 - 4/7*i**3 - 2/7*i**5 + 0*i + o.
-2*i**3*(i - 2)*(i - 1)/7
Let u(x) = 7*x**4 + 10*x**3 + 14*x**2 - 10*x - 21. Let h(c) = -5*c**4 - 10*c**3 - 15*c**2 + 10*c + 20. Let v(t) = -6*h(t) - 5*u(t). What is b in v(b) = 0?
-1, 1, 3
Factor 1/3*q**5 + 0 + 0*q**3 + 0*q**2 + 0*q - q**4.
q**4*(q - 3)/3
Let z be (-1 - 2 - -4)/(3/21). Suppose -9*f + z*f + 4 = 0. Factor -1/5*q**4 + 0 + 2/5*q**f + 0*q - 1/5*q**3.
-q**2*(q - 1)*(q + 2)/5
Let r(c) be the second derivative of c**7/252 - c**6/90 - c**5/40 + c**4/18 + c**3/9 + 2*c - 63. Factor r(x).
x*(x - 2)**2*(x + 1)**2/6
Suppose -3*v = -2*o + 4*o, 3*v - 3 = -o. Let q(r) be the first derivative of -9 - 3/5*r**5 + 0*r + 0*r**v + 3/2*r**4 + 3*r**3. Factor q(l).
-3*l**2*(l - 3)*(l + 1)
Let a(w) = 2*w**2 + 11*w + 19. Let m be a(-6). Factor -5*x**3 + 271*x**2 - 85 + m - 266*x**2 + 40*x.
-5*(x - 2)**2*(x + 3)
Let z(y) = y - 1. Let v(w) be the first derivative of 2*w**3 - 4*w**2 + 5*w - 11. Let s(n) = -v(n) - 5*z(n). Find j, given that s(j) = 0.
0, 1/2
Let z = -811 - -814. Let v be (-9)/(-28) - 7/(-28). Factor 4*u**z - 12/7*u**4 + 2/7*u**5 + 18/7*u - 32/7*u**2 - v.
2*(u - 2)*(u - 1)**4/7
Let u(j) be the first derivative of -j**2 + 2/5*j**5 - 3 + 4/3*j**3 - j**4 - 4*j - 1/15*j**6. Let i(f) be the first derivative of u(f). Factor i(p).
-2*(p - 1)**4
Let j(a) = -2*a**2 - a - 1. Let m(v) = 2*v**2 + 20*v + 10. Let l(i) = 4*j(i) + m(i). Solve l(y) = 0.
-1/3, 3
Let q(s) = -s**5 - 7*s**4 + 15*s**3 - 13*s**2 + 6*s. Let j(f) = 2*f**5 + 16*f**4 - 30*f**3 + 24*f**2 - 12*f. Let c(v) = 2*j(v) + 5*q(v). Factor c(n).
-n*(n - 1)**3*(n + 6)
Let m be (-1 - 10/(-6))/((-32)/(-12)). Let q(j) be the second derivative of 0 + m*j**4 - j**3 + 3/2*j**2 + 4*j. Factor q(p).
3*(p - 1)**2
Suppose -8 = -0*l - 4*l - 2*j, -3*j = -5*l + 21. Suppose -6*h + 8*h - 16 = 0. Find n, given that h*n**l + 1/2 + 4*n**2 - 7/2*n = 0.
-1, 1/4
Let l(s) =