actor 2/3*r**2 + 0*r + 0 + s*r**3.
2*r**2*(r + 1)/3
Let c(q) be the first derivative of -61/3*q**3 - 63*q + 1/4*q**4 + 125 - 125/2*q**2. Determine s, given that c(s) = 0.
-1, 63
Suppose -26 = -4*d - 2*p, -4*p = 4*d + 9 - 41. Suppose 5*b = -w + 11, -b - 4*w - 8 - d = 0. Factor 0 + 64/7*z**4 + 0*z + 32/7*z**b + 4/7*z**2.
4*z**2*(4*z + 1)**2/7
Let u be (-1350)/(-112) + (-79 - -67). Let x(v) be the second derivative of 1/10*v**5 - 2/3*v**3 + 0 - 1/5*v**6 + 2/3*v**4 + 0*v**2 + 5*v - u*v**7. Factor x(r).
-r*(r + 2)**2*(3*r - 2)**2/4
Factor -18 + a**3 + 18*a**2 + 4299*a - 4*a**3 - 4296*a.
-3*(a - 6)*(a - 1)*(a + 1)
Let c(f) be the second derivative of f**6/35 - 11*f**5/70 + 11*f**4/42 - f**3/21 - 2*f**2/7 + 3330*f. Suppose c(i) = 0. What is i?
-1/3, 1, 2
Let y(u) = u**3 - 36*u**2 + 210*u - 46. Let i be y(7). Factor -6*k + 1/2*k**i + 18 - 5/2*k**2.
(k - 6)*(k - 2)*(k + 3)/2
Let n be -3*(30/(-45))/1. Let s(d) be the third derivative of 0*d + 1/40*d**4 + 1/300*d**5 + 4*d**n + 1/15*d**3 + 0. Factor s(i).
(i + 1)*(i + 2)/5
Suppose q - 4*h - 14 = 0, 44*h - 7 = -q + 41*h. Factor -5*a**2 - 394 + 414 + q*a + 5*a.
-5*(a - 4)*(a + 1)
Let u(f) = -3*f**2 + f + 4. Let a(t) = -2*t**2 + 2. Let p be -4 - (-9)/3 - 42*-1. Let i = p + -46. Let g(q) = i*a(q) + 3*u(q). Factor g(y).
(y + 1)*(y + 2)
Find t such that -110 + 160*t + 50*t**2 + 91 - 7*t**2 + 91 + t**3 + 84 = 0.
-39, -2
Let o(l) = -2*l**2 + 132*l - 1128. Let j be ((300/(-48))/(-25))/(1/12). Let i(r) = 25*r**2 - 1590*r + 13535. Let g(u) = j*i(u) + 35*o(u). Factor g(y).
5*(y - 15)**2
Let p(s) = 5*s**2 - 4*s - 4. Let z(i) be the first derivative of 5*i + 5/2*i**2 - 10 - 5/3*i**3. Let d(h) = 5*p(h) + 4*z(h). Factor d(b).
5*b**2
Let g(o) be the second derivative of 2*o**6/15 - 12*o**5/5 + 37*o**4/3 - 28*o**3 + 32*o**2 + o - 731. Let g(w) = 0. What is w?
1, 2, 8
Let s = 500 - 496. Let z be ((-1)/(-3))/(23/(-6) + s). Factor -2/3*f + 2/3*f**z + 0.
2*f*(f - 1)/3
Let v(i) be the first derivative of 4*i**3/21 + 428*i**2/7 + 658. Determine h so that v(h) = 0.
-214, 0
Let c be (10 + -6 + 6)/116. Let u = 1337/638 + c. Let u - 18/11*l**2 + 0*l + 6/11*l**3 = 0. Calculate l.
-1, 2
Let h(g) = 132 - 46 + 226 + 21*g**2 + 20 + 336*g + 271. Let r(u) = 3*u**2 + 48*u + 86. Let t(y) = -2*h(y) + 15*r(y). Factor t(b).
3*(b + 2)*(b + 14)
Let q = -19371 + 19374. Let h(j) be the first derivative of -4*j + 15 - 4*j**2 + 1/5*j**5 + 1/2*j**4 - j**q. Factor h(x).
(x - 2)*(x + 1)**2*(x + 2)
Factor -14*z - 2*z**2 - 527186 + 527173 + 4*z**2 - 3*z**2.
-(z + 1)*(z + 13)
Let h(l) be the second derivative of 0 - 1/30*l**4 + 14/15*l**3 + 22*l + 0*l**2. Solve h(p) = 0.
0, 14
Let k(c) be the second derivative of 0 + 1/3*c**4 + 0*c**2 + 1/20*c**5 - 4/3*c**3 - 1/180*c**6 + 13*c. Let x(i) be the second derivative of k(i). Factor x(v).
-2*(v - 4)*(v + 1)
Let x(d) be the second derivative of d**4/48 + 53*d**3/24 - 27*d**2/4 + 1341*d. Factor x(t).
(t - 1)*(t + 54)/4
Let n(m) = -6*m**3 - 72*m**2 + 767*m - 674. Let l(w) = 15*w**3 + 180*w**2 - 1917*w + 1686. Let y(r) = 5*l(r) + 12*n(r). Find u, given that y(u) = 0.
-19, 1, 6
Factor 48840 + 125*y**2 + 28*y**2 - 48840 - 3*y**3 + 156*y.
-3*y*(y - 52)*(y + 1)
Let x(b) = -b**2 - 20*b + 227. Let d(t) = 4*t + 136. Let i be d(-41). Let c be x(i). Determine r, given that -8/15 + 0*r**c + 2/3*r**2 + 0*r - 2/15*r**4 = 0.
-2, -1, 1, 2
Let x = -2417 + 2432. Let j(y) be the first derivative of -12*y**2 - 2/3*y**3 - 72*y - x. Let j(h) = 0. What is h?
-6
Let i(f) be the third derivative of -5*f**7/168 + f**6/72 + 47*f**3/3 + 7*f**2 + 7. Let q(t) be the first derivative of i(t). Factor q(j).
-5*j**2*(5*j - 1)
Let s = 95052 + -665348/7. Suppose 8/7 + 8/7*i**4 + 2/7*i + 2/7*i**5 - s*i**2 - 4/7*i**3 = 0. What is i?
-4, -1, 1
Let z = -80007 - -80019. Factor -z*q**2 - 6*q**4 + 0*q + 3/4*q**5 + 15*q**3 + 0.
3*q**2*(q - 4)*(q - 2)**2/4
Let v(b) = -3*b - 46. Let q be 40/(-2)*204/255. Let m be v(q). Factor 6/5*z - 2/5*z**m - 4/5.
-2*(z - 2)*(z - 1)/5
Let c(l) be the third derivative of l**7/1575 + 2*l**6/225 - 11*l**5/150 - 135*l**2. Factor c(v).
2*v**2*(v - 3)*(v + 11)/15
Let w be 4251/(-1526)*21/(-52). Determine u, given that -w*u**3 - 11/8*u - 33/8*u**2 + 3/4 + 7/8*u**4 = 0.
-1, 2/7, 3
Let c = 2081/1077 + -574/359. Factor c*x**2 + 0 + 1/3*x.
x*(x + 1)/3
Let u(m) be the second derivative of -46/3*m**3 + 0 - 41*m + 0*m**2 - 1/3*m**4. Factor u(p).
-4*p*(p + 23)
Let h = 403/165 + -41/33. Factor -1/5*g**4 + h*g**2 + 0*g**3 + 8/5*g + 3/5.
-(g - 3)*(g + 1)**3/5
Let l(k) = -k**2 - 63*k - 40. Let y(h) be the third derivative of 21*h**4/8 + 41*h**3/6 + 9*h**2 + 7. Let b(q) = -5*l(q) - 4*y(q). Determine s so that b(s) = 0.
-12, -3/5
Let u(r) be the first derivative of 5*r**6/6 - 15*r**5 + 295*r**4/4 - 55*r**3 - 270*r**2 + 8960. Determine x, given that u(x) = 0.
-1, 0, 3, 4, 9
Let h(u) = 32*u**2 + 517*u + 125. Let g(w) = -62*w**2 - 1032*w - 250. Suppose 0 = -10*m + 86 - 196. Let t(q) = m*h(q) - 6*g(q). Factor t(j).
5*(j + 25)*(4*j + 1)
Suppose 25*v + 25 = 20*v. Let d be -3 - ((-20)/15 + v). Let -4/3*m**2 + 4/3*m**4 + d*m**5 - 10/3*m**3 + 0 + 0*m = 0. What is m?
-1, -2/5, 0, 1
Let v(x) be the second derivative of 8*x**6/15 - 18*x**5 + 117*x**4 - 333*x**3 + 486*x**2 + 3*x - 302. Solve v(z) = 0.
3/2, 18
Let l(u) be the first derivative of -4/3*u**3 - 3/2*u**4 + 19 - 1/5*u**5 + 3*u**2 + 5*u. Solve l(c) = 0 for c.
-5, -1, 1
Let h be (13 - (-2889)/(-243))*9/4. What is b in -h*b**3 + 13/2*b**2 + 13*b + 4 = 0?
-1, -2/5, 4
Let g be (4 - 1)*70/(-15). Let j = g - -16. Solve -3 - 60 + 4 + 176*m - 36*m**3 - 96*m**j - 5 = 0.
-4, 2/3
Let i = -8097 + 24298/3. Let s(x) be the first derivative of -16*x - 24 + i*x**3 + 4*x**2 + 1/4*x**4. Factor s(g).
(g - 1)*(g + 4)**2
Let d(s) = -22*s**3 - 3552*s**2 + 7051*s - 3613. Let i(p) = -4*p**3 - 592*p**2 + 1175*p - 603. Let b(t) = -6*d(t) + 34*i(t). Factor b(f).
-4*(f - 294)*(f - 1)**2
Let k = -81415 - -81418. Factor 0*v + 0 + 2/7*v**4 + 4/7*v**2 + 6/7*v**k.
2*v**2*(v + 1)*(v + 2)/7
Let f be 6/(-4)*(-278)/(-417). Let a be (134/603)/(-1*f/9). Factor 2*l**4 - 6*l**a - 1 - 1/2*l**3 + 11/2*l.
(l - 1)**2*(l + 2)*(4*l - 1)/2
Let j = -15203295/2 + 14640765851/1926. Let f = 7/321 - j. Factor -f*m**3 - 20*m**2 - 2/9*m**4 + 48 - 24*m.
-2*(m - 1)*(m + 6)**3/9
Let h(d) be the second derivative of 0*d**3 + 1/2*d**4 + 2 + 135*d + 21/20*d**5 - 2/5*d**6 + 0*d**2. Factor h(x).
-3*x**2*(x - 2)*(4*x + 1)
Let k = 761 + -299. Let u be (k/35)/6 - -1. Find t such that 4/5*t**3 + u*t**2 - 4/5*t + 0 - 16/5*t**4 = 0.
-1, 0, 1/4, 1
Let t(p) = -8*p**3 + 544*p**2 - 2030*p + 1529. Let r(x) = 28*x**3 - 1904*x**2 + 7108*x - 5352. Let j(y) = -7*r(y) - 24*t(y). Factor j(m).
-4*(m - 64)*(m - 3)*(m - 1)
Let x(o) = 2*o + 48. Let h be (-275)/(-10)*(-4)/5. Let c be x(h). Factor -c - 18 + 2*a**2 - 14*a + 34.
2*(a - 6)*(a - 1)
Suppose -14*i = -i + 312. Let f be i/(-15) + -2 - (-308)/20. Factor 10*s**2 - 37*s + 30*s**3 - f - 3*s**5 + 12*s + 5*s**4 - 2*s**5 + 0*s**4.
-5*(s - 3)*(s - 1)*(s + 1)**3
Factor 46/13*x + 264/13 + 2/13*x**2.
2*(x + 11)*(x + 12)/13
Factor -124*y + 1/3*y**5 + 227/3*y**2 + 71/3*y**3 - 25*y**4 + 148/3.
(y - 74)*(y - 1)**3*(y + 2)/3
Suppose 0 = -4*f - 4*d - 124, 6*f + d + 85 = 3*f. Let y be ((-6)/(-4))/(f/24)*-2. Let -25/3*l**4 + y - 15*l**3 + 12*l + 26/3*l**2 = 0. What is l?
-2, -2/5, 1
Let b(z) be the third derivative of -z**7/280 + 7*z**6/40 + 31*z**5/20 + 4*z**4 + 162*z**2 + 2*z. What is s in b(s) = 0?
-2, 0, 32
Solve 50*w**5 + 3868*w**2 - 4002*w - 3370*w**4 + 1480*w**4 + 6518*w**3 - 1270*w - 1850*w**4 + 1168 = 0 for w.
-1, 2/5, 2, 73
Let j(b) be the first derivative of -1/16*b**4 - 1/12*b**3 + 0*b + 73 + 1/20*b**5 + 1/8*b**2. Find h such that j(h) = 0.
-1, 0, 1
Suppose -3*s - 2*c + 23 = 0, -1304*s = -1301*s - 3*c + 12. Let u(a) be the second derivative of -8/21*a**3 - s*a - 4 + 1/21*a**4 - 10/7*a**2. Factor u(g).
4*(g - 5)*(g + 1)/7
Solve -1520/7 + 1524/7*f - 4/7*f**2 = 0.
1, 380
Let d(q) be the third derivative of q**5/390 + q**4/13 + 35*q**3/39 - 59*q**2 - 2*q. Determine x, given that d(x) = 0.
-7, -5
Let g(b) be the first derivative of 2*b**6 + 232*b**5/5 - 175*b**4 + 40*b**3 + 344*b**2 - 352*b + 1449. Determine a so that g(a) = 0.
-22, -1, 2/3, 1, 2
Suppose z + 6 = i, 18 = i - z - 4*z. Solve -3*r**4 + 2*r**5 + 11*r**3 - r**5 - 18*r**