+ 2)
Factor -403*i**4 + 5 + 4*i + 807*i**4 - 2*i**3 - 6*i**2 - 2*i**3 - 403*i**4.
(i - 5)*(i - 1)*(i + 1)**2
Let y(l) = -4*l**2 + 10*l. Let w(m) = -3*m**2 + 9*m - 1. Let c(k) = k**2 + 8*k + 2. Let j be c(-7). Let r(t) = j*y(t) + 6*w(t). Factor r(s).
2*(s - 1)*(s + 3)
Suppose 5*u + 3*c - 19 = 0, -2*c - 14 = -5*u + 3*u. Determine w, given that 2*w**2 - 13*w**3 - 9*w**2 + u*w**3 - 2*w - 3*w**4 = 0.
-1, -2/3, 0
Let s(c) be the first derivative of -c**5/5 - 25*c**4/16 + 11*c**3/6 + 7*c**2/8 + 71. Factor s(k).
-k*(k - 1)*(k + 7)*(4*k + 1)/4
Let d(o) be the second derivative of -o**4/96 + o**3/2 - 23*o**2/16 - 204*o - 2. Determine m, given that d(m) = 0.
1, 23
Let p(l) be the first derivative of l**3/12 + 9*l**2/8 + 26. Factor p(u).
u*(u + 9)/4
Let u be ((-10)/6 + 0)/((-330)/(-36) - 10). Find m, given that 6/5*m + 0 - 9/5*m**u + 9/5*m**4 - 3/5*m**3 - 3/5*m**5 = 0.
-1, 0, 1, 2
Let k = -18 - -20. Factor 5*o**k - 11*o**2 + 3*o**5 + 0*o**3 - 9*o**3.
3*o**2*(o - 2)*(o + 1)**2
Let k(x) be the first derivative of -3*x**5/5 - 3*x**4/4 + 3*x**3 + 15*x**2/2 + 6*x + 73. Solve k(m) = 0.
-1, 2
Let i be (3 - 3/6)/(3/18). Factor 20 + 3*w + 13*w - 19*w**2 + i*w**2.
-4*(w - 5)*(w + 1)
Let l = -2 + -1. Let r(w) = w**2 + w**3 - 6 - 10 + 13 - 2*w - 2*w**2. Let b(z) = -z**3 + z + 2. Let g(p) = l*b(p) - 2*r(p). Factor g(s).
s*(s + 1)**2
Let z be 174/12 - 1/2. Let f be z/3 + (-5)/(-15). Find i such that 2*i**5 + 2*i**5 - 5*i**5 + 4*i**4 + 2*i**2 - f*i**3 = 0.
0, 1, 2
Let 0*c + 0*c**3 - 60/7*c**2 + 6/7*c**4 + 54/7 = 0. What is c?
-3, -1, 1, 3
Factor -2/3*h**4 + 0*h**2 + 0 + 0*h - 14/3*h**3.
-2*h**3*(h + 7)/3
Let x(r) be the first derivative of 5/2*r - 5/2*r**2 - 1 + 5/6*r**3. Find v, given that x(v) = 0.
1
Suppose 36*z - 41*z - 5*o + 15 = 0, 10*z = -3*o + 51. Let 3/7*h**2 - z*h + 21 = 0. Calculate h.
7
Suppose -2*n = -f - 0 - 3, -f = -5*n + 3. Let m(b) be the third derivative of -1/5*b**3 + 5*b**2 + n*b + 0 + 13/60*b**4 - 2/75*b**5. Factor m(y).
-2*(y - 3)*(4*y - 1)/5
Let w(u) = 3*u**2 + 19*u. Let n(k) = 2*k**2 + 18*k. Let f(i) = 5*n(i) - 4*w(i). Factor f(b).
-2*b*(b - 7)
Let f = -1/411 + 6725/4932. Let w = f + 5/36. Factor w - 1/2*q**2 + q.
-(q - 3)*(q + 1)/2
Solve 2/9*w**2 - 2 + 16/9*w = 0 for w.
-9, 1
Determine h, given that 0*h**2 - 3*h**5 + 5*h**2 - 4*h**2 - 4*h**2 - 9*h**3 - 9*h**4 = 0.
-1, 0
Let p be 6/(-18) - (-20)/54. Let v(w) be the second derivative of 0 + 0*w**2 + 1/90*w**5 - 1/27*w**4 + 3*w + p*w**3. Factor v(k).
2*k*(k - 1)**2/9
Let i(r) = -26*r + 1355. Let a be i(52). Let -3/4*v**a - 1/4*v**4 + 1/4*v**5 + 1/2*v + 0 + 1/4*v**2 = 0. Calculate v.
-1, 0, 1, 2
Let x(g) be the second derivative of g**7/147 - 4*g**6/105 + 2*g**5/35 + g**4/21 - 5*g**3/21 + 2*g**2/7 - 3*g + 27. Factor x(n).
2*(n - 2)*(n - 1)**3*(n + 1)/7
Suppose 4*g - 33 = -4*a + 11, -3*g - 5*a = -43. Let q be (2/g)/(-1) + 1. Factor -2/3*b**2 + 0 - q*b.
-2*b*(b + 1)/3
Let h be ((-6)/(-12))/(3/12). Let o(c) be the first derivative of 5 + 0*c**3 + 1/8*c**4 - 1/4*c**h + 0*c. Solve o(y) = 0.
-1, 0, 1
Let x(t) be the first derivative of t**4/18 - 10*t**3/9 + 16*t**2/3 - 88*t/9 - 191. Let x(y) = 0. Calculate y.
2, 11
Let n(p) be the first derivative of -2*p**5/35 + 17*p**4/14 - 60*p**3/7 + 108*p**2/7 + 432*p/7 + 81. Let n(l) = 0. Calculate l.
-1, 6
Let m(f) be the second derivative of -f + 2/5*f**5 + 8*f**3 - 8*f**2 - 3*f**4 - 7. Factor m(d).
4*(d - 2)**2*(2*d - 1)
Let w = 16058 + -16054. Let 0 + 58/25*q**3 - 48/25*q**2 - 18/25*q**w + 8/25*q = 0. Calculate q.
0, 2/9, 1, 2
Let i be 1/(3/52) - 5/15. Suppose -5*m + 2*u = 5*u, -4*m + u + i = 0. What is w in 3 - 3/4*w**m + 3*w - 3/4*w**2 = 0?
-2, -1, 2
Let s(t) be the third derivative of 147*t**6/160 - 35*t**5/16 + 11*t**4/12 - t**3/6 - 80*t**2 + 3*t. Suppose s(l) = 0. What is l?
2/21, 1
Suppose 60 = -37*d + 42*d. Determine s so that -8*s**3 - d*s**2 + 12*s + 8*s**3 + 3*s**3 = 0.
0, 2
Let d(u) be the first derivative of -1/540*u**6 - 1/108*u**4 + 0*u**3 + 0*u - 5*u**2 + 12 - 1/135*u**5. Let x(f) be the second derivative of d(f). Factor x(i).
-2*i*(i + 1)**2/9
Let x(a) be the second derivative of a**5/10 + 5*a**4/24 + a**3/12 + 289*a. Let x(o) = 0. Calculate o.
-1, -1/4, 0
Suppose -18*q + 25 + 11 = 0. Factor 0*u**q + u - 1/4*u**4 + 0 - 3/4*u**3.
-u*(u - 1)*(u + 2)**2/4
Suppose -8/11*t - 2/11*t**2 - 6/11 = 0. Calculate t.
-3, -1
Let n(v) = v**2 - 8*v - 17. Let f be n(-2). Let u(h) be the third derivative of 0*h - 1/240*h**5 - 2*h**2 - 1/12*h**f + 0 + 1/32*h**4. Let u(w) = 0. What is w?
1, 2
Let f(b) = 15*b**4 + 10*b**3 + 10*b**2 - 10*b + 5. Let r be ((-2)/6)/(4/(-12)). Let q(p) = p**2. Let s(j) = r*f(j) - 30*q(j). Determine i, given that s(i) = 0.
-1, 1/3, 1
Let d be (-33)/77*(-56)/48. Factor -3/2*h + 1/2 + 3/2*h**2 - d*h**3.
-(h - 1)**3/2
Let v(l) = l + 10. Let g be v(-8). Factor -k**4 + 7*k**3 + 2*k**4 + k**5 + 4 - 6*k**4 + k**g - 8*k.
(k - 2)**2*(k - 1)**2*(k + 1)
Let n(a) be the second derivative of -a**6/15 - 3*a**5/10 + 4*a**3/3 - 685*a. Factor n(m).
-2*m*(m - 1)*(m + 2)**2
Factor -4/5*i + 0 - 6/5*i**2 - 2/5*i**3.
-2*i*(i + 1)*(i + 2)/5
Factor 5/4 + 3/8*r - 1/8*r**2.
-(r - 5)*(r + 2)/8
Let s = 6549/12274 + -3/722. Let a = s - 1/34. What is d in -2/3*d**2 + 1/3 - 5/6*d + a*d**3 = 0?
-1, 1/3, 2
Let h(r) be the third derivative of r**5/12 + 35*r**4/24 + 25*r**3/3 + 164*r**2. Factor h(m).
5*(m + 2)*(m + 5)
Solve 862*s**2 + 5*s**3 - 24*s - 952*s**2 + 184*s = 0 for s.
0, 2, 16
Let h(g) be the first derivative of -5*g**4/3 + 25*g**3/2 + 10*g**2 + 23*g - 17. Let z(q) be the first derivative of h(q). Let z(y) = 0. What is y?
-1/4, 4
Suppose -114*y + 172 + 34 = -11*y. Suppose 4/5*n + 4 - 16/5*n**y = 0. What is n?
-1, 5/4
Let n be (-84)/(-54) - 16/(-36). Factor 1/3*r**n + 0 + 2/3*r.
r*(r + 2)/3
Let x(a) be the second derivative of 0 - 2/315*a**6 + 1/210*a**5 + 0*a**4 + 19*a + 1/441*a**7 + 0*a**3 + 0*a**2. Find k such that x(k) = 0.
0, 1
Factor 0*k + 0 - 27/7*k**2 + 15/7*k**4 + 3/7*k**5 + 9/7*k**3.
3*k**2*(k - 1)*(k + 3)**2/7
Let r(z) = -10*z - 19. Let o be r(-9). Let o + 5*c**2 + 5*c**3 - 71 = 0. What is c?
-1, 0
Let w(v) be the first derivative of v**8/2520 - v**6/540 - 10*v**3/3 - 18. Let l(f) be the third derivative of w(f). Let l(i) = 0. What is i?
-1, 0, 1
Let u(b) be the second derivative of -9*b**5/40 - 5*b**4/8 - b**3/2 + 32*b + 2. Solve u(x) = 0 for x.
-1, -2/3, 0
Find v, given that -84*v + 143*v + 18*v**2 - 140 + 5*v**2 + 281*v + 2*v**2 = 0.
-14, 2/5
Suppose -3*c + 2*c = 0. Suppose -3*x - 2*x + 15 = c. Let m(o) = -2*o**2 - 8*o. Let t(u) = -u**2 - 7*u. Let g(a) = x*m(a) - 4*t(a). Solve g(q) = 0.
0, 2
Let g be -15*1 - (-2209)/141. Factor 1/3*p + 1/3*p**3 + 0 - g*p**2.
p*(p - 1)**2/3
Let x(i) be the first derivative of -i**3/6 + 15*i**2/4 - 7*i - 105. Suppose x(v) = 0. What is v?
1, 14
Let u be 2 + 0 + -4 + 23 + -16. Factor 0*f**4 - 3/8*f + 0*f**2 + 3/4*f**3 + 0 - 3/8*f**u.
-3*f*(f - 1)**2*(f + 1)**2/8
Let x be (-1083)/(-7) - (-14)/49. Let q be 2/(-5) + 527/x. Factor 0*b**2 + 4/5 + 2/5*b**q - 6/5*b.
2*(b - 1)**2*(b + 2)/5
Factor 5*y**2 - 5/4*y - 25/4.
5*(y + 1)*(4*y - 5)/4
Let c(g) = -4*g**2 - 8*g - 10. Let k be c(-3). Let x be -2 + 4/2 + (k - -22). Factor -5/2*y**4 + 0*y + x*y**2 + 0 + y**3.
-y**3*(5*y - 2)/2
Suppose -112 = -6*m - m. Factor 52*b + 2 - 8*b**2 + 6 + 87*b**2 + 68*b**3 + 17*b**2 + m*b**4.
4*(b + 1)**2*(b + 2)*(4*b + 1)
Factor 0 + 18*v**2 - 33/2*v**3 + 0*v - 3/2*v**4.
-3*v**2*(v - 1)*(v + 12)/2
Let m(a) = -a**3 - 20*a**2 - 18*a + 19. Let r be m(-19). Suppose 5*u**4 + u**4 - 3*u**2 - 5*u**4 - 2*u + r*u**4 = 0. Calculate u.
-1, 0, 2
Factor 0 - 7/3*u**3 - 1/3*u**4 + 16/3*u + 10/3*u**2.
-u*(u - 2)*(u + 1)*(u + 8)/3
Let r(f) be the third derivative of -2*f**7/735 - 3*f**6/70 + 2*f**5/21 + 104*f**2. Factor r(w).
-4*w**2*(w - 1)*(w + 10)/7
Let m(i) be the first derivative of 0*i - 3 + 0*i**2 + 2/55*i**5 + 4/33*i**3 - 3/22*i**4. Find z such that m(z) = 0.
0, 1, 2
Let q = 111 - 110. Let v be (6 + q + -10)*2/(-24). Solve -3/4*a + 1/2 + v*a**2 = 0 for a.
1, 2
Let t = -7063 + 35317/5. Factor t*j**4 - 8/5*j**2 - 2/5*j**3 + 8/5*j + 0.
2*j*(j - 2)*(j - 1)*(j + 2)/5
Let y(u) be the first derivative of 2*u**6/15 + 3*u**5/5 - u**4/3 - 2*u**3 + 43*u - 40. Let z(q) be the first derivative of y(q). Let z(p) = 0. Calculate p.
-3, -1, 0, 1
Let f(o) = -o**5 + o**4 + o