 83*a**2. Factor p(w).
-w**3*(w + 1)*(w + 2)/4
Let r(o) be the first derivative of o**7/231 + 4*o**6/165 + o**5/22 + o**4/33 + 2*o + 36. Let i(f) be the first derivative of r(f). Let i(u) = 0. Calculate u.
-2, -1, 0
Let j(m) be the second derivative of -m**4/3 - 4*m**3 + 32*m**2 - 3*m + 47. Factor j(l).
-4*(l - 2)*(l + 8)
Let r = 92701/45 - 10299/5. Suppose -8/9*m**3 - r*m**5 + 4/9*m**2 + 10/9*m + 4/9 - 8/9*m**4 = 0. Calculate m.
-2, -1, 1
Suppose 2*n - 5*y - 122 = -0*n, -5*y - 254 = -4*n. Let r be 1/2*n/55. Solve -3/5*f**2 + 3/5*f**3 + 0*f + 0 + r*f**4 - 3/5*f**5 = 0.
-1, 0, 1
Let r(q) = -q**3 - 9*q - 8. Let z(s) = -s**3 - 2*s**2 - 10*s - 8. Let d(c) = -4*r(c) + 6*z(c). Determine l, given that d(l) = 0.
-2
Let x be ((-1)/6)/((-28)/(-56)) + (-4)/(-12). Suppose 9/5*j**4 + 24/5*j + x + 6/5*j**3 - 3/5*j**5 - 36/5*j**2 = 0. Calculate j.
-2, 0, 1, 2
Suppose 1 = -2*d + 5. Let m be 6*5/15 - d. Determine h, given that 2/9*h**2 - 2/9 + m*h = 0.
-1, 1
Let c(n) = n**2 - 86*n - 3190. Let d be c(-28). Suppose 64/3*s**3 - 12*s + 12 - 64/3*s**d = 0. Calculate s.
-3/4, 3/4, 1
Let o(c) be the third derivative of -c**7/168 + 37*c**6/120 - 71*c**5/16 - 75*c**4/16 + 258*c**2. Factor o(a).
-a*(a - 15)**2*(5*a + 2)/4
Let -117/2 - 93*v + 100*v**3 + 119/2*v**2 - 8*v**4 = 0. Calculate v.
-3/4, 1, 13
Let x = 11566 - 34697/3. Factor 3*a + 0 + x*a**2.
a*(a + 9)/3
Let s(x) be the second derivative of -x**8/53760 + x**7/2880 - x**6/960 + x**4/3 - x**3/6 + 3*x - 7. Let w(f) be the third derivative of s(f). Factor w(z).
-z*(z - 6)*(z - 1)/8
Let k(v) = v**3 + 4*v**2 + 3*v. Let n = 37 - 39. Let o be k(n). Solve 110*c**o + 45 + 15*c + 140*c + 40*c**3 + 5*c**4 - 35*c = 0.
-3, -1
Let j(u) be the third derivative of -5/3*u**4 + 0*u - 39/20*u**5 + 8*u**2 + 0 - 2/3*u**3 - 27/40*u**6. Determine m, given that j(m) = 0.
-1, -2/9
Let k be 18/270 + 8/60. Determine w so that -2/5*w + 1/5*w**2 + k = 0.
1
Solve 216*w**2 + 214*w**2 - 431*w**2 - 7 - 8*w = 0.
-7, -1
Let s(t) be the third derivative of t**5/15 - 83*t**4/6 + 129*t**2. Let s(y) = 0. What is y?
0, 83
Factor 0*f**2 + 1/3*f + 0 - 1/3*f**3.
-f*(f - 1)*(f + 1)/3
Let m be ((-28)/3 + 11/33)/(75/(-40)). Factor 3/5*p**4 - m*p**3 + 36/5 + 69/5*p**2 - 84/5*p.
3*(p - 3)*(p - 2)**2*(p - 1)/5
Let w(k) = 4*k**3 + k**2 + k + 1. Let p(t) = 19*t**3 + 6566*t**2 + 307376*t - 88364. Let v(i) = -p(i) - 4*w(i). Factor v(x).
-5*(x + 94)**2*(7*x - 2)
Let a(o) be the third derivative of o**6/320 - o**4/64 - 50*o**2. Determine p, given that a(p) = 0.
-1, 0, 1
Let l(m) be the second derivative of 23*m + 0 - 1/11*m**2 + 1/66*m**3 + 1/132*m**4. Factor l(h).
(h - 1)*(h + 2)/11
Let g be (-1)/(6/(-21) - 2/42). Let h be 0 + g + (-16)/6. Factor 1/6*j**2 - h*j + 0.
j*(j - 2)/6
Let z be (-92)/120 + 49/42. Suppose -6/5*m + z*m**2 + 4/5 = 0. What is m?
1, 2
Let j(o) be the first derivative of 13/3*o**3 + 7/6*o**6 + 0*o + 23/5*o**5 + 27/4*o**4 + o**2 + 18. Factor j(k).
k*(k + 1)**3*(7*k + 2)
Suppose -d + 4 = -3*b - 14, -4*d - 3*b - 3 = 0. Suppose -2*a**3 - 4*a**d + 3*a - 6*a - 6*a**2 + 3*a**3 = 0. Calculate a.
-1, 0
Let c(i) = 179*i + 179. Let j be c(-1). Factor j - 2/7*q**2 - 2/7*q.
-2*q*(q + 1)/7
Let u(k) be the second derivative of -1/90*k**6 - 8*k - 1/10*k**5 + 5/3*k**3 + 0*k**2 - 1/3*k**4 + 0. Let r(h) be the second derivative of u(h). Factor r(n).
-4*(n + 1)*(n + 2)
Let m(q) be the first derivative of 2/15*q**3 - 8/5*q - 18 + 3/5*q**2. Find r such that m(r) = 0.
-4, 1
Let p(u) be the third derivative of 1/90*u**5 + 1/9*u**3 - 17*u**2 + 1/18*u**4 + 0*u + 0. What is h in p(h) = 0?
-1
Let m(r) be the first derivative of -1/14*r**4 + 0*r**3 + 0*r + 1/7*r**2 + 14. Factor m(n).
-2*n*(n - 1)*(n + 1)/7
Let 90*f - 3 - 483*f**2 - 2 + 78*f**2 + 0 = 0. What is f?
1/9
Let f(l) = l**3 - 19*l**2 + 31*l - 232. Let x be f(18). Factor -1/7*j**x + 6/7*j - 5/7.
-(j - 5)*(j - 1)/7
Let l(n) = 9*n**3 + 72*n**2 + 235*n - 805. Let j(g) = 14*g**3 + 108*g**2 + 352*g - 1208. Let z(i) = 5*j(i) - 8*l(i). Factor z(x).
-2*(x - 2)*(x + 10)**2
Factor 0*s**2 + 4*s**2 - 114*s - 3*s**2 + 20 + 21*s**2.
2*(s - 5)*(11*s - 2)
Solve 31104/7*g - 746496/7 + 2/7*g**3 - 432/7*g**2 = 0.
72
Let c(w) be the third derivative of 5*w**8/336 - w**7/7 + w**6/3 - 2*w**2 + 133*w. Factor c(v).
5*v**3*(v - 4)*(v - 2)
Let c(x) be the second derivative of -65*x**4/6 + x**3 + 2*x**2 - x + 7. Determine m, given that c(m) = 0.
-2/13, 1/5
Let k(f) = 8*f**3 + 25*f**2 - 35*f - 17. Let q(t) = -t**3 - 2*t**2 + 3*t - 1. Let p(l) = -5*k(l) - 35*q(l). Factor p(x).
-5*(x - 2)*(x + 1)*(x + 12)
Let z(f) be the second derivative of -1/2*f**2 - 15*f - 13/36*f**3 - 1/18*f**4 + 1/40*f**5 + 0. Determine w so that z(w) = 0.
-1, -2/3, 3
Let -24/7*z**3 - 21*z - 18/7 - 309/7*z**2 + 48/7*z**4 = 0. What is z?
-2, -1/4, 3
Let x(u) = -5*u**3 + 15*u**2 + 28*u - 42. Let q(r) = -35*r**3 + 105*r**2 + 195*r - 295. Let w(s) = 2*q(s) - 15*x(s). Factor w(t).
5*(t - 4)*(t - 1)*(t + 2)
Let k(x) be the second derivative of -1/20*x**5 + x**2 + 1/8*x**4 + 0*x**3 + 0 + 4*x. Let h(i) be the first derivative of k(i). Factor h(c).
-3*c*(c - 1)
Suppose 18*u**2 + 15*u**2 - 35*u**2 + 908*u - 260*u - 52488 = 0. Calculate u.
162
Let i = 3052/1135 - -5/454. Let n = 69/20 - i. Factor 0 - 3/2*d + n*d**3 + 3/4*d**2.
3*d*(d - 1)*(d + 2)/4
Let i = -875/6 - -146. Let s(q) be the second derivative of 0*q**2 - 4*q + 1/20*q**5 + 0*q**3 + 0 - i*q**4. Factor s(v).
v**2*(v - 2)
Factor -1/7*i**2 + i - 6/7.
-(i - 6)*(i - 1)/7
Let z be 19 + 2/6*3. Let v = 23 - z. Factor 42*i**2 + 36*i**v + 38*i - 19*i - 32 + 94*i**2 + 93*i.
4*(i + 2)**2*(9*i - 2)
Let u(w) be the first derivative of w**4/4 - 5*w**3/3 - 11*w**2 - 16*w - 174. Let u(n) = 0. What is n?
-2, -1, 8
Let u = 820327/120 - 6836. Let f(m) be the third derivative of 0*m + 5/16*m**4 + 1/240*m**6 - u*m**5 - 3/4*m**3 + 0 - 5*m**2. Factor f(w).
(w - 3)**2*(w - 1)/2
Suppose 22/7*z - 2*z**2 - 8/7 = 0. What is z?
4/7, 1
Let z(k) be the third derivative of -k**8/560 - 3*k**7/175 - 3*k**6/50 - k**5/10 - 3*k**4/40 - 97*k**2. Factor z(h).
-3*h*(h + 1)**3*(h + 3)/5
Let q(y) be the first derivative of -2*y**6/21 + 2*y**5/5 - 20*y**3/21 + 2*y**2/7 + 6*y/7 - 84. Solve q(o) = 0.
-1, -1/2, 1, 3
Let c(f) be the second derivative of -f**7/315 - f**6/180 + f**5/90 + f**4/36 - f**2 - 4*f. Let b(a) be the first derivative of c(a). Factor b(x).
-2*x*(x - 1)*(x + 1)**2/3
Let a(t) = -t**3 - 6*t**2 + 6. Let o be a(-6). Suppose 20*h**2 + 12*h**4 + 5*h**3 + 4*h**5 + o*h + 4*h**5 - 6*h**5 + 19*h**3 = 0. What is h?
-3, -1, 0
Let k(g) be the second derivative of -2/105*g**6 + 1/7*g**5 - 8/21*g**3 + 22*g + 16/7*g**2 + 0 - 2/7*g**4. Suppose k(m) = 0. Calculate m.
-1, 2
Let q be 256/(-576) + (-1)/((-18)/62). Factor -2/15*p**4 + 0 - 2/3*p**2 + 8/15*p**q + 4/15*p.
-2*p*(p - 2)*(p - 1)**2/15
Let t(h) be the third derivative of -3*h**7/56 + 5*h**6/12 - 7*h**5/6 + 5*h**4/3 - 29*h**3/6 + 25*h**2. Let j(z) be the first derivative of t(z). Factor j(g).
-5*(g - 2)*(3*g - 2)**2
Let f(i) be the third derivative of -i**7/105 + 17*i**6/240 - i**5/5 + 13*i**4/48 - i**3/6 + 16*i**2 - 3*i. Let f(x) = 0. Calculate x.
1/4, 1, 2
Let v(q) be the second derivative of q**10/6048 - q**9/1008 + q**7/126 - 7*q**4/6 + 2*q. Let m(s) be the third derivative of v(s). Solve m(r) = 0 for r.
-1, 0, 2
Let i(n) be the first derivative of n**7/21 - 2*n**6/15 + n**5/10 + 19*n - 50. Let u(s) be the first derivative of i(s). Determine k so that u(k) = 0.
0, 1
Solve 24/7*k**2 - 2/7*k**3 + 0 + 0*k = 0.
0, 12
Let q = 48 + -45. Suppose 3*b + 3 = -0*p - 3*p, -q*p - 3 = 2*b. Factor -4/7*a**3 - 2/7*a**2 + b + 0*a - 2/7*a**4.
-2*a**2*(a + 1)**2/7
Let o(y) = 5*y**4 + 14*y**3 + 16*y**2 + 1. Let j(k) = -k**4 + 2*k**3 - 1. Let h(r) = -j(r) - o(r). Factor h(c).
-4*c**2*(c + 2)**2
Let z(r) = r**2 - 20*r - 2. Let v be z(21). Let m = -15 + v. Factor -1/6*a**3 + 1/6*a**2 + 0 + 1/6*a - 1/6*a**m.
-a*(a - 1)*(a + 1)**2/6
Let t = -119 - -121. Let g(a) be the second derivative of 5/6*a**3 + 3/20*a**5 + 0 - 7/12*a**4 - 6*a - 1/2*a**t. Factor g(u).
(u - 1)**2*(3*u - 1)
Let d(n) = 2*n**3 + 2*n**2 - 4*n. Let f(m) = -11*m**3 - 12*m**2 + 23*m. Let l = -28 - -62. Let u(t) = l*d(t) + 6*f(t). Let u(h) = 0. What is h?
0, 1
Suppose 139 - 161 = -11*o. Factor 5*r**4 + 0 + 0*r - 1/3*r**5 + 49/3*r**o - 21*r**3.
-r**2*(r - 7)**2*(r - 1