 be the first derivative of -z**4/8 - z**3/2 + z**2 + 82. Factor r(c).
-c*(c - 1)*(c + 4)/2
Let r(s) = -s**3 + 6*s**2 + 20*s + 2. Let y be r(10). Let u be -6 + 5/((-120)/y). Factor 3/4*p**3 - u*p**2 + 9/4*p - 3/4.
3*(p - 1)**3/4
Let j(z) be the first derivative of z**5/25 - 7*z**4/20 - 6*z**3/5 + 152. Factor j(s).
s**2*(s - 9)*(s + 2)/5
Let w(z) = 6*z**3 + 6*z**2 + 2. Let s(c) = -6*c**3 - 7*c**2 - c - 3. Let y(x) = -x**3 - 2*x**2 - 2*x. Let n be y(-2). Let r(h) = n*s(h) + 6*w(h). Factor r(g).
4*g*(g + 1)*(3*g - 1)
Factor 64/17*s + 0 - 2/17*s**2.
-2*s*(s - 32)/17
Let h(n) = -64*n - 1984. Let o be h(-31). Solve 3/2*u**4 + 3/2*u**3 + 1/2*u**5 + o*u + 1/2*u**2 + 0 = 0 for u.
-1, 0
Let s(r) be the third derivative of 0*r + 0*r**3 + 1/20*r**5 + 0 - 1/32*r**4 + 2*r**2. Determine n so that s(n) = 0.
0, 1/4
Let b(t) = 14*t**4 + 7*t**3 + 19*t**2 + 5*t + 3. Let x(o) = 18*o**4 + 6*o**3 + 20*o**2 + 4*o + 4. Let j(k) = 4*b(k) - 3*x(k). Factor j(a).
2*a*(a + 1)*(a + 2)**2
Let n(z) be the second derivative of -2*z**2 + 7/3*z**3 + 14*z + 1/5*z**5 - 7/6*z**4 + 0. Factor n(c).
2*(c - 2)*(c - 1)*(2*c - 1)
Suppose -4*w + k + 0*k = 21, k + 3 = 0. Let n(c) = -22*c**3 + 66*c**2 - 34. Let m(j) = -2*j**3 + 6*j**2 - 3. Let y(q) = w*n(q) + 68*m(q). Factor y(f).
-4*f**2*(f - 3)
Let r be ((-543)/(-36))/((-10)/(-8)). Let m = r - 35/3. Factor -2/5 - 2/5*h + 2/5*h**2 + m*h**3.
2*(h - 1)*(h + 1)**2/5
Let a(k) = k + 25. Let y be a(-7). Let x be -5*y/(-30) + 1. Find f, given that -7/6*f**x + 1/3*f + 1/2*f**2 - 1/2*f**5 + 0 - 1/2*f**3 = 0.
-1, 0, 2/3
Let q(w) be the third derivative of 0 - 1/300*w**6 - 15*w**2 + 0*w + 0*w**4 + 1/50*w**5 - 4/15*w**3. Suppose q(m) = 0. Calculate m.
-1, 2
Let l be (-156)/(-13) - ((-12)/8*4 - -13). Let 25/3*x**4 - 15*x**3 + 0 + 35/3*x**2 - 5/3*x**l - 10/3*x = 0. Calculate x.
0, 1, 2
Let s(g) = 2*g**3 - 38*g**2 - 300*g + 2. Let j be s(25). Factor -3/2*i**j + 3 + 3/2*i.
-3*(i - 2)*(i + 1)/2
Suppose -14*r + 8*m = -13*r - 18, -14 = -4*r + 3*m. Suppose -3*v + 14 - 2 = 0. Factor 1/5*x**5 - 1/5*x**r + 3/5*x**3 + 0*x - 3/5*x**v + 0.
x**2*(x - 1)**3/5
Suppose 5*r - v - 10 = v, 0 = 3*r - 4*v + 8. Let b be r/(-7)*((-49)/6)/7. Factor 0 + b*i + 2/3*i**2.
2*i*(i + 1)/3
Let l(y) be the first derivative of -12/7*y - 1/7*y**2 + 2/21*y**3 + 45. Find v, given that l(v) = 0.
-2, 3
Let i(g) be the first derivative of -g**6/480 - g**5/480 + 7*g**3/3 + 16. Let j(v) be the third derivative of i(v). Factor j(y).
-y*(3*y + 1)/4
Let b(f) be the third derivative of 7/60*f**6 + 2/3*f**3 + 0 - 11*f**2 - 1/4*f**4 - 1/10*f**5 - 1/35*f**7 + 0*f. Let b(g) = 0. What is g?
-2/3, 1
Let n = 179 - 159. Let l be (2/6)/(-2 - (-45)/n). Factor -l*q**2 - 2/3 + 1/3*q**3 + 5/3*q.
(q - 2)*(q - 1)**2/3
Let c(b) = b**2 - 2*b - 1. Let u(t) = -21*t**2 - 48*t + 18. Let p(r) = -18*c(r) - u(r). Factor p(y).
3*y*(y + 28)
Solve 32*r - 100*r**2 - 92*r + 109 - 109 - 45*r**3 - 5*r**4 = 0 for r.
-6, -2, -1, 0
Let r(j) be the second derivative of -j**9/3024 + j**7/840 + 5*j**3/3 + 4*j. Let c(b) be the second derivative of r(b). Factor c(h).
-h**3*(h - 1)*(h + 1)
Let x = -619/4 - -27859/180. Let a(f) be the third derivative of 0*f**4 - 5*f**2 - x*f**5 + 0 + 0*f + 0*f**3 + 1/180*f**6 + 1/315*f**7. Factor a(r).
2*r**2*(r - 1)*(r + 2)/3
Let q be (1 + 4 - 3) + 8 + -8. Let n(r) be the first derivative of 9 + 0*r**q - 2/27*r**3 + 2/9*r. Determine c, given that n(c) = 0.
-1, 1
Let q(n) = -3*n**4 + 8*n**3 - 12*n**2 + 6*n - 1. Let o(i) = 24*i - 48*i**2 + 30*i**3 + i**3 + 3 - 7 - 12*i**4. Let b(c) = -4*o(c) + 18*q(c). Factor b(v).
-2*(v - 1)**3*(3*v - 1)
Let t(r) be the third derivative of -r**6/280 + r**5/140 + 9*r**4/56 - 9*r**3/14 + 205*r**2. Find s such that t(s) = 0.
-3, 1, 3
Let a = -6302 + 6302. Solve 12/7*g**4 + a + 0*g + 16/7*g**2 - 32/7*g**3 = 0.
0, 2/3, 2
Let b(l) be the third derivative of -l**5 + 23*l**4/6 - 16*l**3/3 + 12*l**2. Let x(r) = -20*r**2 + 31*r - 11. Let w(n) = 6*b(n) - 17*x(n). Factor w(j).
-5*(j - 1)*(4*j - 1)
Let i(n) be the third derivative of 0 + 25/24*n**6 + 0*n - 5/2*n**5 - 20/3*n**3 - 15/2*n**4 - 9*n**2. Factor i(l).
5*(l - 2)*(5*l + 2)**2
Let c(i) be the second derivative of 17*i**5/5 + 41*i**4/2 + 65*i**3/3 + 6*i**2 + 35*i. Factor c(x).
2*(x + 3)*(2*x + 1)*(17*x + 2)
Let g(b) be the first derivative of 2*b**6 - 44*b**5/5 - 42*b**4 - 16*b**3/3 + 48*b**2 + 383. Suppose g(z) = 0. What is z?
-2, -1, 0, 2/3, 6
Suppose -l - 5*d + 6*d + 2 = 0, -l = 2*d - 2. Solve -14*u**l - u**2 + 5*u**3 + 5*u**5 - 10*u - 9*u**4 + 24*u**4 = 0.
-2, -1, 0, 1
Let k be (120/(-140))/(33/(-35)). Suppose k*a - 4/11 + 14/11*a**2 = 0. What is a?
-1, 2/7
Let j(t) be the third derivative of 1/540*t**6 - 1/108*t**4 + 0*t**3 + 0 - 20*t**2 + 0*t + 0*t**5. Factor j(n).
2*n*(n - 1)*(n + 1)/9
Let n(s) = s**2 - s - 1. Let h(a) = -15*a - 3. Let y(u) = h(u) - 3*n(u). Determine f so that y(f) = 0.
-4, 0
Let k = -31 + 27. Let n(l) = -2*l**2 + 2*l + 2. Let z(d) = -d - 1. Let o(s) = k*z(s) - 2*n(s). Factor o(y).
4*y**2
Let p be 7 - (0 - (-133)/28). Let u(t) be the first derivative of 2 - p*t**2 - 5/2*t**3 + 3*t. Find b such that u(b) = 0.
-1, 2/5
Find i such that -14*i**2 + 0*i + 0 - 2/7*i**3 = 0.
-49, 0
Let -17*q**2 - 1210*q + 2483*q - 130 - 1478*q - 5*q**3 - 84*q**2 + 21*q**2 = 0. What is q?
-13, -2, -1
Solve 172/17*l - 2/17*l**2 - 10 = 0.
1, 85
Let h(i) = -100*i**3 - 210*i**2 - 45*i + 400. Let t(w) = -9*w**3 - 19*w**2 - 4*w + 36. Let d(u) = -4*h(u) + 45*t(u). Solve d(p) = 0 for p.
-2, 1
Let o(y) = -3*y**2 + 40*y - 10. Let j(h) = -3*h**2 + 39*h - 12. Let a(c) = -5*j(c) + 6*o(c). Factor a(m).
-3*m*(m - 15)
Let v be (-8)/(-96) + (740/336 - 2). Let o(x) be the first derivative of 8/7*x - 4/21*x**3 + v*x**2 - 4. Find p, given that o(p) = 0.
-1, 2
Suppose 0 = 4*y + 4*j - 20, -7*y + 4*j - 20 = -2*y. Let x(r) be the second derivative of y - 3/80*r**5 + 0*r**2 + 1/8*r**3 + 0*r**4 - 12*r. Solve x(w) = 0.
-1, 0, 1
Factor -317 - 19*o**2 - 75*o**3 - 196*o**2 + 585 + 320*o - 348.
-5*(o + 4)*(3*o - 1)*(5*o - 4)
Factor -1/3*t**3 - 1/9*t**2 - 1/3*t**4 - 1/9*t**5 + 0 + 0*t.
-t**2*(t + 1)**3/9
Let l = 11 - -4. Suppose -2*c - 3 = -l. Factor 5*w**2 + c*w**3 - w**3 - 8*w**2 - 2*w**2.
5*w**2*(w - 1)
Let h(o) be the second derivative of o**4/3 - 20*o**3/3 + 18*o**2 + 58*o. Factor h(s).
4*(s - 9)*(s - 1)
Let f(w) be the third derivative of -13*w**2 + 0*w + 2/9*w**3 + 0 - 1/36*w**4 - 1/30*w**5. Factor f(i).
-2*(i + 1)*(3*i - 2)/3
Let y be 1/6 - (-12)/36. Let r(c) be the second derivative of -c + 2*c**3 + 0 + 1/20*c**5 - y*c**4 - 4*c**2. Factor r(j).
(j - 2)**3
Solve -45/4*j**3 - 1/4*j**5 + 0*j - 4*j**4 + 0 + 81/2*j**2 = 0 for j.
-9, 0, 2
Suppose 3941*x = 3935*x + 30. Suppose -1/3*q**x + 1/3 + 2/3*q**2 - 2/3*q**3 + q - q**4 = 0. What is q?
-1, 1
Suppose 484 = -4914*w + 5035*w. What is y in 1/4*y**3 - 1/4*y**2 + 0 + 0*y + 1/4*y**w - 1/4*y**5 = 0?
-1, 0, 1
Let t(r) = 128*r + 1666. Let i be t(-13). Determine v, given that -2/3*v**i - 8/3 + 10/3*v = 0.
1, 4
Let q be 126/(-18) + 717/99. Let p(m) be the second derivative of q*m**3 - 1/165*m**6 + 0*m**5 + 1/11*m**4 + 3/11*m**2 - 6*m + 0. Factor p(l).
-2*(l - 3)*(l + 1)**3/11
Let p be (20 - 8 - 11) + 1*3. Let b(n) be the third derivative of 1/8*n**p + 0*n + 0 - 1/20*n**5 + n**3 + 4*n**2. Factor b(v).
-3*(v - 2)*(v + 1)
Let d(o) = -3*o**2 - 7*o + 24. Let g be d(-4). Factor -2/7*i**g - 2/7*i + 0 + 2/7*i**3 + 2/7*i**2.
-2*i*(i - 1)**2*(i + 1)/7
Let 17*f + 3*f**2 + 50*f - 38*f + 7*f = 0. Calculate f.
-12, 0
Let g(j) = -8*j**3 + 8*j - 4. Let m(q) = q**4 + 25*q**3 - q**2 - 25*q + 11. Let v(f) = -6*f + 1. Let x be v(2). Let c(l) = x*g(l) - 4*m(l). Factor c(u).
-4*u*(u - 1)*(u + 1)*(u + 3)
Let v be -3 + 3 + -4 - (8 + -14). Let p(o) be the first derivative of 2/15*o**3 + 8 + 1/25*o**5 + 3/20*o**4 + 0*o + 0*o**v. Find a such that p(a) = 0.
-2, -1, 0
Let t = 7/19049 - 3258079/1904900. Let y = -24/25 - t. Factor 3/2*f**4 + 5/2*f**2 + 0 - 1/4*f**5 - y*f - 3*f**3.
-f*(f - 3)*(f - 1)**3/4
Let s(r) be the second derivative of -1/12*r**4 + 0*r**2 + 0*r**5 + 1/90*r**6 + 32*r + 0 + 1/9*r**3. Solve s(x) = 0.
-2, 0, 1
Let 30*m**2 + 120*m - 7*m**2 + 14*m**2 - 44*m**3 - 8*m**2 + 45*m**3 = 0. Calculate m.
-24, -5, 0
Let g(c) be the first derivative of -50 + 45/4*c**4 + 10/3*c**3 - 6*c**5 + 0*c + 0*c**2 - 25/6*c**6. Suppose g(k) = 0. W