ative of 0*u - 1/2*u**2 - 1/9*u**3 + 12. Factor k(t).
-t*(t + 3)/3
Suppose -u - 2 = 4*j + 3, -1 = -2*u + 3*j. Let r be -2 + 25/7 + u. Factor 2*t**5 + 0*t**2 + 0 + 0*t**3 + 0*t + r*t**4.
2*t**4*(7*t + 2)/7
Let w(a) be the third derivative of -a**9/7560 + a**7/2100 + a**3/2 + 14*a**2. Let j(x) be the first derivative of w(x). Let j(t) = 0. What is t?
-1, 0, 1
Let r(y) = -8*y**4 + 20*y**3 - 14*y**2 + 6*y. Let p(h) = -h**5 + h**4 + h**3 + h. Let c(l) = -2*p(l) + r(l). Factor c(m).
2*m*(m - 2)*(m - 1)**3
Let g(p) be the third derivative of p**7/42 - 7*p**6/6 + 13*p**5/6 + 35*p**4/6 - 45*p**3/2 + 7*p**2 - 2*p. What is j in g(j) = 0?
-1, 1, 27
Let f(x) be the second derivative of -x**6/1800 - 7*x**5/600 - x**4/20 + 7*x**3/6 + 25*x. Let w(a) be the second derivative of f(a). Factor w(n).
-(n + 1)*(n + 6)/5
Let g(o) be the first derivative of -o**4/28 - 4*o**3/21 - 3*o**2/14 + 13. Factor g(z).
-z*(z + 1)*(z + 3)/7
Solve 125 - 16*y**5 - 656*y - 772*y**3 + 208*y**4 + 58 + 1136*y**2 - 55 = 0.
1/2, 2, 8
Let p(s) be the first derivative of -6*s**5/5 + 2*s**4 - 2*s**3/3 + 243. Factor p(n).
-2*n**2*(n - 1)*(3*n - 1)
Suppose 5 = b - 4. Suppose b*s = 7*s. Let 2*z**2 - 2*z + 2 - 2*z + 8*z + s*z**2 = 0. What is z?
-1
Let k = -1/610 + 2147/7320. Let s = 37/72 - k. Factor -10/9*q**4 + 0 + 4/9*q**5 - 2/9*q + s*q**2 + 2/3*q**3.
2*q*(q - 1)**3*(2*q + 1)/9
Let j(m) = -16*m**2 - 2*m**2 - 6*m + 7*m**2 + 2 + 5*m**4. Let i(l) = -51*l**4 + 111*l**2 + 60*l - 21. Let y(x) = 2*i(x) + 21*j(x). Find z, given that y(z) = 0.
-1, 0, 2
Factor 84/5*s + 17 - 1/5*s**2.
-(s - 85)*(s + 1)/5
Let b be (-66)/(-44) - (-858)/4. Factor -1248*v - 196*v**3 - 176 - 943*v**2 - 1109*v**2 - b*v**2.
-4*(v + 11)*(7*v + 2)**2
Factor -4*u + 2/7*u**2 + 14.
2*(u - 7)**2/7
Factor 36980/3 - 860/3*f + 5/3*f**2.
5*(f - 86)**2/3
Let f(d) be the first derivative of -d**4/40 - 2*d**3/15 + d**2/5 + 8*d/5 - 91. Factor f(h).
-(h - 2)*(h + 2)*(h + 4)/10
Let i = 19 - 14. Let u(s) be the second derivative of s**4/2 + s**3/3 - 2*s**2 + 3*s. Let b(q) = 13*q**2 + 5*q - 8. Let n(f) = i*u(f) - 2*b(f). Factor n(j).
4*(j - 1)*(j + 1)
Solve 837/5*r - 486/5 - 261/5*r**3 + 1047/5*r**2 + 3*r**4 = 0 for r.
-1, 2/5, 9
Let g(b) be the first derivative of 3*b**5/50 - b**4/2 + 4*b**3/5 + 21*b + 20. Let z(t) be the first derivative of g(t). Factor z(v).
6*v*(v - 4)*(v - 1)/5
Let a(f) be the second derivative of f**4/4 - 7*f**3/2 + 15*f**2 + 2*f - 233. Solve a(n) = 0 for n.
2, 5
Let z = -15 - -46/3. Let g be 8/(-20) - (2/(-5))/1. Factor z*v**2 + g + 0*v.
v**2/3
Let f(a) be the second derivative of -a**6/70 - 3*a**5/35 - a**4/14 + 2*a**3/7 + 9*a**2/14 + 318*a. Suppose f(j) = 0. What is j?
-3, -1, 1
Let s(b) = 7*b**3 + b**2 + 2*b - 8. Let i(f) = -2*f**3 + f**2 - f. Let v(p) = 4*i(p) + s(p). Factor v(k).
-(k - 4)*(k - 2)*(k + 1)
What is x in -6*x**3 + 8*x**4 + 4977*x - 20*x**2 - 20*x**2 - 5002*x - x**5 = 0?
-1, 0, 5
Let p(n) be the second derivative of 1/36*n**4 + 0 - 3*n - 4*n**2 - 1/18*n**3 - 1/180*n**5. Let w(i) be the first derivative of p(i). Factor w(y).
-(y - 1)**2/3
Let o(f) = 5*f**2 - 97*f + 38. Let x be o(19). Factor -2/5*b**2 - 2*b + x.
-2*b*(b + 5)/5
Suppose 20*a - 21*a - 16 = 4*c, 4*c + 16 = -4*a. Let r(f) be the first derivative of -3 + a*f**2 + 5*f - 5/3*f**3. Find z such that r(z) = 0.
-1, 1
Let z(c) = -4*c + 60. Suppose -7*t + 63 = -42. Let g be z(t). Find a, given that -2/3*a + g - 1/3*a**2 = 0.
-2, 0
Suppose 36*l - 143 - 217 = 0. Determine a, given that 7/2*a**4 + 13*a**3 + 0 + l*a**2 - 4*a = 0.
-2, 0, 2/7
Factor 14/5*t - 2/5*t**5 - 4/5*t**4 + 4/5 + 16/5*t**2 + 4/5*t**3.
-2*(t - 2)*(t + 1)**4/5
Let z(w) be the third derivative of w**6/216 + 5*w**5/72 + 5*w**4/18 + 35*w**3/6 - 28*w**2. Let v(k) be the first derivative of z(k). Factor v(t).
5*(t + 1)*(t + 4)/3
Let l(s) = -s**2 - s - 4. Let r(d) = -7*d**2 - 13*d + 100. Let x(c) = -5*l(c) + r(c). Factor x(i).
-2*(i - 6)*(i + 10)
Let m(l) be the second derivative of -l**7/42 + l**6/5 + l**5/10 - l**4 - l**3/6 + 3*l**2 - 73*l - 3. Factor m(t).
-(t - 6)*(t - 1)**2*(t + 1)**2
Let d(g) = 10*g**3 - 2*g**2 + 3*g - 1. Let n be d(1). Determine v, given that -n - 15*v + 17*v - 7*v + 5*v**2 = 0.
-1, 2
Let d = -4 + 10. Let a be -4 - (0 + -25 + 5). Find t, given that 3*t**3 + 7*t + d - a*t + 0 = 0.
-2, 1
Let v(o) be the second derivative of o**4/72 + 25*o**3/18 + 625*o**2/12 - 20*o + 2. Suppose v(b) = 0. Calculate b.
-25
Factor -8/3 - 1/9*v**5 + 20/9*v + 14/9*v**2 - 7/3*v**3 + 8/9*v**4.
-(v - 3)*(v - 2)**3*(v + 1)/9
Let b be 5/(20/3*(-139)/(-4448)). Factor -121/2*g**3 - 2 - b*g - 165/2*g**2.
-(g + 1)*(11*g + 2)**2/2
Let b(a) be the third derivative of a**6/30 - 2*a**5/5 - 61*a**4/6 + 44*a**3 + 26*a**2. Factor b(o).
4*(o - 11)*(o - 1)*(o + 6)
Suppose 4*h + 3*k - 18 = 0, 2*k = 5*h - 0 - 11. What is d in 6*d**3 - 3*d**4 - 17 + 4*d**2 + d**4 - 24*d - 1 + 2*d**h = 0?
-1, 3
Let l(x) be the second derivative of -1/4*x**5 + 27*x + 0*x**3 - 5/12*x**4 + 0 + 0*x**2. Determine m so that l(m) = 0.
-1, 0
Let c(z) be the third derivative of -z**8/1512 + z**7/945 + z**6/108 + z**5/90 + 8*z**2 + 2*z. Find b, given that c(b) = 0.
-1, 0, 3
Let z(r) be the third derivative of -2/135*r**6 + 2/27*r**4 + 0 + 11*r**2 + 1/18*r**5 + 1/27*r**3 + 0*r - 16/945*r**7. What is g in z(g) = 0?
-1, -1/4, 1
Let f = -61 - -61. Let z(j) be the second derivative of 1/3*j**3 + 1/6*j**4 + 4*j + 0 - 1/10*j**5 + f*j**2 - 1/15*j**6. Factor z(v).
-2*v*(v - 1)*(v + 1)**2
Let x(b) be the first derivative of -2*b**3/15 - 7*b**2/5 - 24*b/5 + 212. Find l such that x(l) = 0.
-4, -3
Let w be ((-414)/42)/(-3) + (13 - 16). Solve 0 + w*l - 8/7*l**2 = 0.
0, 1/4
Let m(q) be the third derivative of q**6/180 - q**5/60 - q**4/6 - q**3/6 - 18*q**2. Let y(f) be the first derivative of m(f). Let y(l) = 0. What is l?
-1, 2
Let r(l) be the first derivative of -4*l**3/3 + 64*l - 5. Suppose r(w) = 0. Calculate w.
-4, 4
Let f(o) be the third derivative of -o**5/240 - 25*o**4/96 - 230*o**2. Factor f(b).
-b*(b + 25)/4
Let x(k) be the first derivative of -k**4/18 - 782. Factor x(r).
-2*r**3/9
Let p(g) be the first derivative of g**3/27 - 23*g**2/6 + 68*g/9 + 734. Factor p(t).
(t - 68)*(t - 1)/9
Factor 6*i**3 + 8/3*i**4 + 4/3*i**2 + 0*i + 0.
2*i**2*(i + 2)*(4*i + 1)/3
Let o be 258/(-3096) - 2/(-6). Factor 27/4*b + o*b**3 - 27/4 - 9/4*b**2.
(b - 3)**3/4
Let t(l) be the third derivative of l**5/540 - l**4/9 - 26*l**3/27 - 3*l**2 + 29*l. Solve t(d) = 0 for d.
-2, 26
Let l(a) be the first derivative of a**6/4 - a**5/5 - 13*a**4/12 + 2*a**3 - 5*a**2/4 + a/3 - 111. Find r such that l(r) = 0.
-2, 1/3, 1
Let a(f) be the second derivative of -f**6/18 + 8*f**5/15 - 2*f**4 + 32*f**3/9 - 8*f**2/3 - 110*f. Factor a(w).
-(w - 2)**3*(5*w - 2)/3
Let z be (-48)/(-15) + 2/(-10). Let r be (((-130)/60)/13)/(0 - (-3)/(-9)). Factor 0*l**z + r*l**4 + 1/2 + 0*l - l**2.
(l - 1)**2*(l + 1)**2/2
Let k(f) be the first derivative of -f**6/12 - 17*f**5/5 - 361*f**4/8 - 150*f**3 + 756*f**2 - 864*f + 154. Determine o, given that k(o) = 0.
-12, 1
Let j = 3 + 1. Let o(x) = -x**3 + 4*x**2 + x - 1. Let s be o(j). Factor 8*m**5 - 36*m**4 + 3*m + 52*m**3 + 8 - 10*m - 8*m + s*m - 20*m**2.
4*(m - 2)*(m - 1)**3*(2*m + 1)
Let o be 2/18*3 - (-370)/888. Find a, given that -o*a**2 + 0 + 3/4*a = 0.
0, 1
Let k(t) = 575*t**3 + 7810*t**2 - 9560*t - 16830. Let r(i) = i**4 - 288*i**3 - 3905*i**2 + 4779*i + 8416. Let o(v) = 3*k(v) + 5*r(v). Find n such that o(n) = 0.
-29, -1, 2
Let t(s) be the first derivative of 13 + 1/5*s - 1/15*s**3 + 0*s**2. Solve t(w) = 0 for w.
-1, 1
Suppose 5*n = 9*n - 36. Suppose 4*b - n*b + 11 = 4*g, 2*b - 3*g - 9 = 0. Let 4*w**5 + 3*w**4 + 0*w**4 - 4*w**3 + 3*w**b = 0. Calculate w.
-1, 0, 1/4
Let i(a) be the second derivative of -a**4/15 - 44*a**3/5 - 2178*a**2/5 + 2*a - 252. Solve i(d) = 0.
-33
Suppose -j + 7 + 12 = -5*k, 33 = 2*j - 5*k. Suppose 4*q - 60 = -4*w, 0*w - 2*w + 4*q = -48. Factor 2*d**2 - 6*d**3 + w*d - 4*d**2 - j*d.
-2*d*(d + 1)*(3*d - 2)
Let a(r) = -5*r**2 - 3*r - 4. Let j(m) = 9*m**2 + 7*m + 8. Let n(z) = 5*a(z) + 3*j(z). Factor n(x).
2*(x + 1)*(x + 2)
Let h(o) be the second derivative of o**6/10 + 9*o**5/20 - 3*o**4/2 - 14*o**3 - 36*o**2 - 7*o + 6. Factor h(p).
3*(p - 3)*(p + 2)**3
Suppose 0*g = -5*g - 70. Let k be (-4*(-9)/(-42))/(9/g). Factor 10/3*i + k - 10