/2*p + 15*p**2 + 3.
(p + 1)*(p + 3)*(7*p + 2)/2
Let t = -609/32 - -1891/96. Let b(p) be the third derivative of -16*p**2 - 1/30*p**5 + 0*p - 1/4*p**4 + 1/20*p**6 - 1/105*p**7 + 0 + t*p**3. Factor b(j).
-2*(j - 2)*(j - 1)**2*(j + 1)
Let a(u) be the third derivative of u**7/630 - u**6/36 + u**5/5 + 5*u**4/24 + u**3/3 + 16*u**2 + 3. Let l(g) be the second derivative of a(g). Factor l(v).
4*(v - 3)*(v - 2)
Factor 2976/11*h**2 - 2952192/11*h + 976191488/11 - 1/11*h**3.
-(h - 992)**3/11
Let o = 2/243657 - -649750/243657. Determine k so that o - 14/3*k**3 + 2/3*k**4 + 10*k**2 - 26/3*k = 0.
1, 4
Let f be -7 + (-6 - (-99)/27)*60/(-14). Factor -2/5*m + 1/10 + 2/5*m**f - 1/10*m**2.
(m - 1)*(m + 1)*(4*m - 1)/10
Let t(m) be the third derivative of -2/195*m**5 + 0*m - 5/156*m**4 + 1 - 2/39*m**3 - 1/780*m**6 - 30*m**2. Factor t(w).
-2*(w + 1)**2*(w + 2)/13
Suppose 28*j - 48 = 39 - 87. Let s(b) be the second derivative of 1/48*b**4 + j + 0*b**2 + 30*b + 1/6*b**3. Solve s(a) = 0.
-4, 0
Let 1/5*a**3 - 18/5*a + 1/2*a**2 + 18/5 = 0. What is a?
-6, 3/2, 2
Let y(g) be the first derivative of -g**6/120 + g**5/40 - g**3/12 + g**2/8 + 172*g + 96. Let u(x) be the first derivative of y(x). Factor u(f).
-(f - 1)**3*(f + 1)/4
Let h(l) be the third derivative of l**5/240 - 193*l**4/96 - 97*l**3/12 + 859*l**2. Let h(w) = 0. Calculate w.
-1, 194
Let c(i) be the third derivative of i**5/420 + 31*i**4/56 - 47*i**3/21 + 113*i**2 + 3*i. Determine f, given that c(f) = 0.
-94, 1
Suppose -2*i - 36 = -407*m + 404*m, 9*i - 86 = -2*m. Factor i - 9/2*y**4 + 3/2*y**5 - 3/2*y**3 - 18*y + 33/2*y**2.
3*(y - 2)*(y - 1)**3*(y + 2)/2
Let q(o) be the second derivative of -o**4/66 - 69*o**3/11 - 410*o**2/11 - 2646*o. Factor q(z).
-2*(z + 2)*(z + 205)/11
Let k(w) = w + 2. Let m(u) = -9*u - 100. Let z(y) = -k(y) - m(y). Let v be z(-12). Factor 6/11*o**v + 2/11*o**3 + 0 + 0*o.
2*o**2*(o + 3)/11
Let g(a) be the second derivative of -a**4/12 + 344*a**3/3 - 687*a**2/2 - 11939*a. Find h such that g(h) = 0.
1, 687
Suppose 2*l - 7*l - i = -22, -30 = -3*l + 5*i. Suppose 1 = 3*j - l*d, -5*d = 5*j - 0 - 15. Find x such that -9 - 3*x - 1/4*x**j = 0.
-6
Let y be (-12 - 53/(-5))/((-1)/5). Factor -176*n + 72*n - 9*n**2 + 16 + y*n**2 + 90.
-2*(n - 1)*(n + 53)
Let f(n) = 4*n**2 - n + 2. Let x(t) = -105*t**2 + 25085*t - 31400230. Let l(r) = -25*f(r) - x(r). Let l(o) = 0. Calculate o.
2506
Let w(f) be the second derivative of -13*f**7/3 + 1171*f**6/15 + 1215*f**5/2 + 5369*f**4/6 + 352*f**3/3 - 204*f**2 + f + 2076. Let w(u) = 0. Calculate u.
-3, -1, -2/7, 2/13, 17
Let g = 793 - 553. What is a in -48*a**2 - 3*a**3 - 4*a**2 + a**2 - 192 - g*a = 0?
-8, -1
Let l(g) be the third derivative of 0*g**3 - 1/48*g**4 + 1/420*g**7 - 32*g**2 + 7/240*g**5 + 0*g - 7/480*g**6 - 2. Factor l(c).
c*(c - 2)*(c - 1)*(2*c - 1)/4
Let n = 744401722/457749 + -14/50861. Let h = n - 1626. What is l in h*l**3 + 0*l**2 + 0*l**4 - 2/9*l**5 + 0 + 0*l = 0?
-1, 0, 1
Let k be ((-12)/76*-19 + (-16)/12)*1. Factor k*l**3 + 5/6*l**4 + 5/6*l + 1/6*l**5 + 1/6 + 5/3*l**2.
(l + 1)**5/6
Let j be (-378)/216*(-2)/7 + 5/((-15)/(-12)). Determine w, given that 0 + j*w**2 + 3/2*w**3 - 1/2*w**4 + 5/2*w = 0.
-1, 0, 5
Let o be 8/14 - (-34)/14. Solve 9 + 3*c - 4*c**2 - 17*c**2 - 19*c**3 + 4*c**o = 0 for c.
-1, 3/5
Let o be 35/3 + -237 + 226. Solve -1/6*b**5 - 1/3*b**4 + 1/3*b**3 - 1/3 + o*b**2 - 1/6*b = 0 for b.
-2, -1, 1
Suppose -2*z = 8, z - 4*z = -2*v + 1010. Suppose 361 = 5*n - v. Solve -128 - 4*r**2 - n + 60*r + r**2 = 0 for r.
10
Suppose -14*r + 40*r - 130 = 0. Let o(t) = -6*t**2 + 233*t - 2161. Let s(m) = 3*m**2 - 116*m + 1081. Let z(a) = r*s(a) + 2*o(a). Factor z(d).
3*(d - 19)**2
Suppose 0 = -0*y - 2*y + 6. Suppose 10 = y*w - 14. Factor w*i**2 + 7*i**2 + 0*i**4 + 15*i**3 + 5*i + 5*i**4.
5*i*(i + 1)**3
Suppose -152*g**2 - 6680 + 148*g**2 - 814*g - 5870*g = 0. Calculate g.
-1670, -1
Factor 0 - 2/11*d**3 - 4/11*d**2 + 0*d + 6/11*d**4.
2*d**2*(d - 1)*(3*d + 2)/11
Let s(f) be the first derivative of 0*f + 4/3*f**3 + 13 - 18*f**2. What is n in s(n) = 0?
0, 9
Let q(h) = -4*h**2 + 20*h - 16. Let m(o) = -27*o + 18 + 4*o**2 + 7*o - 2. Let v(c) = 6*m(c) + 5*q(c). Find i, given that v(i) = 0.
1, 4
Factor -12/7*k**3 - 16/7*k**2 + 0*k + 4/7*k**4 + 0.
4*k**2*(k - 4)*(k + 1)/7
Let k(y) be the second derivative of -280*y + 2/21*y**7 + 0 + 0*y**3 + 0*y**2 + 14/15*y**6 - 17/5*y**5 + 3*y**4. Let k(t) = 0. Calculate t.
-9, 0, 1
Let k be (1962/(-702) - -14 - 11/1)*36/8. Let r = 3499/13 - 269. Solve -k*m**3 + 12/13*m - 2/13 + r*m**2 = 0.
-1, 1/6, 1
Let j(l) be the second derivative of 0 + 21/5*l**2 - 8*l + 22/15*l**3 + 1/30*l**4. Factor j(o).
2*(o + 1)*(o + 21)/5
Let m(v) = 9*v**2 - 14*v**2 + 50 + v**2 + 0*v**2 - 53*v + 7*v**2. Let d(z) = 4*z**2 - 54*z + 50. Let a(o) = 5*d(o) - 6*m(o). Factor a(t).
2*(t - 1)*(t + 25)
Suppose -4*x + 11 = 3*o - 11, -60 = -5*o + 5*x. Suppose 0 = -o*m + 3*m + 56. Suppose -16*u**2 - 15*u**3 - m*u**2 - 5*u**4 - 5*u + 9*u**2 = 0. Calculate u.
-1, 0
Let v(o) = -14*o**3 - 10*o**2 - 378*o + 432. Let t(d) = 4*d**3 + 3*d**2 + 128*d - 144. Let g(z) = -10*t(z) - 3*v(z). Solve g(l) = 0.
-9, 1, 8
Let v(c) = c**4 - 112*c**3 + 233*c**2 - 118*c + 4. Let i(l) = -2*l**4 + 113*l**3 - 235*l**2 + 119*l - 5. Let x(j) = 4*i(j) + 5*v(j). Factor x(q).
-3*q*(q - 1)**2*(q + 38)
Determine h, given that 8/7*h**4 + 28*h**2 + 90/7*h + 78/7*h**3 - 36/7 = 0.
-6, -3, -1, 1/4
Let x(p) be the first derivative of 1/12*p**6 - 19 - 2197/2*p**2 + 37/10*p**5 + 1183/6*p**3 + 429/8*p**4 + 0*p. Factor x(v).
v*(v - 2)*(v + 13)**3/2
Let t be ((-3424)/(-96) + -35)*(7 + -1). Let p(d) be the second derivative of 0 - 19*d + 0*d**3 + 3/4*d**2 - 1/32*d**t. Determine a, given that p(a) = 0.
-2, 2
Let y(p) be the third derivative of -68*p**2 - 1/18*p**4 - 1/135*p**5 + 0*p**3 + 0 + 1/90*p**6 + 2/945*p**7 + 0*p. Factor y(i).
4*i*(i - 1)*(i + 1)*(i + 3)/9
Let k = -157 + 151. Let g be 312/(-1456)*16/k. Factor g*v - 8/7*v**3 - 10/7*v**2 + 6/7.
-2*(v + 1)**2*(4*v - 3)/7
Let m(v) be the first derivative of v**6/24 - 2*v**5/5 + 13*v**4/16 + 11*v**3/6 - 4*v**2 - 8*v - 2476. What is h in m(h) = 0?
-1, 2, 4
Factor -42/13*u**3 - 3072/13 + 240/13*u**2 + 2/13*u**4 + 128/13*u.
2*(u - 8)**3*(u + 3)/13
Suppose -68*y + 71*y - 75 = 0. Solve 6*x + 15*x**2 + y - 9*x + 48*x - 5*x**3 = 0 for x.
-1, 5
Let i = -68 + 5. Let k = i + 66. Suppose -4*a**2 - 3*a - 5*a**2 + 12 + 7 + k*a**4 - 13 + 3*a**3 = 0. What is a?
-2, -1, 1
Let q(r) = 6*r - 1. Let n be q(1). Suppose 5*x + 5*w - n = 3*x, -x - 5*w + 5 = 0. Factor 22*o - 3*o - 5*o**3 + 16*o + x*o + 30.
-5*(o - 3)*(o + 1)*(o + 2)
Suppose -1/8*j**2 - 77/4*j + 155/8 = 0. Calculate j.
-155, 1
Let f = 197/935 + -2/187. Suppose 474 = -769*t + 1006*t. Factor 2/5*h**3 - 1/5*h + 0 + f*h**t.
h*(h + 1)*(2*h - 1)/5
Let i(l) be the first derivative of l**6/60 + 7*l**5/40 + l**4/3 - 4*l**3/3 - 54*l + 167. Let u(d) be the first derivative of i(d). Factor u(z).
z*(z - 1)*(z + 4)**2/2
Factor 28*w**2 - 15*w**2 + 37*w**3 - 42 + w**3 + 23*w**2 + w**4 - 38*w + 5.
(w - 1)*(w + 1)**2*(w + 37)
Solve -24*t**4 + 0 - 2/7*t**5 + 0*t**2 + 0*t + 704/7*t**3 = 0 for t.
-88, 0, 4
Let a(t) = -t + 8. Let o be a(5). Suppose -14*p + 16 = -24 - 16. Determine b, given that 6*b + o*b**2 + 3*b**3 - b - 3*b**p - 8*b = 0.
-1, 0, 1
Suppose h = -4*b + 10, 9*b - 6*b - 3 = 0. Let y be (-4)/(-13)*39/h. Factor 3/5*r - 6/5*r**y - 3/5*r**3 + 6/5.
-3*(r - 1)*(r + 1)*(r + 2)/5
Let x = 17265143/9 - 1918349. Determine d so that -x*d**2 - 10 - 28/9*d = 0.
-9, -5
Let o(r) be the third derivative of -r**8/10080 + r**7/252 + 47*r**5/30 - 47*r**2. Let n(c) be the third derivative of o(c). Determine m so that n(m) = 0.
0, 10
Let z = 28283/11 - 2571. Suppose 0 - 8/11*s + 6/11*s**2 - 6/11*s**4 - z*s**5 + 10/11*s**3 = 0. What is s?
-4, -1, 0, 1
Let a(y) be the third derivative of -y**7/70 + y**6/4 + 21*y**5/5 + 23*y**4 + 64*y**3 + 312*y**2. Factor a(h).
-3*(h - 16)*(h + 2)**3
Let o(n) = 16*n**3 + 11*n**2 - 44*n - 8. Let t(l) = -15*l**3 - 9*l**2 + 45*l + 9. Let k = 390 + -386. Let z(d) = k*t(d) + 3*o(d). Suppose z(g) = 0. Calculate g.
-2, -1/4, 2
Let y(j) be the second derivative of -j**5/200 - 3*j**4/40 + j**3/6 - 1612*j. Factor y(d).
-d*(d - 1)*(d + 10)/10
Let v = -6475 - -6475. Let h(r) be the second derivative of 9*r - 1/3*r**3 + v*r**2 