. Factor l(z).
-4*(z - 2)*(z + 1)*(z + 2)
Let a(s) = 113*s - 449. Let p be a(4). Factor -9/2*f + 3/2*f**2 + p.
3*(f - 2)*(f - 1)/2
Factor 6240*c**2 + 228 + 6400*c**3 + 173 + 204 + 1280*c**4 - 4400*c.
5*(4*c - 1)**2*(4*c + 11)**2
Let f(t) be the third derivative of -t**7/210 - t**6/60 + 7*t**5/60 + 5*t**4/6 + 2*t**3 + 43*t**2. Factor f(j).
-(j - 3)*(j + 1)*(j + 2)**2
Let k(i) = -i**4 + i**3 - i. Let d(w) be the second derivative of -w**6/10 - 9*w**5/20 - 4*w**4/3 - 3*w**3/2 - 9*w. Let v(s) = 2*d(s) - 2*k(s). Factor v(x).
-4*x*(x + 1)*(x + 2)**2
Suppose 0 = -934*v + 958*v. Factor 2/9*n**3 + 0 + 4/9*n**2 + v*n.
2*n**2*(n + 2)/9
Let u(a) be the second derivative of 0 - 1/12*a**4 - 5/6*a**3 + 1/20*a**5 - 4*a - 3/2*a**2. Factor u(y).
(y - 3)*(y + 1)**2
Let p(q) = q**2 - 15*q + 28. Let h be p(12). Let m be (-10)/12*h/5. Suppose -10/3*u**4 + 10/3*u**2 + 0 + 4/3*u**3 - m*u = 0. What is u?
-1, 0, 2/5, 1
Let i(h) be the third derivative of h**6/1260 - h**5/140 + h**4/42 - 3*h**3/2 - 11*h**2. Let r(w) be the first derivative of i(w). Solve r(z) = 0.
1, 2
Factor -1/7*f**2 - 16/7 + 8/7*f.
-(f - 4)**2/7
Let d(q) be the second derivative of 3*q**7/140 - q**6/9 + q**5/15 - q**3/2 - 3*q. Let j(o) be the second derivative of d(o). Let j(h) = 0. What is h?
0, 2/9, 2
Suppose -q + 15 = 4. Factor 19*k + 2*k**3 + 11*k - 4*k**2 + 18 + 7*k**2 + q*k**2.
2*(k + 1)*(k + 3)**2
Let l be (-1)/4 + (-18712)/(-96). Let m = l + -194. Factor 2/3*z**4 - 2/3*z**2 - 2/3*z + 0 + m*z**3.
2*z*(z - 1)*(z + 1)**2/3
Let g(f) be the second derivative of -f**8/1848 + 2*f**7/1155 - f**5/165 + f**4/132 - 25*f**2/2 + 9*f. Let t(q) be the first derivative of g(q). Factor t(m).
-2*m*(m - 1)**3*(m + 1)/11
Suppose b + 8 = -4*d, -93*d = -2*b - 97*d - 4. Let r(t) be the third derivative of 1/4*t**b + 0*t - 9*t**2 + 2/3*t**3 + 0 + 1/30*t**5. Factor r(z).
2*(z + 1)*(z + 2)
Find x, given that -5000/3 + 5200/3*x + 2/3*x**3 - 202/3*x**2 = 0.
1, 50
Let b(y) be the third derivative of 0 + 0*y + 2/15*y**4 - 16/15*y**3 - 1/150*y**5 + 31*y**2. Factor b(n).
-2*(n - 4)**2/5
Let a(x) = -9*x - 13. Let i be a(-2). Determine o so that o**2 + 2*o - 27*o**3 - o**i - 4*o - 14*o**2 - 6*o**5 - 23*o**4 = 0.
-1, -2/7, 0
Let y(u) be the first derivative of -2*u**5/45 + 2*u**3/9 - 2*u**2/9 + 66. Let y(c) = 0. Calculate c.
-2, 0, 1
Let l be -4*6/12 - 121/(-290). Let h = 1/58 - l. Find t such that -4/5*t**3 + 2*t**4 - 2/5 - 8/5*t**2 + h*t - 4/5*t**5 = 0.
-1, 1/2, 1
Let m(f) be the second derivative of f**4/30 + 4*f**3/15 - f**2 + 124*f + 1. Factor m(g).
2*(g - 1)*(g + 5)/5
Let l(t) = -t + 5. Let o be l(2). Find n such that 52*n**4 + 3*n**5 + 4*n**5 + 44*n**2 + 67*n**o + 8*n + 9*n**3 + 5*n**5 = 0.
-2, -1, -1/3, 0
Let g = -110 + 110. Suppose 13*m - 12*m - 2 = g. Let 0*l + 0 + 1/2*l**m = 0. Calculate l.
0
Suppose m = -3*t + 60, 5*t = 2*t + 12. Let y be (-11)/(-44) + 4/m. Solve 0 + y*s**4 - 1/3*s - s**3 + s**2 = 0.
0, 1
Suppose 2*v**5 + 33*v**3 - 8*v**4 - 5*v**5 + 20*v**4 - 84*v + 18*v**2 - 72 - 12*v**4 = 0. Calculate v.
-2, -1, 2, 3
Let o be 2/(-5) + 135/50*2. Factor 6*w**5 + 4*w**3 - 3*w**3 + 3*w**3 - 10*w**o.
-4*w**3*(w - 1)*(w + 1)
Let u(y) be the second derivative of y**6/6 + y**5 + 5*y**4/6 - 10*y**3/3 - 15*y**2/2 + 4*y - 1. Suppose u(l) = 0. What is l?
-3, -1, 1
Let s(r) be the second derivative of r**7/252 + r**6/180 - r**5/40 - r**4/72 + r**3/18 + 49*r. Factor s(m).
m*(m - 1)**2*(m + 1)*(m + 2)/6
What is c in 2/5*c**5 - 128/5*c**2 + 0*c + 0 + 32*c**3 - 34/5*c**4 = 0?
0, 1, 8
Factor 69*u**2 - 1587/2*u + 0 - 3/2*u**3.
-3*u*(u - 23)**2/2
Let c = 2 - -6. Suppose 4*k - 4*m - 36 = 0, c = -5*m + 3. Factor -4*o**3 - 3*o**2 - 6*o + 15*o**3 - k*o**3.
3*o*(o - 2)*(o + 1)
Factor 1/2*u**4 + 7/2*u + 5/2*u**2 - 7/2*u**3 - 3.
(u - 6)*(u - 1)**2*(u + 1)/2
Let l(t) be the first derivative of 9/2*t**2 + 5 + 27*t + 3/4*t**4 - 5*t**3. Find c such that l(c) = 0.
-1, 3
Let m = 8 + -5. Factor -5*i**2 - 5*i + 15*i**2 - 1034*i**m + 1029*i**3.
-5*i*(i - 1)**2
Suppose -21 + 4 = 3*t - 5*h, 5*t - 25 = -5*h. Let a(r) be the first derivative of 1/13*r**2 + 0*r - 2/39*r**3 - t. Factor a(s).
-2*s*(s - 1)/13
Suppose -1 = 5*l - 16. Let p be -3*(1/l - 3). Suppose -p*f - 4 - 78*f**3 + 2*f**4 - 92*f**2 + 20 - 20*f**4 = 0. Calculate f.
-2, -2/3, 1/3
Find c such that -4*c**5 - 16*c**4 - 707*c**2 + 15*c**3 + 180*c + 72 + c**3 + 843*c**2 = 0.
-3, -2, -1, 3
Let n(u) be the third derivative of -49*u**6/360 + 77*u**5/45 + 53*u**4/6 + 16*u**3 + 11*u**2. Solve n(d) = 0 for d.
-6/7, 8
Let h(v) be the first derivative of -125*v**3/3 - 25*v**2 - 5*v + 56. Factor h(m).
-5*(5*m + 1)**2
Let i = 4939 - 4936. Let m be (-4)/24 + 65/12. Factor -3*u - m*u**i + 0 + 12*u**2.
-3*u*(u - 2)*(7*u - 2)/4
Let i(u) = -u**2 - 4*u - 3. Let d = 3 + 1. Let w(t) = 15 + 20*t + 7*t**2 - 3*t**2 + t**2. Let r(p) = d*w(p) + 22*i(p). Determine b so that r(b) = 0.
-3, -1
Factor -5*o**2 + 1/3*o**3 + 28/3 + 4*o.
(o - 14)*(o - 2)*(o + 1)/3
Suppose -o = 6*x - 2*x + 41, 0 = -3*o + 4*x - 43. Let z = o - -23. Find c, given that 0*c - 2*c**z + 2 + c**3 + 3*c - 5*c + c = 0.
-1, 1, 2
Let t(k) = -4*k**2 - 10*k + 26. Let d(a) = 9*a**2 + 20*a - 51. Let b(z) = 2*d(z) + 5*t(z). Factor b(g).
-2*(g - 2)*(g + 7)
Factor -4*a + 315 - 318 - 18*a**2 + 21*a + 4*a.
-3*(a - 1)*(6*a - 1)
Let h(d) be the third derivative of -d**5/15 - 17*d**4/3 - 578*d**3/3 + 2*d**2 + 24. Determine c, given that h(c) = 0.
-17
Let x(h) be the first derivative of -1/11*h**2 + 0*h**3 - 1/33*h**6 + 0*h**5 + 1/11*h**4 - 4 + 0*h. Factor x(q).
-2*q*(q - 1)**2*(q + 1)**2/11
Let z(c) = 11*c**3 + 606*c**2 - 1215*c + 604. Let k(p) = -120*p**3 - 6665*p**2 + 13365*p - 6645. Let v(q) = -6*k(q) - 65*z(q). Find g, given that v(g) = 0.
-122, 1
Let b(t) = -3*t**2 - 7 - 8*t - t**3 - 3*t**2 - 4 + 6. Let v be b(-5). Suppose -9*o**2 + o + 6*o**2 - v*o = 0. What is o?
-3, 0
Let d(s) be the first derivative of s**5/60 - s**4/12 + s**3/6 + 2*s**2 - 10*s - 42. Let f(c) be the second derivative of d(c). Factor f(x).
(x - 1)**2
Let d(m) be the first derivative of m**5/20 + m**4/2 - 16*m**2 - 64*m - 625. Suppose d(c) = 0. Calculate c.
-4, 4
Let k(l) = 43*l**2 - 44*l**2 + 11*l - 5*l**4 + 6*l**3 - 4 - 7*l. Let m(z) = -z**3 + z**2 + z - 1. Let n(j) = k(j) - 4*m(j). Determine y so that n(y) = 0.
0, 1
Let b(z) = 15*z**2 + 30*z + 65. Let j(t) = t**2 - t - 1. Let i(d) = b(d) - 10*j(d). Find o such that i(o) = 0.
-5, -3
Let s(m) be the second derivative of 1/20*m**5 + 1/6*m**3 + 0*m**2 + 0 + m - 1/6*m**4. Factor s(j).
j*(j - 1)**2
Let i(x) be the third derivative of -x**11/498960 + x**9/45360 - x**7/7560 + x**5/60 - 12*x**2. Let h(t) be the third derivative of i(t). Factor h(g).
-2*g*(g - 1)**2*(g + 1)**2/3
Let j(s) be the first derivative of -2*s**3/45 + 62*s**2/15 + 42*s/5 + 277. Factor j(d).
-2*(d - 63)*(d + 1)/15
Let y(d) = 5*d**2 + d - 2. Let j(i) be the first derivative of 3/2*i**2 + 7*i**3 - 1 - 9*i. Let t(w) = 2*j(w) - 9*y(w). Factor t(m).
-3*m*(m + 1)
Suppose -g + 2 = -s, -3*g - 10 = -8*g - 3*s. Determine r so that 1 - r**3 + 2 - 4 - r + 2*r + r**g = 0.
-1, 1
Let n(p) be the second derivative of 0*p**3 - 1/40*p**6 - 3*p + 1/20*p**5 - 9/2*p**2 + 0 + 1/4*p**4. Let u(y) be the first derivative of n(y). Factor u(k).
-3*k*(k - 2)*(k + 1)
Let r(z) = -25*z**3 - 2*z**2 + 2*z - 2. Let m be r(1). Let p = m - -31. Factor 45*l**2 - 3*l - 53*l**2 + p*l**3 - 9*l.
4*l*(l - 3)*(l + 1)
Suppose 45*o - 3450 = -70*o. Factor 6*t**2 + 2/5*t**3 + 50 + o*t.
2*(t + 5)**3/5
Let t be -2 + 3/1 - -2. Let a = -110 - -116. Factor 1 + 2*h**2 - 10*h**2 - 2 + t + a*h.
-2*(h - 1)*(4*h + 1)
Suppose 4*v = 2*g + 44, -3*g + 6 = 2*v - 0. Let x be (30/v)/(6/9). Suppose 6*t**4 + t - 4*t**4 - t**x + t**2 - 3*t**2 = 0. Calculate t.
-1, 0, 1
Let l(a) be the third derivative of 0 + 0*a - 1/60*a**5 - 1/18*a**4 - 1/18*a**3 + 8*a**2. Suppose l(x) = 0. Calculate x.
-1, -1/3
Let z be (-4)/2 - 34/(-2). Suppose -d + z = 4*d. Let -4*c + 4 + 12*c**2 - d*c**3 - 8*c - c**3 = 0. What is c?
1
Factor -165/8*o - 39/8*o**2 - 3/8*o**3 - 225/8.
-3*(o + 3)*(o + 5)**2/8
Let j(o) be the second derivative of o**7/420 - o**6/80 + o**5/120 + o**4/16 - o**3/6 - 3*o**2 - 6*o. Let a(r) be the first derivative of j(r). Factor a(u).
(u - 2)*(u - 1)**2*(u + 1)/2
Find p such that 551 + 64*p + 384 + 506 + 2*p**2 - 1217 = 0.
-28, -4
Suppose 1