*2. Let f(t) be the first derivative of m(t). What is i in f(i) = 0?
0, 1
Let v(i) be the third derivative of -7*i**6/780 - 3*i**5/130 - i**4/78 + 5*i**2. Factor v(w).
-2*w*(w + 1)*(7*w + 2)/13
Suppose 54 + 12 = 2*n. Let p = n - 31. Suppose 0 - 2/13*u - 2/13*u**4 - 6/13*u**p - 6/13*u**3 = 0. Calculate u.
-1, 0
Suppose -5 + 1 = 2*t. Let x(k) = -k**2 - k - 1. Let l(f) = -f**4 - 2*f**3 + 10*f**2 + 11*f + 11. Let d(m) = t*l(m) - 22*x(m). Factor d(g).
2*g**2*(g + 1)**2
Suppose 18 = -6*p + 15*p. Let h(z) be the first derivative of 1 + 1/9*z**3 - 1/12*z**4 - 1/3*z + 1/6*z**p. Solve h(b) = 0.
-1, 1
Let n = -36 + 42. Let b(o) be the third derivative of 2/315*o**7 + 2*o**2 - 7/360*o**n + 1/90*o**5 + 1/72*o**4 + 0*o**3 + 0*o + 0. Factor b(r).
r*(r - 1)**2*(4*r + 1)/3
Let p be 1/((-3)/(24/(-7))). Suppose 5*x + 3 = 6*x. Factor -8/7 + p*h + 30/7*h**2 - 36/7*h**x.
-2*(2*h + 1)*(3*h - 2)**2/7
Let u(x) = x - 1. Let r be u(4). Factor -2*d**4 - d**5 - 3*d**2 - d**5 + 5*d**2 + 2*d**r.
-2*d**2*(d - 1)*(d + 1)**2
Let p(o) be the second derivative of -2/5*o**5 - o**2 + 7/6*o**4 - 2/3*o**3 - 2*o + 0. Solve p(d) = 0 for d.
-1/4, 1
Let h(d) be the third derivative of -11/24*d**4 - 5/24*d**6 + 0*d + 0 - 1/6*d**3 - 7/12*d**5 + d**2. Factor h(s).
-(s + 1)*(5*s + 1)**2
Determine b, given that 5*b + 4*b + 6 - 5*b - b**2 + b = 0.
-1, 6
Factor -233 - 4*g**2 + 2*g**3 + 0*g - 2*g + 237.
2*(g - 2)*(g - 1)*(g + 1)
Let x(p) = p**3 - 10*p**2 + 10*p - 12. Let d be x(9). Let u(v) = v + 6. Let a be u(d). Determine s so that -1/2*s**a - 1/2*s**5 - s**4 + 0*s**2 + 0*s + 0 = 0.
-1, 0
Let o = 9 + -6. Factor 4/7*q**2 + 0 + 2/7*q**5 - 2/7*q + 0*q**o - 4/7*q**4.
2*q*(q - 1)**3*(q + 1)/7
Let q = 12 + -4. Determine x so that -5 - 14*x**2 + 1 - 26*x + q*x = 0.
-1, -2/7
Let p = -91 - -365/4. Factor 5/4*g + p*g**3 + 1/2 + g**2.
(g + 1)**2*(g + 2)/4
Suppose -4*m + 3*t - 4 = -1, 5*m - 5*t + 5 = 0. Suppose -2*l - 1 + 9 = m. Find j such that 1/2*j + 39/4*j**l + 19/2*j**3 + 7/2*j**5 + 0 + 15/4*j**2 = 0.
-1, -1/2, -2/7, 0
Let p = 13 - 10. Factor 2/3*d**4 + 2/3*d - 4/3*d**p + 2/3 + 2/3*d**5 - 4/3*d**2.
2*(d - 1)**2*(d + 1)**3/3
Factor 0 + 6/7*k**2 + 9/7*k - 3/7*k**3.
-3*k*(k - 3)*(k + 1)/7
Let p(r) be the second derivative of r**7/1260 - r**6/180 + r**5/60 - 5*r**4/12 + r. Let h(i) be the third derivative of p(i). Determine m so that h(m) = 0.
1
Let i(m) be the second derivative of m**6/600 + m**5/150 + m**4/120 - 3*m**2/2 + 4*m. Let a(k) be the first derivative of i(k). Solve a(j) = 0.
-1, 0
Let m(x) = -4*x**2 + x + 1. Let o be m(-1). Let n be o/2 - (-36)/14. Find k, given that -4/7*k**2 + n*k**4 - 6/7*k**3 + 6/7*k**5 + 0*k + 0 = 0.
-1, -2/3, 0, 1
Let a(c) = 2*c**3 + 2*c**2 - 4*c. Let v(s) = -2*s**3 - 2*s**2 + 4*s. Let p be 6/10 - 126/35. Let i(o) = p*a(o) - 2*v(o). Solve i(u) = 0.
-2, 0, 1
Let c(n) be the first derivative of 4*n**5 - 25*n**4/4 + 5*n**3/3 - 18. Factor c(d).
5*d**2*(d - 1)*(4*d - 1)
Let a = 77/24 + -15/8. Let b(p) be the first derivative of 2 + 2/9*p**3 + p**2 + a*p. What is z in b(z) = 0?
-2, -1
Let a(x) = -2*x**2 + 2 + 4*x**3 + 5*x**4 - 6*x**3 - 3*x**3. Let r(y) = -y**4 + y**3 + y**2 - 1. Let p(l) = a(l) + 2*r(l). Factor p(f).
3*f**3*(f - 1)
Let h(m) = 3*m**3 + m**2. Let a be h(1). Suppose a*g - 18 = -6. Factor -o**4 + 2*o - 9*o**g - 3*o + 5*o**4 + 6*o**2.
o*(o - 1)**2*(4*o - 1)
Factor 0 - 1/4*l**3 + 1/4*l**5 + 1/2*l**4 - 1/2*l**2 + 0*l.
l**2*(l - 1)*(l + 1)*(l + 2)/4
Let w(j) = 3*j**2 - 11*j. Let t = 2 + 1. Suppose -3*x - x + 1 = -t*a, 4*x - 21 = -a. Let z(m) = -m**2 + 4*m. Let p(y) = x*w(y) + 11*z(y). Factor p(b).
b**2
Let m(s) = 2*s**2 + 4*s. Let x(f) be the third derivative of f**5/30 + 5*f**4/24 - 2*f**2. Let t(p) = -3*m(p) + 2*x(p). Factor t(y).
-2*y*(y + 1)
Let n(o) = -100*o**3 + 157*o**2 - 68*o + 8. Let t(a) = -1100*a**3 + 1728*a**2 - 748*a + 88. Let s(c) = 32*n(c) - 3*t(c). Suppose s(k) = 0. What is k?
1/5, 2/5, 1
Suppose -p + 9 + 3 = 2*w, 3*w - 16 = -p. Solve -9*x**3 - p*x + 0*x**3 - 30*x**2 + 18 + x = 0.
-3, -1, 2/3
Let k(f) be the third derivative of 0 + 1/180*f**6 + 0*f**4 + 1/90*f**5 + 0*f**3 - 3*f**2 + 0*f. Factor k(d).
2*d**2*(d + 1)/3
Suppose 4*d - 2*d**2 - 8*d**3 - 2*d - 4*d**2 = 0. What is d?
-1, 0, 1/4
Let n(t) = -t + 13. Let q be n(12). Let c(y) = -y**3 - y**2 + 1. Let d(w) = -7*w**3 - 7*w**2 + 4*w + 5. Let o(u) = q*d(u) - 5*c(u). Factor o(p).
-2*p*(p - 1)*(p + 2)
Let a(y) be the second derivative of -y**5/90 - y**4/54 - 6*y. Determine x, given that a(x) = 0.
-1, 0
Let i(h) be the second derivative of -3*h**5/20 - h**4/4 + h**3 - h. Factor i(k).
-3*k*(k - 1)*(k + 2)
Suppose 25 = 2*b + 21. Factor 4/9*z**4 + 0 - 2/9*z + 2/9*z**5 + 0*z**3 - 4/9*z**b.
2*z*(z - 1)*(z + 1)**3/9
Let y(x) = 8*x**3 + 98*x**2 - 46*x + 26. Let q(v) = v**3 + 11*v**2 - 5*v + 3. Let i(w) = -52*q(w) + 6*y(w). Factor i(g).
-4*g*(g - 2)**2
Let u(l) = -l**2 + 3*l - 2. Let v(k) = k. Let b be 6/(-9) + (-4)/3. Let n be v(b). Let r(w) = 2*w**2 - 4*w + 3. Let t(y) = n*r(y) - 3*u(y). Factor t(h).
-h*(h + 1)
Let i(w) = 15*w**2 + 6*w - 9. Let h(f) = -8*f**2 - 3*f + 5. Let r be ((-3)/6)/(3/36). Let a(p) = r*i(p) - 11*h(p). Determine l so that a(l) = 0.
-1, -1/2
Factor -5 - 12*r + 7 + 16*r + 2*r**2.
2*(r + 1)**2
Suppose -3*w = 3*p - 30, -w + 0 + 2 = -p. Let d = w + -4. Determine z so that 4*z - z - 6*z**3 - 4 + 4*z**d + 3*z = 0.
-1, 2/3, 1
Factor 0 + 1/4*q**2 + 1/2*q.
q*(q + 2)/4
Let l(j) be the third derivative of -j**8/4320 + j**7/3780 + j**5/60 + j**2. Let m(x) be the third derivative of l(x). Find y such that m(y) = 0.
0, 2/7
Let j = -11 + 14. Let 2*x**4 - x**j + 3*x**3 + x**4 + x**3 = 0. Calculate x.
-1, 0
Let p be (3 - 8/1)*-1. Factor -p*b**3 - 2*b**4 + b**2 + 0*b**2 + 8*b**4 - 2*b**4.
b**2*(b - 1)*(4*b - 1)
Let t(y) be the first derivative of 3*y**5/40 - 9*y**4/32 + y**3/4 - 14. Determine b so that t(b) = 0.
0, 1, 2
Let c(w) be the third derivative of w**5/135 + 10*w**4/27 + 200*w**3/27 - 8*w**2. Suppose c(q) = 0. Calculate q.
-10
Let a = 10 + -8. Factor -7*m - 5*m**3 + m**5 - 8*m**2 + 0*m**4 + 3*m**3 + 2*m**4 - a.
(m - 2)*(m + 1)**4
Let d be ((-1)/(-8)*4)/2. Let y(s) = -s**2 + s. Let o be y(1). Solve o + 0*f - 1/4*f**2 - d*f**3 = 0 for f.
-1, 0
Let b(x) = -x**2 + 10*x - 13. Let r be b(8). Suppose 9 = 6*o - 3*o. Find w, given that 6*w + w**o + 42 + w**r + 6*w**2 - 40 = 0.
-1
Suppose -2/5*q**4 + 0*q + 0 - 4/5*q**3 - 2/5*q**2 = 0. Calculate q.
-1, 0
Determine k so that -14/5*k**3 + 2*k**5 + 6/5*k**2 - 6/5*k**4 + 0 + 4/5*k = 0.
-1, -2/5, 0, 1
Factor 0 + 2/17*s**4 - 2/17*s**3 + 0*s - 4/17*s**2.
2*s**2*(s - 2)*(s + 1)/17
Let s = 27/130 - 1/130. Factor 0*f + 0 + 1/5*f**3 + s*f**2.
f**2*(f + 1)/5
Let k(v) be the first derivative of -2*v**5/25 - v**4/10 - 4. Factor k(f).
-2*f**3*(f + 1)/5
What is w in 6/13*w + 4/13 + 0*w**3 - 6/13*w**5 - 20/13*w**2 + 16/13*w**4 = 0?
-1, -1/3, 1, 2
Let w(x) be the third derivative of -x**6/30 + 3*x**5/5 + x**4/6 - 6*x**3 + 3*x**2 + 2*x. Factor w(s).
-4*(s - 9)*(s - 1)*(s + 1)
Factor -16*h + 2 + 20*h**4 - 2 + 64*h**2 + 43*h**3 - 111*h**3.
4*h*(h - 2)*(h - 1)*(5*h - 2)
Let m(z) = -z**3 + 3*z**2 + 6*z - 8. Let k be m(4). Factor 2/3*u**2 + k*u - 2/3.
2*(u - 1)*(u + 1)/3
Let o(t) be the third derivative of t**8/50400 - t**7/3150 + t**6/450 - t**5/60 + 3*t**2. Let v(i) be the third derivative of o(i). Factor v(s).
2*(s - 2)**2/5
Let t = 125 + -122. Determine y, given that 2/5*y + 1/5*y**t + 3/5*y**2 + 0 = 0.
-2, -1, 0
Let k be 6/4*(-1)/(-81). Let h(p) be the second derivative of -k*p**4 - p + 1/9*p**2 + 0 + 0*p**3. Factor h(u).
-2*(u - 1)*(u + 1)/9
Let k(x) = x**3 - 9*x**2 - 24*x + 25. Let i be k(11). Let r(f) be the first derivative of 0*f - 1/18*f**4 + 0*f**i + 1/9*f**2 - 4. Factor r(z).
-2*z*(z - 1)*(z + 1)/9
Let n(a) be the second derivative of a**5/60 + a**4/3 + 8*a**3/3 + 32*a**2/3 + 8*a + 6. Let n(i) = 0. Calculate i.
-4
Let x be 16/(-72) + 3/(81/60). Suppose 6/11*s - 4/11 + 0*s**x - 2/11*s**3 = 0. What is s?
-2, 1
Let g(y) be the first derivative of -9*y**4/4 - y**3/3 - 1. Let d(p) = 22*p**3 + 2*p**2. Let k(c) = 5*d(c) + 12*g(c). Factor k(x).
2*x**2*(x - 1)
Let h = 44 + -306/7. Factor -2/7*t + h*t**3 + 0*t**2 + 0.
2*t*(t - 1)*(t + 1)/7
Find g, given that 0*g - 6*g + 109*g**2 - 110*g**2 - 9 = 0.
-3
Let v(c) = 20*c**2 - 94*c + 60. Let x(s) = 4*s**2 - 19*s + 12. Let d(n) =