 12 + 6. Determine j, given that -9 - 1/4*j**4 - 37/4*j**2 + s*j + 5/2*j**3 = 0.
2, 3
Let q(m) be the first derivative of m**7/1680 - m**6/80 + 9*m**5/80 - 9*m**4/16 - 2*m**3/3 + m**2/2 - 12. Let f(c) be the third derivative of q(c). Factor f(h).
(h - 3)**3/2
Let f be (5 + 22/(-4))*-20. Let c be (2/10)/(f/100). Factor 0*o**4 + 0*o**c - 1/2*o**3 + 0 + 1/4*o**5 + 1/4*o.
o*(o - 1)**2*(o + 1)**2/4
Let p(g) = -g**2 + 120. Let w be p(-10). Factor 28 + 19 - 4*q**2 - w + 56*q + 33.
-4*(q - 15)*(q + 1)
Suppose 21 = 70*q - 63*q. Find l, given that 0*l**2 + 14*l**3 + 3*l**4 - 9*l**4 - 2*l**2 - 8*l**q + 2*l**5 = 0.
0, 1
Let r(x) be the third derivative of x**5/300 + 13*x**4/20 + 68*x**3/3 - 13*x**2 + 194. Find j such that r(j) = 0.
-68, -10
Let j = 30029 - 89288/3. Let h = j - 197. Solve 308/3*p**4 - 88*p**3 - 32/3*p - h*p**2 + 196/3*p**5 + 0 = 0.
-2, -2/7, 0, 1
Let j(a) = -a**2 - 43*a - 435. Let p be j(-26). Let f(t) = -15*t + 105. Let h be f(p). Factor h - 12/11*s - 38/11*s**2 + 14/11*s**3.
2*s*(s - 3)*(7*s + 2)/11
Let m(a) be the first derivative of 4*a**3/21 - 106*a**2/7 + 960*a/7 - 2201. Factor m(o).
4*(o - 48)*(o - 5)/7
Let h be 245/21 - (597/27 - 22)/(1/(-6)). Solve 7/3*b**3 - h*b + 14/3 - 44/3*b**2 = 0 for b.
-1, 2/7, 7
Let k(b) be the second derivative of b**7/15120 - b**6/540 + b**5/48 - 95*b**4/6 + 2*b - 22. Let h(f) be the third derivative of k(f). Factor h(z).
(z - 5)*(z - 3)/6
Let t = 221/43830 - -1/1948. Let a(g) be the second derivative of 1/120*g**5 - 1/252*g**7 + t*g**6 - 19*g + 0*g**2 + 0 - 1/72*g**4 + 0*g**3. Factor a(j).
-j**2*(j - 1)**2*(j + 1)/6
Suppose 0 = 83*p + 306*p - 328 - 450. Factor 1/3*v**3 + 0 + 2*v + 7/3*v**p.
v*(v + 1)*(v + 6)/3
Let a = -98 + 152. Suppose 0 = 15*t + 32*t - 24*t - 46. Factor 28*q**t + 63*q - 4*q**2 + a + 80*q**3 - 77*q**3.
3*(q + 2)*(q + 3)**2
Let v(z) be the second derivative of 11*z**4/16 + 19*z**3/4 - 45*z**2 + 789*z. Factor v(s).
3*(s - 2)*(11*s + 60)/4
Factor 22 + 78 - 5*t**3 + 4*t**3 - 5*t**3 + 5*t**2 + t**3 + 80*t.
-5*(t - 5)*(t + 2)**2
Let o(b) be the second derivative of -b**4/30 - 307*b**3/15 + 308*b**2/5 + 3*b + 30. What is u in o(u) = 0?
-308, 1
Let h(u) be the second derivative of -u**5/60 - 5*u**4/3 - 38*u**3/3 + 56*u**2 + 176*u. Let j(t) be the first derivative of h(t). Factor j(o).
-(o + 2)*(o + 38)
Let x(j) be the second derivative of -55/8*j**4 + 11*j**3 + 39/20*j**5 - 3/20*j**6 - 11 + j - 9*j**2. Determine p, given that x(p) = 0.
2/3, 1, 6
Let v(t) be the first derivative of 0*t - 10*t**3 - 3/4*t**4 + 100 - 75/2*t**2. Factor v(i).
-3*i*(i + 5)**2
Let q(v) be the third derivative of v**7/1050 - 13*v**6/600 + 11*v**5/150 - 6845*v**2. Factor q(w).
w**2*(w - 11)*(w - 2)/5
Let g(c) be the first derivative of c**4/12 + 13*c**3/9 - 20*c**2/3 - 700*c/3 - 3398. Solve g(m) = 0 for m.
-10, 7
Let f(s) be the third derivative of s**5/120 + 17*s**4/24 - 65*s**3/4 - 2*s**2 - 527*s. Let f(o) = 0. Calculate o.
-39, 5
Let v(i) be the third derivative of i**8/672 + 9*i**7/20 + 3697*i**6/80 + 29279*i**5/24 - 130181*i**4/2 + 902289*i**3 + 38*i**2 - 8*i + 4. Factor v(z).
(z - 6)**2*(z + 67)**3/2
Let l(w) be the first derivative of -w**6/42 - 11*w**5/7 - 27*w**4/14 + 5309. Factor l(i).
-i**3*(i + 1)*(i + 54)/7
Let d be (-3)/((-3)/1) - (7 + -4). Let p be (-6)/18*2*15/d. Determine w, given that 3*w**4 + 3*w**p + 10*w**2 - 34*w**2 - w**4 - 20*w**4 + 36*w**3 = 0.
0, 2
Let m(q) be the first derivative of -85*q**4/4 - 110*q**3 - 215*q**2/2 + 30*q + 3867. Factor m(t).
-5*(t + 1)*(t + 3)*(17*t - 2)
Let o(f) be the second derivative of -13*f**2 + 7*f - 7 - 1/6*f**4 - 14/3*f**3. Factor o(a).
-2*(a + 1)*(a + 13)
Factor -5*u**2 + 0*u**2 + 106178 - 103873 - 906*u - 1394*u.
-5*(u - 1)*(u + 461)
Let j(z) be the second derivative of z + 0*z**2 + 50*z**3 + 0 + 3/20*z**5 - 5*z**4. Factor j(p).
3*p*(p - 10)**2
Let n(y) = 4*y**3 - 480*y**2 - 10*y + 498. Let d(q) = q**3 + 2*q**2 - 2*q + 1. Let i(g) = -6*d(g) + n(g). Determine x so that i(x) = 0.
-246, -1, 1
Let j be (594/(-21))/(1 + (-54)/63). Let k be j/(-10) + -7 - 8. Factor k - 18/5*w + 3/5*w**2.
3*(w - 4)*(w - 2)/5
Let u(k) be the second derivative of 5*k**4/12 + 340*k**3/3 + 11560*k**2 + 2*k + 7. Factor u(q).
5*(q + 68)**2
Let g = 20 + -12. Suppose g*q + 11 = 27. Factor -13*z**3 + 0*z**4 + 7*z**3 - 2*z**4 + z + 5*z + 4 - 2*z**q.
-2*(z - 1)*(z + 1)**2*(z + 2)
Suppose 0 = 5*b - 3*z - 29 + 1, 4*z = 2*b. Let v(u) be the first derivative of -b*u - 7 - 4/3*u**3 - 6*u**2. Find s such that v(s) = 0.
-2, -1
Find d such that -1125*d**3 + 420 + 6485*d**2 + 696*d + 17440*d**2 - 4614*d - 2402*d = 0.
2/15, 21
Let c(l) = l**2 + 2*l - 16. Let y be c(4). Suppose 0 = -2*o - y + 16. Factor -3*x - 12*x**2 + o*x**4 + 6*x + 8*x**2 - 4*x + x**3.
x*(x - 1)*(x + 1)*(4*x + 1)
Let b(v) = 533*v - 5. Let h be b(5). Find w, given that -2*w + 56*w**3 + 24*w**2 + 2658 - h + 0*w + 32*w**4 = 0.
-1, -1/2, 1/4
Let o(j) = j + 24. Let b be o(-32). Let w be 96/340 - b/68. Factor 1/5 - w*p + 1/5*p**2.
(p - 1)**2/5
Determine a, given that 1/4*a - 85/4 + 85/4*a**2 - 1/4*a**3 = 0.
-1, 1, 85
Let j = -62894/5 + 12580. Let t**2 + 13/5*t - j = 0. Calculate t.
-3, 2/5
Let r(x) = 5*x**3 + 225*x**2 - 230*x + 20. Let u(g) = 59*g**2 - 22*g - 27*g**2 - 11*g + g**3 + 3. Let b(p) = 3*r(p) - 20*u(p). Suppose b(f) = 0. Calculate f.
0, 1, 6
Find r, given that 66 + 819/5*r + 153/5*r**3 - 3/5*r**4 + 129*r**2 = 0.
-2, -1, 55
Suppose w = 5*b - 221, 168 = 4*b - 4*w + w. Let o = b + -40. Suppose 5 + c**3 - 2*c + 9*c**3 - 9*c + c - o*c**4 = 0. Calculate c.
-1, 1
Suppose -1709*s + 295 + 1249 = -1874. Factor 2*m + 0 - 1/3*m**s.
-m*(m - 6)/3
Let 20 + 395/3*d**2 + 400/3*d + 55/3*d**3 = 0. What is d?
-6, -1, -2/11
Let h(s) = s**3 - s**2 - 3*s. Let r(d) = -10*d**3 - 554*d**2 + 755*d - 252. Let k(t) = -3*h(t) - 3*r(t). Solve k(y) = 0.
-63, 2/3
Let p(h) be the first derivative of -2*h**4/3 - 28*h**3/9 + 56*h**2/3 - 16*h - 1734. Factor p(s).
-4*(s - 2)*(s + 6)*(2*s - 1)/3
Solve 16*h**5 + 24*h**4 + 2510*h - 2510*h - 18*h**5 - 22*h**3 = 0 for h.
0, 1, 11
Factor 39*d**2 - 12*d**3 + 42*d**2 + d**4 - d**4 - 3*d**4 - 66*d**2.
-3*d**2*(d - 1)*(d + 5)
Let v be (8 - -17) + 5/(3 + -4). Let d be 35/14*v/25. Factor 5/3*p**d + 11/3*p + 2/3.
(p + 2)*(5*p + 1)/3
Let h be (-759)/161 + (-24 - -18 - -15). Solve 0*p + 9/7*p**3 + 0 - h*p**2 + 3/7*p**4 = 0 for p.
-5, 0, 2
Suppose 18*w = -36879 + 2949. Let r be w/(-39) + (-2)/6. Suppose 8/3*d**3 + 22*d**2 + 32/3 + r*d = 0. Calculate d.
-4, -1/4
Let r = -6546 + 6546. Let w(j) be the third derivative of 0*j**3 + 0*j + 1/48*j**6 + 0 - 1/48*j**5 - 4*j**2 - 1/168*j**7 + r*j**4. Factor w(n).
-5*n**2*(n - 1)**2/4
Solve 14704*c + 172*c**5 - 29407*c + 4*c**4 + 14703*c = 0.
-1/43, 0
Suppose 44*n = 35*n + 72. Solve 11*s + 19*s + 19*s + 44*s**2 - 4*s**3 - n*s + 7*s = 0.
-1, 0, 12
Let k(d) = -4*d - 6. Let g be k(-6). Suppose 0*t + t - 4*h - g = 0, -10 = -t + 2*h. Factor 20*r**t - 46*r**3 - 28*r + 24*r**3 + 38*r**3 - 8.
4*(r - 1)*(r + 2)*(4*r + 1)
Let o(x) = 145*x**2 - 2485*x + 10275. Let d(p) = -13*p**2 + 225*p - 934. Let t(n) = -45*d(n) - 4*o(n). Factor t(i).
5*(i - 31)*(i - 6)
Let w(u) be the third derivative of 1/30*u**4 - 1/5*u**3 + 308*u**2 + 0*u + 0 - 13/525*u**7 + 8/75*u**5 - 1/105*u**8 + 1/50*u**6. Find s such that w(s) = 0.
-1, 3/8, 1
Let f(j) be the first derivative of 0*j - 2*j**2 + 0*j**3 + 0*j**4 - 1/240*j**5 - 5. Let l(q) be the second derivative of f(q). Factor l(m).
-m**2/4
Let r(c) be the third derivative of -c**7/945 - c**6/12 - 22*c**5/135 + 4*c**2 - 25*c. Factor r(g).
-2*g**2*(g + 1)*(g + 44)/9
Let w be 6921/(-105) + -5 - 3. Let q = w + 376/5. Factor 2/7 + q*j**4 + 1/7*j**2 - 9/7*j + 3*j**3.
(j + 1)*(j + 2)*(3*j - 1)**2/7
Let p(g) = -g - 2*g + 3*g**2 + 7*g. Let s(z) = -3*z**2 - 5*z. Let f be (85/(-119))/(3/21). Let i(v) = f*p(v) - 4*s(v). Factor i(h).
-3*h**2
Let y be (98/6)/(2 - (-30)/(-18)). Determine m, given that 10*m + 26 - y*m + 6*m**2 + 4 + 3*m**3 = 0.
-5, 1, 2
Let f(l) be the first derivative of l**8/4480 - l**7/280 - l**6/96 + l**5/40 + 9*l**4/64 + 66*l**3 - 105. Let g(s) be the third derivative of f(s). Factor g(i).
3*(i - 9)*(i - 1)*(i + 1)**2/8
Let q be (-3)/7 + 8502/4578. Let -q*c - 2/7*c**2 + 0 = 0. What is c?
-5, 0
Let n be 434/28 - 3/(-6). Determine m so that -n*m**2 + 214*m**3 + 48*m + 4*m**