4/12 - c**3/2 + 10*c. Let y(s) = -s**3. Let i(t) = l(t) - 5*y(t). Factor i(n).
-n*(n + 1)**2*(n + 3)
Let v(q) = 4*q**4 + 38*q**3 + 236*q**2 + 358*q + 164. Let o(n) = -9*n**4 - 75*n**3 - 472*n**2 - 715*n - 329. Let y(x) = -2*o(x) - 5*v(x). Factor y(l).
-2*(l + 1)**2*(l + 9)**2
Determine o so that 1/4*o**2 - 3 + 1/4*o = 0.
-4, 3
Let r(i) be the third derivative of 0 + 4*i**4 + 0*i + 96*i**3 + 28*i**2 + 1/15*i**5. Factor r(c).
4*(c + 12)**2
Let 50 - 15*y - 1/4*y**3 - 9/2*y**2 = 0. What is y?
-10, 2
Let p be -2 - (-1 + 1 + -1). Let n(c) = -c**2. Let i(a) = -9*a**3 - 6*a**2 + 5*a - 1. Let g(s) = p*i(s) + 3*n(s). Find b, given that g(b) = 0.
-1, 1/3
Determine b so that b**4 + 2*b - 2*b + 6*b + b**3 - 3*b**3 + 0*b - 5*b**2 = 0.
-2, 0, 1, 3
Let p(y) = -2*y - 6. Let i be p(-10). Let j be (i - 11)*1/1. Factor 5*a - 2*a**2 - j*a - 1 + a**2.
-(a - 1)**2
Let d(s) be the third derivative of s**8/35280 + s**7/2205 + s**6/315 - 19*s**5/60 + 8*s**2. Let i(w) be the third derivative of d(w). Factor i(z).
4*(z + 2)**2/7
Factor -93636/11 + 612/11*k - 1/11*k**2.
-(k - 306)**2/11
Let k(s) = s**5 - 2*s**4 - s**3 - s**2 - s + 1. Let h(x) = 6*x**5 - 27*x**4 + 45*x**3 - 39*x**2 - 3*x + 3. Let i(b) = h(b) - 3*k(b). Factor i(t).
3*t**2*(t - 3)*(t - 2)**2
Suppose -33*h - 18 = -35*h. Let s be h/(-27)*(5/(-3) - -1). Let s - 2/9*i**2 - 2/9*i + 2/9*i**3 = 0. Calculate i.
-1, 1
Suppose 0 = -135*p + 145*p - 30. Determine s so that 0*s + 0 + 2/5*s**p - 2/5*s**2 = 0.
0, 1
Let h(r) be the second derivative of -4/9*r**3 + 1/6*r**4 + 1/3*r**2 - 14*r + 0. Solve h(l) = 0 for l.
1/3, 1
Let k(w) be the third derivative of -1/60*w**7 - 1/672*w**8 - 1/4*w**3 + 9*w**2 + 0*w - 13/48*w**4 - 11/60*w**5 - 3/40*w**6 + 0. Factor k(p).
-(p + 1)**4*(p + 3)/2
Let x(p) = 20*p**4 - 32*p**3 + 44*p**2 + 24*p - 24. Let s(h) = -h**4 + h**3 - 2*h**2 - h + 1. Let w(q) = 24*s(q) + x(q). Factor w(y).
-4*y**2*(y + 1)**2
Let n(f) be the third derivative of 2/25*f**5 + 0*f**3 - 11*f**2 + 0*f**4 + 0*f - 6/175*f**7 + 0 + 1/6*f**6. Find i, given that n(i) = 0.
-2/9, 0, 3
Suppose 1360 = -t + 5*t - o, o = -3*t + 1020. Let h be (-40)/t - 112/(-85). Solve -6/5*r + 9/5 - 9/5*r**2 + h*r**3 = 0.
-1, 1, 3/2
Factor -12*h**2 - 72/7*h + 0 - 32/7*h**3 - 4/7*h**4.
-4*h*(h + 2)*(h + 3)**2/7
Let c(b) be the first derivative of b**5/30 - 4*b**3/3 + 13*b**2/2 - 1. Let x(h) be the second derivative of c(h). Factor x(o).
2*(o - 2)*(o + 2)
Let s = -555/56 - -72/7. Factor 3/8*u**2 + 0 + s*u.
3*u*(u + 1)/8
Let h = -829/8 - -104. Let f = h + -5/24. Factor 1/6*r**2 + f + 1/3*r.
(r + 1)**2/6
Let m(p) be the second derivative of -p**5/20 - p**4/2 - 11*p**3/6 - 3*p**2 - 5*p - 8. Factor m(d).
-(d + 1)*(d + 2)*(d + 3)
Factor 0 + 16/5*i**2 + 4*i**4 + 0*i + 4/5*i**5 + 32/5*i**3.
4*i**2*(i + 1)*(i + 2)**2/5
Let c = 142 - 208. Let r = 68 + c. Factor -512/15*b - 512/15 - 32/15*b**3 - 2/15*b**4 - 64/5*b**r.
-2*(b + 4)**4/15
Let d(p) be the third derivative of 0 - 1/1008*p**8 + 0*p**4 + 0*p + 0*p**3 + 1/72*p**6 + 10*p**2 + 1/630*p**7 + 1/60*p**5. Factor d(b).
-b**2*(b - 3)*(b + 1)**2/3
Find o, given that 45*o**4 + 60 - 385 - 1680*o - 685*o**2 - 5*o**5 + 65*o**3 - 822 + 167 = 0.
-2, -1, 7
Let f(m) be the third derivative of 0*m - 1/15*m**5 - 1/3*m**3 - 24*m**2 - 1/30*m**6 + 1/4*m**4 + 1/35*m**7 - 1/168*m**8 + 0. Factor f(v).
-2*(v - 1)**4*(v + 1)
Let i(m) = 4*m**3 - 3*m**2 - 3*m. Let f(j) = -j**3 + j**2 + j. Suppose 5*r + u + 1 = -5, -3*r = -3*u. Let s(n) = r*i(n) - 3*f(n). Factor s(c).
-c**3
Solve -24*m + 48 - 12*m + 2*m**2 - 3*m + 19*m = 0 for m.
4, 6
Suppose -90*l = 86*l + 118*l - 588. Factor 3/7*t**l - 12/7 + 9/7*t.
3*(t - 1)*(t + 4)/7
Let p = 37 + -35. Determine n so that 12*n**3 - 6*n**4 + 2*n**4 - 24 + p*n**2 - 2*n**2 - 28*n + 12*n**2 = 0.
-1, 2, 3
Let m be 5/3 + -1 + 13175/(-75). Let v be (-8)/(-10) + (-110)/m. Suppose 4/7*b + 8/7*b**3 + 0 - 2/7*b**4 - v*b**2 = 0. Calculate b.
0, 1, 2
Factor -96*g + 82 - 795*g**2 - 11*g**3 - 233 - g**3 - 882*g - 44.
-3*(g + 1)*(g + 65)*(4*g + 1)
Let w(r) = 9*r**2 - 24*r**2 + 11*r**2 - 16*r. Let s(b) = -3*b**2 - 11*b. Let c(n) = 8*s(n) - 5*w(n). What is q in c(q) = 0?
-2, 0
Factor 11*f**2 - 60*f - 2*f**4 - f**4 + 17*f**2 + 114*f**3 - 111*f**3 + 2*f**4.
-f*(f - 6)*(f - 2)*(f + 5)
Let z = 1425/11 - 1893869/14619. Let p = 166141/5316 + z. Factor 75/2*g**4 + p*g**5 - 2 - 15*g - 71/2*g**2 - 65/4*g**3.
(g - 1)*(g + 1)*(5*g + 2)**3/4
Let g(t) be the third derivative of -t**8/560 + t**6/60 - t**4/8 - 17*t**3/3 - 3*t**2. Let y(x) be the first derivative of g(x). Factor y(r).
-3*(r - 1)**2*(r + 1)**2
Suppose 0 = -5*s + 6*s + 12. Let p be s/(-9) + (-2)/(-3). Factor 1/3*v**p + 1/3*v - 1/3*v**3 - 1/3.
-(v - 1)**2*(v + 1)/3
Let z(c) = 11*c**2 + c. Let q be z(-1). Suppose -2*d + 5*b = -3 + q, -5*d + 8 = -4*b. Let 0*h**3 + 3*h**3 + 4*h**2 - d*h**2 - 3*h**4 = 0. What is h?
0, 1
Let w(b) = b - 5. Let d be w(5). Let t = d - -2. Factor 3*m - 2*m**3 + 14*m**t - 4*m**3 - 6*m**3 - 5*m**2.
-3*m*(m - 1)*(4*m + 1)
Let k = -2/1211 - -197/14532. Let u(b) be the second derivative of 0*b**2 + 1/12*b**6 + 0 - 9/40*b**5 - 1/6*b**3 - k*b**7 + b + 7/24*b**4. Factor u(w).
-w*(w - 2)*(w - 1)**3/2
Let n(k) be the third derivative of k**7/70 - k**6/5 - 17*k**5/4 + k**4 + 42*k**3 + 491*k**2. What is g in n(g) = 0?
-6, -1, 1, 14
Factor -64*t + 36*t**2 + 17 - 36*t + 11*t**3 - 19 + 5*t**3 + 50.
4*(t - 1)*(t + 4)*(4*t - 3)
Determine c, given that 2/5*c**3 - 30*c + 100 + 0*c**2 = 0.
-10, 5
Let u = 8 - 8. Let n(l) be the second derivative of 2*l**3 + 9/2*l**2 + 1/4*l**4 - 2*l + u. Determine y, given that n(y) = 0.
-3, -1
Let q(v) be the third derivative of v**8/672 + v**7/420 - 7*v**6/120 + 13*v**5/60 - 19*v**4/48 + 5*v**3/12 + 3*v**2 + 1. Solve q(z) = 0.
-5, 1
Suppose -3*f = 5*c - 116, 2*c = f + 3*c - 36. Let m(q) = 3 - 10 - f*q**2 - 2*q + 23*q**2 - 2. Let w(x) = -x**2 - x. Let i(u) = 3*m(u) - 24*w(u). Factor i(d).
-3*(d - 3)**2
Let v(t) be the second derivative of -t**7/168 + t**6/36 - t**3/3 - 20*t. Let g(r) be the second derivative of v(r). Find o, given that g(o) = 0.
0, 2
Let t(b) be the second derivative of -1/36*b**4 + 1/18*b**3 + 1/90*b**6 + 0 - 1/60*b**5 - 18*b + 0*b**2. Find w such that t(w) = 0.
-1, 0, 1
Let d(s) = s**4 - s**3 + s**2 - s + 1. Let w(x) = -2*x**4 - 22*x**3 - 5*x**2 + 5*x - 5. Let p(i) = -5*d(i) - w(i). Factor p(j).
-3*j**3*(j - 9)
Let u = -13521/13 - -1041. Solve 10/13*b - 6/13*b**5 + u*b**2 - 14/13*b**4 + 2/13 - 4/13*b**3 = 0 for b.
-1, -1/3, 1
Let z = -39497 + 39499. Factor 0*n**z + 0*n - 1/2*n**4 + n**3 + 0.
-n**3*(n - 2)/2
Let z(o) be the first derivative of -o**4/132 + 2*o**2/11 - 11*o + 22. Let r(w) be the first derivative of z(w). Factor r(s).
-(s - 2)*(s + 2)/11
Determine h, given that -h + 5/4*h**4 + 1 - 1/2*h**3 - 15/4*h**2 = 0.
-1, 2/5, 2
Let l(o) = o**3 - 537*o**2 + 96123*o - 5735331. Let t(b) = 1. Let u(h) = 5*l(h) - 40*t(h). Factor u(a).
5*(a - 179)**3
Let r be ((-6)/4 - -2)*45/225. Factor 0 - r*p**2 + 3/10*p.
-p*(p - 3)/10
Determine a so that -4*a**2 - 6*a**2 + 20*a + 9*a**2 - a**2 = 0.
0, 10
Suppose 4*v - 65 = -25. Suppose -v*o + 6*o = -8. Factor 8*u**o + u**4 + 3*u**3 - 4*u**4 - 2*u**2.
-3*u**2*(u - 2)*(u + 1)
Let j = 171 - 166. Suppose -4*c = 3*g + 8, 3*g - 8 = 4*c + 24. Factor 2*d**5 + 0*d**4 + j*d**4 - 3*d**g.
2*d**4*(d + 1)
Let b(w) = -w**2 - 3*w - 5. Let l = 20 - 14. Let n be (-3)/(-2)*4/l. Let f(d) = -d**2 - d - 1. Let p(c) = n*b(c) - 3*f(c). Let p(q) = 0. Calculate q.
-1, 1
Let a(b) = -2*b + 21. Let x be a(9). Factor -5*j**4 + 4*j + 6*j**3 - 2*j**5 + 7*j**4 + 3*j**4 - x*j**4 - 10*j**2.
-2*j*(j - 1)**3*(j + 2)
Suppose 0 = -4*s - 4*g + 87 - 31, -2*g = 5*s - 64. Factor -s*p**2 + 7*p**3 + 4*p + 15*p**5 + 7*p**5 + 6*p**3 - 21*p**5 - 6*p**4.
p*(p - 2)**2*(p - 1)**2
Let x(c) be the second derivative of -c**8/53760 - c**7/20160 + c**6/5760 + c**5/960 - 17*c**4/6 + 38*c. Let z(b) be the third derivative of x(b). Factor z(f).
-(f - 1)*(f + 1)**2/8
Factor -14/13*v**2 + 2/13*v**4 + 0*v**3 - 12/13*v + 0.
2*v*(v - 3)*(v + 1)*(v + 2)/13
Let b be (3 - (8 - 5))/((-2)/(-1)). Factor 2/5*j**5 + b + 2/5*j**3 + 0*j**2 + 0*j + 4/5*j**4.
2*j**3*(j + 1)**2/5
Let k = 202 - 197. Let a(l) be the second derivative of 0 + 1/3*l**3 - 7/30*l**6 - 11/12*l**4 + 0*l**2 + 10*l + 4/5*l**k. Solve a(t) = 0 for t.
0, 2/7, 1
Let h be ((-24