f). Factor m(u).
u*(u - 2)**2*(u - 1)/5
Let q(f) = -5*f**3 + f - 4. Let i(w) = -w**2 + 9*w - 10. Let o be i(7). Suppose 2*t - 10 = -0*t. Let n(a) = 5*a**3 + 5. Let z(k) = o*n(k) + t*q(k). Factor z(u).
-5*u*(u - 1)*(u + 1)
Suppose -248*f**2 + 14*f**5 - 64/5*f - 638/5*f**4 + 1744/5*f**3 + 128/5 = 0. Calculate f.
-2/7, 2/5, 1, 4
Factor 1/4*p**2 - 6 + 1/2*p.
(p - 4)*(p + 6)/4
Solve -3/2*h**5 + 0 - 3/2*h - 9*h**3 - 6*h**4 - 6*h**2 = 0 for h.
-1, 0
Let g(d) be the first derivative of d**4/48 + d**3/24 - 15*d + 15. Let h(i) be the first derivative of g(i). Factor h(j).
j*(j + 1)/4
Factor 0 - 5/4*b**4 - 15/4*b**3 + 15/4*b + 5/4*b**2.
-5*b*(b - 1)*(b + 1)*(b + 3)/4
Let a(o) be the first derivative of 3*o**5/2 - 29*o**4/6 - 4*o**3/3 + 4*o**2 - 8*o - 6. Let b(s) be the first derivative of a(s). Solve b(i) = 0 for i.
-2/5, 1/3, 2
Suppose 3*z = 5*n + 7, 4 = 2*z - 3*n - n. Determine a so that 12*a**5 - 4*a**3 - 7*a**4 - 13*a**5 + 2*a**4 + 0*a**z = 0.
-4, -1, 0
Suppose -360*w = -371*w. Let c(p) be the third derivative of -1/660*p**6 + 0*p**4 - p**2 + 0 + 0*p + w*p**5 + 0*p**7 + 0*p**3 + 1/1848*p**8. Factor c(q).
2*q**3*(q - 1)*(q + 1)/11
Let r(j) be the third derivative of j**6/24 - 2*j**5 + 195*j**4/8 - 135*j**3 + 274*j**2. What is g in r(g) = 0?
3, 18
Let g(u) be the third derivative of u**5/80 + u**4/2 + 7*u**3/2 + 26*u**2 + u. Factor g(m).
3*(m + 2)*(m + 14)/4
Solve 242/9 - 44/9*c + 2/9*c**2 = 0 for c.
11
Solve -2*c + 9/2*c**3 - 1/2*c**4 - 9*c**2 + 12 = 0.
-1, 2, 6
Let o = -1594 + 1598. Let l(z) be the second derivative of -5/3*z**4 + 9/5*z**5 - o*z**2 + 0 + 6*z - 6*z**3 + 14/15*z**6. Factor l(q).
4*(q - 1)*(q + 1)**2*(7*q + 2)
Suppose -3*p + 2*p + 1 = 0. Let i(u) = 3*u**2 + 2*u - 1. Let k be i(p). Factor 0*s**3 - 48*s - 2*s**4 + 52*s - k*s**3 + 2.
-2*(s - 1)*(s + 1)**3
Suppose 27*a**3 - 33*a**3 + 14*a**4 - 14*a**2 + 12*a - 4*a**3 - 2*a**5 = 0. Calculate a.
-1, 0, 1, 6
Find r, given that -2/5*r**4 + 0*r + 2/5*r**2 + 2/5*r**5 + 0 - 2/5*r**3 = 0.
-1, 0, 1
Let y(i) be the first derivative of -i**4 - 22*i**3/9 + 4*i**2 + 10*i/3 + 163. Find o, given that y(o) = 0.
-5/2, -1/3, 1
Let l(m) be the second derivative of -3*m + 0*m**2 + 8/45*m**5 + 0 - 128/135*m**6 + 32/27*m**3 + 64/27*m**4 + 2/9*m**7. Determine k, given that l(k) = 0.
-2/3, -2/7, 0, 2
Let q(d) = -2*d**4 - 6*d**3 - 16*d**2 + 6*d + 6. Let c(j) = 6*j**4 + 19*j**3 + 47*j**2 - 17*j - 17. Let x(l) = 6*c(l) + 17*q(l). Find t such that x(t) = 0.
-5, -1, 0
Let t(g) be the first derivative of -2*g**6/3 - 12*g**5/5 - 3*g**4 - 4*g**3/3 - 41. Find j such that t(j) = 0.
-1, 0
Let q(m) be the second derivative of -2*m**7/147 + m**6/21 + 3*m**5/35 - 4*m**4/21 - 4*m**3/21 + 3*m**2/7 - 4*m - 21. Let q(c) = 0. What is c?
-1, 1/2, 1, 3
Let p(k) = 4*k**2 + k**5 + 1 + k - 4*k**4 + k**2 + 0*k**2. Let j(v) = v**4 - v**2 - v - 1. Let q(u) = -5*j(u) - 5*p(u). Suppose q(l) = 0. What is l?
-1, 0, 2
Let p = -72884/5 + 14578. Factor 4/5 + p*n + 1/10*n**3 + 3/5*n**2.
(n + 2)**3/10
Let s(v) = -6*v**2 + 6*v + 2. Let h(u) = 7*u**2 - 7*u - 2. Suppose 0 = 14*w - 9*w - 30. Let p(o) = w*s(o) + 5*h(o). Factor p(g).
-(g - 2)*(g + 1)
Let t(o) = -2*o**3 - 164*o**2 + 166*o + 2. Let p be t(-83). Factor 1/4*z**3 - 1/2*z**p + 1/4*z + 0.
z*(z - 1)**2/4
Let g(c) be the third derivative of -c**8/168 + 23*c**7/735 + 19*c**6/140 + 17*c**5/210 - 5*c**4/42 - 2*c**2 + 103. Suppose g(i) = 0. What is i?
-1, 0, 2/7, 5
Let r(x) be the third derivative of x**5/12 - 5*x**3/6 - 19*x**2 - 1. Factor r(t).
5*(t - 1)*(t + 1)
Let g = -138 + 138. Let k(o) be the third derivative of o**2 + 1/60*o**5 + 1/24*o**4 + 0*o + g*o**3 + 0. Factor k(a).
a*(a + 1)
Suppose 15*h - 6*h - 9 = 0. What is a in -a**2 + 2*a - 11*a - h + 11*a = 0?
1
Let o(k) be the first derivative of -27*k - 27/2*k**2 - 23 - 3*k**3 - 1/4*k**4. Factor o(x).
-(x + 3)**3
Let q be (7 + (-85)/10)*2/(-21). Let y(p) be the second derivative of -q*p**3 + 2*p - 1/84*p**4 - 9/14*p**2 + 0. Suppose y(h) = 0. What is h?
-3
Let w = 107 - 104. Let c(t) be the first derivative of 1/2*t**4 - 2*t**w + 3*t**2 - 2*t + 2. Factor c(o).
2*(o - 1)**3
Let v(w) = -5*w**3 + 3*w**2 - 10*w + 6. Let i(s) = 11*s**3 - 6*s**2 + 20*s - 13. Let k(t) = 6*i(t) + 13*v(t). Let k(b) = 0. What is b?
-5, 0, 2
Let h(w) be the first derivative of 0*w**2 - 2/39*w**3 + 6 + 0*w. Let h(s) = 0. Calculate s.
0
Suppose -g + 0 = -3, 5*d = -2*g + 21. Let m(k) be the first derivative of -2/39*k**d + 0*k**2 + 4 + 0*k. Determine h so that m(h) = 0.
0
Let f = 3227/4 - 788. Let u = f + -371/20. Solve u*s**3 + 9/5*s + 4/5 + 6/5*s**2 = 0.
-4, -1
Suppose 5*f = 27 - 7. Factor 4*q**4 - 4*q**f - 10*q + 5*q**4 - 8 + 10*q**3 + 3.
5*(q - 1)*(q + 1)**3
Let v be (-2 - -6) + 6/((-150)/(-1915)). Let r = -80 + v. Find l such that 3/5*l**4 - r*l**2 - 6/5*l**3 + 0 + 6/5*l = 0.
-1, 0, 1, 2
Let g(t) be the first derivative of -2*t**5/15 - t**4/3 + 26*t**3/3 - 68*t**2/3 + 64*t/3 + 299. Find y, given that g(y) = 0.
-8, 1, 4
Let j(b) = 2*b**2 - 9*b - 1. Let d be j(10). Let p = d + -433/4. Factor 3/4*u**2 + 3/2*u + p.
3*(u + 1)**2/4
Let z be 1/18 - (-4550)/2340. Factor 8/7*k + 24/7 + 2/21*k**z.
2*(k + 6)**2/21
Factor 1/4*n**2 + 21/4 - 5/2*n.
(n - 7)*(n - 3)/4
Let a(d) be the second derivative of 28*d - 1/24*d**4 - 1/3*d**3 + 0*d**2 + 0. Factor a(n).
-n*(n + 4)/2
Let 10*v + 55*v**5 - 16*v - 7*v**2 + v**4 - 51*v**5 + 8*v**3 + 12*v**4 = 0. What is v?
-2, -1, 0, 3/4
Let f(y) be the first derivative of -y**3/12 + 77*y**2/8 + 39*y/2 - 158. Find i, given that f(i) = 0.
-1, 78
Let v be 2 + 2/(-4 - -2). Let h be 4*-1*(v - 3). Factor 4*c**3 + h - 4*c**4 - 9 + 1.
-4*c**3*(c - 1)
Suppose -d + 2*l - 9 = -l, 2*l = 8. Suppose 2/9*x**d + 0 + 0*x**2 + 0*x = 0. Calculate x.
0
Let i be 77/((-2310)/(-288)) + -1 + -2. Suppose i*w + 9/5 - 12/5*w**2 = 0. Calculate w.
-1/4, 3
Factor 12 - 9*y**2 + 42*y**2 - 6*y - 10*y + 88*y.
3*(y + 2)*(11*y + 2)
Determine t, given that 0*t**2 + 30/7*t**3 - 27/7*t + 0*t**4 + 0 - 3/7*t**5 = 0.
-3, -1, 0, 1, 3
Factor -3*h**2 - 45 + 74632*h - 74515*h + 0*h**2 - 69.
-3*(h - 38)*(h - 1)
Let k(m) be the first derivative of m**4/16 - 13*m**3/12 + 3*m**2/2 + 214. Factor k(u).
u*(u - 12)*(u - 1)/4
Let k(y) be the second derivative of -y**5/100 + y**4/12 - y**3/5 + 37*y - 1. Factor k(p).
-p*(p - 3)*(p - 2)/5
Let y(o) = -61*o**3 - 43*o**2 - 16*o. Let t(k) = 15*k**3 + 11*k**2 + 4*k. Let v be 2 - 3 - 3*-1 - -24. Let r(w) = v*t(w) + 6*y(w). Factor r(g).
4*g*(2*g + 1)*(3*g + 2)
Let b = 2/2485 + 39754/7455. Solve -56/3*j - 44/3*j**3 - 1/2*j**5 - 24*j**2 - 13/3*j**4 - b = 0 for j.
-2, -2/3
Let g(h) be the third derivative of 0 + 3/2*h**4 - 2*h**2 + 0*h + 18*h**3 + 1/20*h**5. Factor g(v).
3*(v + 6)**2
Find h such that 47/6*h**3 - 1/2*h**5 - 1/6*h**4 + 38/3*h - 10/3 - 33/2*h**2 = 0.
-5, 2/3, 1, 2
Suppose 8 = 2*a, -p + 2*p - 3*a = 71. Let z = p + -329/4. Suppose 3/4*t**3 + 0 + 1/4*t**4 + z*t**2 + 1/4*t = 0. Calculate t.
-1, 0
Determine b so that 5765*b**3 + 82*b + 595*b**2 - 372*b - 2 - 3 - 6065*b**3 = 0.
-1/60, 1
Let b(w) be the first derivative of -5*w**3/9 + 55*w**2/6 - 30*w + 63. Factor b(s).
-5*(s - 9)*(s - 2)/3
Factor 4*u + 0 - 1/3*u**4 + 8/3*u**2 - 1/3*u**3.
-u*(u - 3)*(u + 2)**2/3
Let a(u) be the third derivative of -u**6/220 + u**5/33 - u**4/33 - 8*u**3/33 - 2*u**2 - 65*u. Find s, given that a(s) = 0.
-2/3, 2
Let j = -33 + 36. Let w be j/2 + 3/6. Factor -1/2*l**3 + 0*l**w + 1 + 3/2*l.
-(l - 2)*(l + 1)**2/2
Suppose -3*q = -14 + 5. Suppose 0 = 4*h + 3*r - 217, 5*h - q*r - 2*r - 280 = 0. Determine n so that -h*n + 12*n + 27 - 8*n**3 - 11*n + 36*n**2 = 0.
3/2
Find x such that 4/3*x + 0 + 2/9*x**2 = 0.
-6, 0
Let t(r) = -5*r**3 - 8*r**2. Let b(g) = 15*g - 6*g**2 - 10*g**2 - 14*g - 10*g**3. Let l(u) = 3*b(u) - 7*t(u). Factor l(x).
x*(x + 1)*(5*x + 3)
Let i be (9 - (19 - 14)) + (0 - 3 - -2). Determine m, given that -1/2*m**2 + m**i + 0 + 0*m - 1/2*m**4 = 0.
0, 1
Let c = 1103/2204 - 1/2204. Let x(g) be the third derivative of 0 + 1/6*g**4 - 1/60*g**5 + 0*g - c*g**3 - 5*g**2. Suppose x(o) = 0. What is o?
1, 3
Let 8/3 - 2/3*n**3 + 4*n**2 - 6*n = 0. What is n?
1, 4
Let b be 12/3 - 1846/(-1398). Let h = b - -3/233. Factor -16/3 + 4*l**2 + 4/3*l**4 + h*l**3 - 16/3*l.
4*(l - 1)*(l + 1)*(l + 2)**2/3
Suppose 16 = -60*a + 56*a. Let u be 3 - ((-2)/a - 21/(-18)). Find j, given that 2/3 - u*j + 2