et k(g) be the first derivative of -g**7/210 - g**6/90 + g**5/6 - g**4/2 + 16*g**3/3 - 9. Let v(d) be the third derivative of k(d). Factor v(x).
-4*(x - 1)**2*(x + 3)
Factor -1/2*x**2 - 61/2 + 31*x.
-(x - 61)*(x - 1)/2
Let s(l) = 2338*l - 37408. Let b be s(16). Let d be (1/(-3))/(-1)*2. Factor b*h + d*h**3 + 0 + 8/3*h**2.
2*h**2*(h + 4)/3
Let n(c) be the third derivative of 12*c**2 - 1/180*c**6 + 4/45*c**5 + 0 + 2*c**3 + 0*c - 7/12*c**4. Find p such that n(p) = 0.
2, 3
Let b(u) be the first derivative of -u**3/6 + 11*u**2/4 - 107. Factor b(i).
-i*(i - 11)/2
Let u = 807/2 + -399. Let p(q) be the first derivative of 7 - u*q**4 - 12/5*q**5 + 0*q**2 + 0*q - 1/3*q**6 + 0*q**3. Factor p(n).
-2*n**3*(n + 3)**2
Let g(i) be the third derivative of -i**5/60 + i**4/8 + 2*i**3/3 - 66*i**2. Suppose 0 = -a - 0*a + 4. Let h(c) = -1. Let s(z) = a*h(z) + g(z). Factor s(r).
-r*(r - 3)
Let m be 25/130*494/380. Let 1/4 - 1/4*l**3 - m*l**2 + 1/4*l = 0. Calculate l.
-1, 1
Let t be ((-2)/4*-1)/(23/644). Let y(i) be the second derivative of 1/21*i**4 - 9/7*i**2 - 2/35*i**5 + t*i + 0 + 4/7*i**3 - 1/105*i**6. Factor y(b).
-2*(b - 1)**2*(b + 3)**2/7
Find i such that 106/5*i**2 + 14/5*i + 224/5*i**3 + 96/5*i**4 + 0 = 0.
-7/4, -1/3, -1/4, 0
Solve -64*r**2 - 9/2*r**3 - 469/2*r - 49 = 0.
-7, -2/9
Let i(o) be the second derivative of -o**6/6 + o**5 - 5*o**4/4 - 10*o**3/3 + 10*o**2 + 24*o - 5. Solve i(w) = 0.
-1, 1, 2
Let z(s) = 2*s + 8. Let p be z(0). Solve p*f**2 - 69 - 43*f + 81 + 15*f = 0 for f.
1/2, 3
Let l(a) = a**2 + 1. Let y(v) = v**3 + v + 1. Let d(g) = -9*g**3 - 21*g. Let i(f) = -d(f) - 18*y(f). Let m(p) = -i(p) - 12*l(p). Let m(u) = 0. Calculate u.
-2/3, 1
Let l(n) = -16*n**4 - 180*n**3 - 1053*n**2 - 1451*n. Let p(i) = -5*i**4 - 60*i**3 - 351*i**2 - 484*i. Let z(t) = -2*l(t) + 7*p(t). Factor z(x).
-3*x*(x + 2)*(x + 9)**2
Let s(a) be the second derivative of -a**4/12 + 2*a**3/3 + 5*a**2/2 - 4*a + 2. Factor s(x).
-(x - 5)*(x + 1)
Let k(n) be the third derivative of -n**6/360 + n**5/180 + 5*n**4/72 + n**3/6 + 3*n**2 - 81. Factor k(i).
-(i - 3)*(i + 1)**2/3
Let y(m) be the third derivative of m**7/42 - m**6/24 - 4*m**5/3 - 25*m**4/6 - 87*m**2 + 3. Factor y(s).
5*s*(s - 5)*(s + 2)**2
Let s(o) be the second derivative of -o**8/6720 - o**7/630 - o**6/144 - o**5/60 - 17*o**4/12 - 12*o. Let a(t) be the third derivative of s(t). Factor a(z).
-(z + 1)**2*(z + 2)
Suppose 3*g - 29 = -4*c, 0*c - 20 = -4*c. Let y be g/(-14) - (-15)/30. What is i in 0 + 2/7*i**5 + 2/7*i**2 - y*i**3 - 2/7*i**4 + 0*i = 0?
-1, 0, 1
Let t be 36/(-9)*2/4. Let f be (-9)/t + -4 + (-6)/44. What is m in f - 2/11*m**2 + 2/11*m = 0?
-1, 2
Let m(v) = 2*v**4 - 4*v**3 - 35*v**2 + 137*v - 95. Let u(j) = -j**4 + 2*j**3 + 18*j**2 - 68*j + 47. Let s(o) = -2*m(o) - 5*u(o). Factor s(b).
(b - 3)**2*(b - 1)*(b + 5)
Let g be 296/(-104) + 3 - ((-192)/(-26))/(-4). Factor 3/4*j**3 - 3/2*j + 3/4*j**g + 0.
3*j*(j - 1)*(j + 2)/4
Let m = 55/577 - -1923/4039. Solve 64/7 - 32/7*t - 32/7*t**2 - 2/7*t**5 + m*t**4 + 16/7*t**3 = 0.
-2, 2
What is t in 1/7*t**2 + 8/7 - 10/7*t + 1/7*t**3 = 0?
-4, 1, 2
Suppose 6*n - 20*n = 0. Let u(v) be the third derivative of 0 - 3*v**2 - 1/36*v**4 + 1/45*v**5 - 2/9*v**3 + 1/180*v**6 + n*v. Factor u(a).
2*(a - 1)*(a + 1)*(a + 2)/3
Let q(w) be the second derivative of 5/3*w**3 + 4*w - 5/4*w**4 + 0*w**5 + 1 + 0*w**2 + 1/6*w**6. What is b in q(b) = 0?
-2, 0, 1
Let t = -70/19 - -4. Determine r so that -t*r - 2/19*r**2 + 0 = 0.
-3, 0
Let o = -102/169 + 1189/1690. Let -o*v**2 + 1/2 + 2/5*v = 0. Calculate v.
-1, 5
Let o(x) be the second derivative of x**4/48 + 5*x**3/6 - 9*x + 1. Find d, given that o(d) = 0.
-20, 0
Let x be ((-40)/(-275))/((-5)/(-225)*9). Find b, given that -x + 10/11*b**4 + 32/11*b - 30/11*b**2 - 4/11*b**3 = 0.
-2, 2/5, 1
Let x(n) be the second derivative of -3*n**5/20 + 3*n**4/4 + 2*n**3 - 18*n**2 - 221*n + 1. Suppose x(z) = 0. Calculate z.
-2, 2, 3
Let d be (-9 + 11)/(-9*(0 + -5)). Let f(g) be the first derivative of 1/27*g**6 - 1/18*g**4 - d*g**5 + 3 + 2/27*g**3 + 0*g**2 + 0*g. Let f(c) = 0. What is c?
-1, 0, 1
Factor 21/2*m - 1/4*m**2 - 441/4.
-(m - 21)**2/4
Let m(b) be the first derivative of 7*b**5/30 + b**4/2 + 2*b**3/9 + 8*b - 10. Let s(g) be the first derivative of m(g). Factor s(u).
2*u*(u + 1)*(7*u + 2)/3
Let w(t) be the third derivative of 1/735*t**7 + 0*t**4 + 0 + 0*t + 0*t**3 + 1/210*t**5 + 26*t**2 - 1/210*t**6. Factor w(n).
2*n**2*(n - 1)**2/7
Let d(b) be the first derivative of b**3/6 + b**2/2 - 31. Solve d(x) = 0 for x.
-2, 0
Let b be -4*((-27)/6 - -4). Determine t so that -3*t**3 + 12*t**b + 0*t**2 - 13*t + 7*t**3 - 3*t = 0.
-4, 0, 1
Suppose -5*u = -u. Let b(w) be the third derivative of 0*w + u - 1/90*w**5 - 1/18*w**4 + 7*w**2 + 0*w**3. Factor b(m).
-2*m*(m + 2)/3
Suppose -14*t = 33*t. Let k(v) be the first derivative of t*v + 0*v**3 - 3/10*v**2 - 3 + 3/20*v**4. Factor k(u).
3*u*(u - 1)*(u + 1)/5
Let w(r) be the first derivative of -r**5/100 + r**4/40 + r**3/5 - 25*r**2/2 + 25. Let n(h) be the second derivative of w(h). Find v, given that n(v) = 0.
-1, 2
Let y = 81 + -63. Factor y*b - 925*b**2 - 6*b + 921*b**2.
-4*b*(b - 3)
Let g(w) = 2*w**2 + 7*w. Let t be g(-5). Find o such that 9*o**3 + 5*o - 13*o**3 + 7*o**3 + t*o**2 + 12*o**3 + 5*o**4 = 0.
-1, 0
What is f in f**4 + 0*f + 7*f**2 - 36*f**3 - 6*f**5 + 10*f**5 + 12 + 53*f - f = 0?
-3, -1, -1/4, 2
What is r in 14*r**3 + 2/5*r**4 + 0*r**2 + 0 + 0*r = 0?
-35, 0
Let u = 15 - -1. Suppose -5*g + 4*o + o + 10 = 0, -3*o - u = -5*g. Determine j, given that 3*j**2 - 3*j**3 - 2*j**g + 4*j**2 - 6*j**4 - 3*j**3 - 9*j**2 = 0.
-1, 0
Let m = 7539 + -995143/132. Let b(z) be the second derivative of 4/33*z**3 - 2/11*z**2 - m*z**4 + 9*z + 1/220*z**5 + 0. Determine k so that b(k) = 0.
1, 2
Let d(b) be the first derivative of b**3/4 + 45*b**2/8 + 33*b - 797. Solve d(w) = 0.
-11, -4
Let i be (-6)/(-10) - ((-2581)/145 + 18). Solve -i + 1/5*o**3 - 4/5*o**2 + o = 0 for o.
1, 2
Let u be 9/12 + 2/8 + 0. Let j be u + -2 - 78/(-30). Factor -2/5*x**3 - j - 16/5*x - 2*x**2.
-2*(x + 1)*(x + 2)**2/5
Let u(q) be the third derivative of q**5/480 + 7*q**4/192 + q**3/4 - 101*q**2. Let u(i) = 0. What is i?
-4, -3
Let t(f) = f**5 - 22*f**4 - 52*f**3 - 20*f**2 + 3*f + 6. Let g(b) = -2*b**5 + 65*b**4 + 155*b**3 + 60*b**2 - 8*b - 16. Let c(r) = 3*g(r) + 8*t(r). Factor c(q).
q**2*(q + 4)*(q + 5)*(2*q + 1)
Let n(f) = -f**3 - 9*f**2 + 2*f - 216. Let y be n(-11). Find s, given that 0 + 9/7*s**y + 9/7*s**5 + 2/7*s - s**3 - 5/7*s**2 = 0.
-1, 0, 1/3, 2/3
Factor 1/3*a**5 + 7/3*a**2 + 5*a**3 + 0*a + 3*a**4 + 0.
a**2*(a + 1)**2*(a + 7)/3
What is l in 60*l**3 - 2*l**4 - 431*l + 20*l**3 - 1169*l + 2000 + 7*l**4 + 120*l**2 = 0?
-10, 2
Let y(u) = u. Let r(p) = -2*p**3 - 8*p**2 - 11*p. Let q(w) = r(w) + 3*y(w). Suppose q(j) = 0. Calculate j.
-2, 0
Let v(y) = 4*y**2 + 16*y - 80. Let k(o) = o - 1. Let c(m) = -16*k(m) + v(m). Factor c(n).
4*(n - 4)*(n + 4)
Let x be (-5)/(-10) + (-59)/(-2). Let t be 12/x - 3/(-30). Determine w, given that 0*w + t*w**4 - w**2 + 0*w**3 + 1/2 = 0.
-1, 1
Suppose -h = -2 - 2. Solve -3*v**4 + 3*v**3 + 0*v**h + v**3 + v**5 - v**3 - v**2 = 0 for v.
0, 1
Let m(o) = -3*o**2 + 1. Suppose -7*t + 13 + 1 = 0. Suppose -2*w = -5*w, j = w - 5. Let c(f) = -7*f**2 + f + 1. Let h(s) = j*m(s) + t*c(s). Factor h(l).
(l - 1)*(l + 3)
Let h = -3 + 3. Suppose 3*l + h*l - 9 = 0. Factor -t + 4*t**3 + 0 - l*t + 0 + 2*t**4 - 2.
2*(t - 1)*(t + 1)**3
Solve 3087/4 + 81/4*d**4 - 2499/2*d + 756*d**2 - 405/2*d**3 = 0 for d.
7/3, 3
Let m be 1/(-9) + (-1845)/(-2025). Factor -8/5*j**2 + 18/5*j - m.
-2*(j - 2)*(4*j - 1)/5
Let p = -32 + 34. Let j(f) = -5*f**4 + 2*f**3 - 6*f**2 - 9*f - 3. Let i(q) = q**4 + q + 1. Let z(b) = p*j(b) + 14*i(b). Suppose z(y) = 0. Calculate y.
-2, -1, 1
Suppose -3*h + 29*q + 19 = 24*q, -3*q - 21 = -5*h. Factor 0 + 0*p**2 - 5/4*p**h + 5/4*p.
-5*p*(p - 1)*(p + 1)/4
Suppose -9*u - 540 = -558. Let d(y) be the third derivative of 1/90*y**5 + 0*y + 1/27*y**3 + 0 + 1/36*y**4 + 1/540*y**6 - 3*y**u. Suppose d(l) = 0. Calculate l.
-1
Let h = 18 - 2. Let c = 35/2 - h. Solve 6*m + 9/2 + c*m**2 = 0.
-3, -1
Let w(v) be the third derivative of -v**8/72 + 11*v**7/105 - v**6/10 - 4*v**5/45 - 229*v**2. What is g in w(g) = 0?
-2/7, 0, 1, 4
Let o(x) = -31*x**2 + 412*x + 101.