*5 + 0*k**6 + 2/3*k**4 + 2/21*k**7 + 9*k + 2*k**3 + 0 - 4*k**2. Factor b(m).
4*(m - 1)**3*(m + 1)*(m + 2)
Let h(r) be the third derivative of -r**6/720 - r**5/180 - r**4/144 - 2*r**2 - 108*r. Let h(i) = 0. Calculate i.
-1, 0
Let b(r) be the first derivative of 4*r**2 - 11 - 4/3*r**3 - 4*r. Determine o so that b(o) = 0.
1
Let a(o) be the first derivative of o**6/30 + 18*o**5/25 + 113*o**4/20 + 268*o**3/15 + 24*o**2/5 - 448*o/5 + 21. Factor a(h).
(h - 1)*(h + 4)**3*(h + 7)/5
Let c = 151/9075 + -2/605. Let j(u) be the second derivative of -4/15*u**3 + 0*u**4 - c*u**6 + 3/50*u**5 + 9*u + 0*u**2 + 0. Factor j(q).
-2*q*(q - 2)**2*(q + 1)/5
Factor a**3 + 0*a**2 - 3/4*a + 1/4.
(a + 1)*(2*a - 1)**2/4
Let n(y) be the second derivative of 2/69*y**4 + 5*y + 0 + 3/23*y**2 + 13/69*y**3. Determine w so that n(w) = 0.
-3, -1/4
Let y(l) = -l**2 + 440*l + 2678. Let x be y(-6). Suppose 1/3*z**x + 121/3 + 22/3*z = 0. What is z?
-11
Let r(j) be the first derivative of j**4/2 - 20*j**3/3 - 23*j**2 - 24*j - 77. Suppose r(h) = 0. What is h?
-1, 12
Let k = 3740 + -3738. Solve -2/7*g**3 + 0 + 2/7*g**4 + 2/21*g**k + 0*g - 2/21*g**5 = 0 for g.
0, 1
Let o(c) = c + 2. Let y(g) = 2*g**2 + 4*g. Let t(s) = -4*o(s) - 2*y(s). What is f in t(f) = 0?
-2, -1
Let m = -3905 + 78119/20. Let c = 6/5 - m. Suppose c*y**3 - 1/2 + 1/2*y**2 - 1/4*y = 0. Calculate y.
-2, -1, 1
Let o(r) = -4*r**3 - 1 - 1 + 3*r + r. Let n(j) = -9*j**3 + j**2 + 8*j - 5. Let b = -28 + 26. Let i(s) = b*n(s) + 5*o(s). Find a such that i(a) = 0.
-2, 0, 1
Suppose 0 = -1800*p + 1818*p - 90. Let s(j) be the third derivative of -3/5*j**4 - 27/50*j**5 - 4/15*j**3 + 0*j + p*j**2 + 0. Factor s(o).
-2*(9*o + 2)**2/5
Let y(n) = -n**2 + 3*n. Let x(u) = 2*u**2 + 102*u + 50. Let f(r) = 2*x(r) + 14*y(r). Let f(p) = 0. What is p?
-2/5, 25
Factor -5*x**3 + 13*x - 3*x**3 - 2*x**4 + 2*x**3 - 5*x.
-2*x*(x - 1)*(x + 2)**2
Let h(k) be the first derivative of 4 + 1/44*k**4 - 1/330*k**5 + 0*k - 3/2*k**2 - 2/33*k**3. Let g(y) be the second derivative of h(y). What is c in g(c) = 0?
1, 2
Let s(l) be the third derivative of -5*l**8/336 + 2*l**7/21 + l**6/8 - 17*l**5/6 + 65*l**4/6 - 20*l**3 + 10*l**2 + 3. What is b in s(b) = 0?
-3, 1, 2
Let j = 11010 - 11006. Factor j*s**3 + 4/3*s**4 - 20/3*s**2 + 0 + 8/3*s - 4/3*s**5.
-4*s*(s - 1)**3*(s + 2)/3
Let g(c) be the first derivative of -2/25*c**5 + 8/15*c**3 - 31 + 0*c - 4/5*c**2 + 1/10*c**4. Solve g(v) = 0 for v.
-2, 0, 1, 2
Let f = -412 + 827/2. Let r(u) be the first derivative of 0*u**3 + 0*u**2 - 4 + f*u**4 + 0*u + 3/5*u**5. Factor r(z).
3*z**3*(z + 2)
Suppose -5*c**4 + 35*c + 100*c - 15*c**3 + 90 + 91*c**2 - 56*c**2 = 0. Calculate c.
-3, -2, -1, 3
Let c(g) be the second derivative of 2/15*g**4 + 0 + 4/25*g**5 - 8/5*g**3 - 2/75*g**6 - g - 18/5*g**2. Factor c(l).
-4*(l - 3)**2*(l + 1)**2/5
Let x(o) = -7*o**2 - 5 - 186*o + 187*o + 16*o**3 + 3*o**3 + 32*o**2. Let l(t) = -56*t**3 - 75*t**2 - 4*t + 15. Let k(y) = -4*l(y) - 11*x(y). Factor k(f).
5*(f + 1)**2*(3*f - 1)
Let w(a) be the third derivative of a**7/175 - 7*a**6/300 + a**5/50 + a**4/20 - 2*a**3/15 - 94*a**2. What is d in w(d) = 0?
-2/3, 1
Suppose 3 = -m + 9. Factor 3*s**2 - 2*s**2 + 8*s**2 - 22*s - 6 + m*s**3 + 13*s.
3*(s - 1)*(s + 2)*(2*s + 1)
Let o(f) be the first derivative of 2*f**6 - 39*f**5 + 9*f**4 + 65*f**3 - 24*f**2 - 377. Let o(k) = 0. Calculate k.
-1, 0, 1/4, 1, 16
Suppose 2*m - m + 40 = 5*g, -8 = -g - m. Suppose 0 = 3*w - 7 - 5, 2*n - 3*w = -g. Solve 0*z - 1/4 + 1/4*z**n = 0.
-1, 1
Let k(o) = -7*o**3 + 22*o**2 + 17*o - 31. Let r(a) = a**3 - a**2 - a + 1. Let y(s) = -k(s) - 5*r(s). Let c(l) be the first derivative of y(l). Factor c(w).
2*(w - 6)*(3*w + 1)
Suppose 2/3 - 1/3*k - 1/3*k**2 = 0. Calculate k.
-2, 1
Factor 18*a + 28 + 4*a**3 - 16*a**2 + 24*a - 46*a - 12*a**2.
4*(a - 7)*(a - 1)*(a + 1)
Factor -12*r**3 + 4*r**4 + 5*r**2 + 0*r**2 - 4*r + 0*r**2 + 7*r**2.
4*r*(r - 1)**3
Suppose 0*t**3 + 2/9*t**5 + 2/3*t**4 - 8/9*t**2 + 0 + 0*t = 0. What is t?
-2, 0, 1
Let v = 2680 + -13399/5. Factor -t**2 - v*t**3 - 3/5 - 7/5*t.
-(t + 1)**2*(t + 3)/5
Let u(v) be the second derivative of 0 - 14*v + 1/16*v**4 + 3/80*v**5 - 1/40*v**6 - 1/56*v**7 + 0*v**3 + 0*v**2. Factor u(f).
-3*f**2*(f - 1)*(f + 1)**2/4
Let l(y) be the first derivative of 7*y**6/3 - 12*y**5 + y**4/2 + 20*y**3 - 8*y**2 + 30. Find b such that l(b) = 0.
-1, 0, 2/7, 1, 4
Let w(a) = 88*a**2 + 21*a - 17. Let d(h) = -31*h**2 - 7*h + 6. Let v(i) = -17*d(i) - 6*w(i). Let v(t) = 0. Calculate t.
-7, 0
Let v be (396/660)/(18/20). Let v*b + b**2 - 1/3*b**4 + 0*b**3 + 0 = 0. Calculate b.
-1, 0, 2
Factor 6*q**3 + 5/3*q**2 + 0 - 2/3*q.
q*(2*q + 1)*(9*q - 2)/3
Let d = -19 - 0. Let b = d - -20. Let f(m) = -2*m**2 + 8*m - 6. Let r(x) = -x + 1. Let o(u) = b*f(u) + 4*r(u). Factor o(c).
-2*(c - 1)**2
Let n be (1 + (-204)/(-9))*(25 + 8). Determine c so that -16*c**2 - 8*c**3 + 12*c**4 + 6 - n*c - 2 + 789*c = 0.
-1, -1/3, 1
Let d(i) be the third derivative of -21/80*i**6 + 5/48*i**4 - 6*i**2 + 0 + 0*i + 1/6*i**3 - 1/5*i**5. Solve d(f) = 0.
-1/3, 2/7
Suppose 0 = 128*u - 126*u - 34. Factor -u*g - 23*g + 14*g + 8*g**2 + 6.
2*(g - 3)*(4*g - 1)
Let t(x) be the third derivative of 0*x**5 + 0*x - 1/490*x**7 + 0 - 1/784*x**8 + 0*x**6 - 2*x**2 + 0*x**4 + 0*x**3. Solve t(l) = 0.
-1, 0
Let u be (-1 - (-13)/3)*(-222)/(-370). Let z(w) be the first derivative of -6*w**u - 21/5*w**5 - 20*w**3 - 7 - 69/4*w**4 + 0*w. Solve z(y) = 0.
-2, -1, -2/7, 0
Let d(n) be the first derivative of 2*n**6/3 - 8*n**5 + 8*n**4 + 40*n**3/3 - 18*n**2 - 98. Factor d(s).
4*s*(s - 9)*(s - 1)**2*(s + 1)
Let i(z) be the first derivative of z**3 + 3*z**2 - 4*z - 10. Let k(c) = 2*c**2 + 3*c - 2. Let w(q) = 3*i(q) - 5*k(q). Let w(h) = 0. What is h?
1, 2
Suppose t = -10*t - 4*t. Let v(y) be the third derivative of t*y**3 + 0*y**4 + 0*y**6 + 1/20*y**5 - 1/70*y**7 + 0 + 0*y - y**2. Factor v(k).
-3*k**2*(k - 1)*(k + 1)
Suppose 0 = -7*s + q + 23, 5*s + 5*q - q - 7 = 0. Factor -9*c**2 - 108 - 8*c**4 + 1/2*c**5 + 73/2*c**s - 162*c.
(c - 6)**3*(c + 1)**2/2
Let y be (7/((-21)/5))/(2/(-18)). Suppose -3 = -4*o - i, y = -5*o + 6*i - i. Factor 1/4*m**3 + m**2 + o + m.
m*(m + 2)**2/4
Let g = -29 - -57. Let y = g - 25. Let -y*b - 9/2 + 3/2*b**2 = 0. What is b?
-1, 3
Factor -720/7*f - 2/7*f**3 - 800/7 + 78/7*f**2.
-2*(f - 20)**2*(f + 1)/7
Let b(c) = c + 16. Let d be b(-12). Suppose -2*w + 0*w = -d. What is u in -w - 16*u**2 - 4 + 2 - 16*u = 0?
-1/2
Let y(x) = 9*x**2 - 20*x - 83. Let b(r) = -4*r**2 + 11*r + 41. Let h(d) = -7*b(d) - 3*y(d). Let h(v) = 0. What is v?
-2, 19
Suppose -3 = -n + 4*n. Let g(u) = u**2 + u + 1. Let k(m) = 26 + 36 - 22*m + 8*m**2 - 6*m + 6. Let q(j) = n*k(j) + 4*g(j). Factor q(d).
-4*(d - 4)**2
Let w = 8 - 6. Factor 2*f**2 - 3*f**5 - 3*f**4 - f**4 + w*f**5 + f + 2*f**4.
-f*(f - 1)*(f + 1)**3
Let m(b) = b**3 - 9*b**2 - b - 5. Let v be m(9). Let o be (192/v)/(0 + -1*2). Factor -24/7*j**3 + 52/7*j**2 + 16/7 + 4/7*j**4 - o*j.
4*(j - 2)**2*(j - 1)**2/7
Let t be (55/33*-6)/((-5)/2). Let k be (-2 - -1)*(1 + -3). Suppose t*q**4 - 2*q - 4*q**k - 36*q**5 + 4*q + 34*q**5 = 0. What is q?
-1, 0, 1
Let m = 16491/272167 - -59/659. Let p = m + 8/59. Factor -p*t**2 + 2/7 - 2/7*t**3 + 2/7*t.
-2*(t - 1)*(t + 1)**2/7
Suppose -712 = -9*x - 703. Let b(j) be the first derivative of -1/2*j**3 + 0*j**2 - x - 9/16*j**4 + 0*j**5 + 0*j + 1/8*j**6. Factor b(i).
3*i**2*(i - 2)*(i + 1)**2/4
Suppose 2*m - 3*m = -4. Suppose -85*h = -86*h + 3. Factor 0*j**2 - j + 2*j + 3*j**2 + j**m + 0*j**4 + 3*j**h.
j*(j + 1)**3
Let d(o) = -31*o - 928. Let a be d(-30). Let -3 + 1/3*b**a - 8/3*b = 0. What is b?
-1, 9
Let k(s) be the third derivative of s**5/240 + 7*s**4/24 + 49*s**3/6 + 23*s**2 + 6*s. Factor k(n).
(n + 14)**2/4
Let w(l) be the second derivative of -1/4*l**4 + 2*l + 1/2*l**3 + 0*l**2 + 0. Factor w(d).
-3*d*(d - 1)
Let b = -56 + 58. Factor -y - 5 - 149*y**5 - b*y**2 + 148*y**5 + 2*y**3 + 6 + y**4.
-(y - 1)**3*(y + 1)**2
Let c(p) = 2*p**3 + 5*p**2 + 2*p**3 - 2 - 8*p**2 + 1. Let x(f) = -7*f**3 + 5*f**2 + f + 1. Let l(q) = -5*c(q) - 3*x(q). Factor l(k).
(k - 1)**2*(k + 2)
Factor -3*n**2 - 5/3*n**3 + 2/3 + 5/3*n + 7/3*n**4.
(n - 1)**2*(n + 1)*(7*n + 2)/3
Let y = -7100 - -7100. Factor -2/11*d**2 + 2/11 + y*d.
-2*(d - 1)*(d + 1)/11
Suppose 130 = -27*u + 3*u + 89*u. Fac