4, 32
Suppose 6*d - 3*l + 21 = 0, -2*l + 42 = -175*d + 178*d. Determine w so that 7/6 - 5/3*w**3 + 1/6*w**d + 4*w**2 - 11/3*w = 0.
1, 7
Let j(g) be the first derivative of -g**6/2 + 3*g**5 + 45*g**4/2 - 20*g**3 - 300*g**2 - 576*g + 1049. Factor j(u).
-3*(u - 8)*(u - 3)*(u + 2)**3
Factor 0 + 2/3*a**3 - 2/3*a**4 + 32/3*a**2 - 32/3*a.
-2*a*(a - 4)*(a - 1)*(a + 4)/3
Let n(d) be the third derivative of -d**7/630 + 11*d**6/45 + 189*d**2. Let n(a) = 0. Calculate a.
0, 88
Factor -22*h**3 + 172*h**4 + 167*h**4 + 170*h**4 + 169*h**4 + 148*h**2 - 192*h - 680*h**4.
-2*h*(h - 3)*(h - 2)*(h + 16)
Let t(q) be the third derivative of 0*q**4 + 1/315*q**7 + 8/5*q**5 + 0 + 2/15*q**6 + 0*q**3 + 0*q + 148*q**2. Factor t(b).
2*b**2*(b + 12)**2/3
Let w(x) be the second derivative of x**4/6 + 7*x**3/9 - 20*x**2/3 + 592*x. What is t in w(t) = 0?
-4, 5/3
Let o(z) = -4*z**4 - 84*z**3 - 228*z**2 + 4314*z - 8094. Let g(a) = 8*a**4 + 166*a**3 + 458*a**2 - 8627*a + 16187. Let w(y) = 6*g(y) + 13*o(y). Factor w(v).
-4*(v - 3)**2*(v + 15)**2
Let m = -49033/2 - -24517. Let v(j) be the first derivative of 18 + 21/4*j**2 + m*j**3 + 15*j. Determine r so that v(r) = 0.
-5, -2
Let y be (-4)/62 + (-141488)/(-1984) + -65. Let -19/2*z**2 - y*z - 1 - 2*z**3 = 0. Calculate z.
-4, -1/2, -1/4
Let k = 14269/13 + -1097. Let h be (-96)/(-24) - (0 + 2). Factor -k + 2/13*p**3 + 2/13*p**h - 8/13*p.
2*(p - 2)*(p + 1)*(p + 2)/13
Let k(n) be the first derivative of -n**5/50 - 20*n - 15. Let y(w) be the first derivative of k(w). Factor y(g).
-2*g**3/5
Let h = 917 + 244. Let d = -5803/5 + h. Determine v, given that 0 + 0*v**2 + d*v - 2/5*v**3 = 0.
-1, 0, 1
Let w(b) be the third derivative of -b**7/945 - b**6/540 + 3*b**5/5 + 184*b**4/27 - 896*b**3/27 - 689*b**2 - 1. Suppose w(i) = 0. What is i?
-8, 1, 14
Factor 0 - 2/5*k**3 + 0*k - 56/5*k**2.
-2*k**2*(k + 28)/5
Factor 3/2*p**3 + 55/3*p - 39/2*p**2 - 4.
(p - 12)*(3*p - 2)*(3*p - 1)/6
Let j = -167 + 171. Factor -3 - j - 6 - 6*t**2 + 7 - 23*t - t**2.
-(t + 3)*(7*t + 2)
Let m(q) be the second derivative of -11*q + 1/6*q**3 - 1/60*q**5 + 0 + 4*q**2 - 1/24*q**4 + 1/120*q**6. Let d(h) be the first derivative of m(h). Factor d(s).
(s - 1)**2*(s + 1)
Factor -688 - 615 - 32*r + 2*r**2 + 2044 - 645.
2*(r - 12)*(r - 4)
Let h(p) be the second derivative of 0 + 1/12*p**4 + 21*p**2 + 23*p - 17/6*p**3. Factor h(b).
(b - 14)*(b - 3)
Suppose 2*f + 4886 = -3*z + 4894, 5*z = -f + 18. Factor -155/2*p**2 + 0 - 3250*p**z + 825*p**3 + 5/2*p + 2500*p**5.
5*p*(p - 1)*(10*p - 1)**3/2
Let u(p) be the second derivative of p**4/36 - 23*p**3/6 + 1862*p. Factor u(l).
l*(l - 69)/3
Let q = -6083 + 6090. Let a(o) be the third derivative of -1/20*o**5 - 3/40*o**6 + 3/8*o**4 + 0 + o**3 + 0*o - 14*o**2 - 1/70*o**q. Factor a(u).
-3*(u - 1)*(u + 1)**2*(u + 2)
Let -19*w + 10063 + 4*w**3 - 10063 - 127*w**2 - 821*w - 21*w**2 = 0. Calculate w.
-5, 0, 42
Let y(r) be the first derivative of r**6/6 + 34*r**5/5 + 66*r**4 + 3164. Suppose y(i) = 0. Calculate i.
-22, -12, 0
Let n(v) = v**3 - 5*v**2 - 425*v + 413. Let w(q) = -5*q**2 + 2*q + 1. Let k(y) = n(y) - 8*w(y). Factor k(o).
(o - 9)*(o - 1)*(o + 45)
Let t(s) = 10*s**2 + 541*s - 1062. Let m be t(-56). Factor -b + 1/4*b**m + 1.
(b - 2)**2/4
What is o in 195*o**2 - 66*o**3 - 2*o**4 - 107*o**2 - 152*o**2 = 0?
-32, -1, 0
Let g(n) be the first derivative of -2*n**4/3 - 58*n**3/27 - 22*n**2/9 - 10*n/9 + 3215. Factor g(v).
-2*(v + 1)**2*(12*v + 5)/9
Factor 5*a**4 + 372*a + 226 + 7*a**4 - 4*a**3 - 162 + 63*a**2 + 296 - 323*a**2.
4*(a - 3)**2*(a + 5)*(3*a + 2)
Let t be (-133)/(-49) - (-4)/14. Solve 12*o - o**2 - t - 1 - 20*o + 12*o = 0.
2
Let o(q) be the first derivative of -q**5/5 - 29*q**4/4 + 109*q**3 - 595*q**2/2 - 950*q + 7219. Solve o(m) = 0 for m.
-38, -1, 5
Let u(a) be the first derivative of 66 + 0*a + 1/6*a**3 + 0*a**2 + 1/32*a**4. Find h, given that u(h) = 0.
-4, 0
Suppose -161*m + 175*m + 840 = 0. Let k be m/(-35)*(-10)/(-30). Factor 2/7*l**2 - k*l - 6/7.
2*(l - 3)*(l + 1)/7
Suppose -64*s = -168 - 101 - 51. Let a(x) be the second derivative of 0*x**2 + 0 - x + 1/165*x**6 + 0*x**3 - 3/110*x**s + 1/33*x**4. Let a(d) = 0. What is d?
0, 1, 2
Let z(x) be the second derivative of -x**5/10 + 41*x**4/2 - 818*x**3/3 + 696*x**2 - 1947*x. Suppose z(d) = 0. Calculate d.
1, 6, 116
Let z = 195 + -192. Factor 32*v + 16*v**2 - 19750 + 2*v**z + 19750.
2*v*(v + 4)**2
Let d(n) = 11 + 7*n + 16 + 12*n - 7*n**2 + n**2 + 32*n. Let l be d(9). Solve 10/11*q - 12/11*q**2 + l + 2/11*q**3 = 0.
0, 1, 5
Suppose -12*y + 14 = -46. Factor -20*j - 10*j**2 - 5*j**5 + 5*j**3 + 15*j**3 + 5*j + 5 + y.
-5*(j - 1)**3*(j + 1)*(j + 2)
Factor -19/5*l - 4 - 1/5*l**4 + 21/5*l**2 + 19/5*l**3.
-(l - 20)*(l - 1)*(l + 1)**2/5
Let k(g) = g**3 + 12*g**2 - 23*g + 75. Let a be k(-14). Let d(p) be the second derivative of 0*p**3 + 0 - a*p - 3/2*p**2 + 1/4*p**4. Solve d(c) = 0.
-1, 1
Let h(b) be the first derivative of -2/21*b**3 + 207 + 0*b + 24/7*b**2. Let h(p) = 0. Calculate p.
0, 24
Let -1122 + 24*g**2 - 2024 + 3153*g - 338 + 307*g = 0. Calculate g.
-871/6, 1
Let u(c) be the second derivative of -1/24*c**4 + 2*c + 0*c**3 - 10 + 0*c**2. Factor u(o).
-o**2/2
Let n be (-27)/15 + (1 - -1). Let h = -1902763 + 1902763. Factor -n*w**2 + h*w + 1/5.
-(w - 1)*(w + 1)/5
Suppose -46 = -9*q - 10. Factor -g + 5*g**q + 52*g - 21*g + 20*g**3 - 55*g**2.
5*g*(g - 1)**2*(g + 6)
Let o be -5*((-6)/(-4))/((-85)/34). Let p = 6 + -2. Factor -9*k**3 + 0*k**o - 9*k**2 - p*k + k - 3*k**4.
-3*k*(k + 1)**3
Factor 105 - 3/2*h**2 + 3/4*h**3 - 129/4*h.
3*(h - 5)*(h - 4)*(h + 7)/4
Let h(d) be the second derivative of 19 + 147*d**2 - 27/8*d**4 + 2*d + 42*d**3 + 3/40*d**5. Factor h(b).
3*(b - 14)**2*(b + 1)/2
Let -2832489/2 + 1683*s - 1/2*s**2 = 0. Calculate s.
1683
Let 0 + 192*j**2 - 400/9*j**5 - 3376/9*j**3 + 260*j**4 - 256/9*j = 0. What is j?
0, 1/4, 4/5, 4
Suppose -y = 4*x - 11 + 13, -4*y = -5*x + 50. Factor 2/5*n**x + 14/5*n + 12/5.
2*(n + 1)*(n + 6)/5
Let a(m) = -2*m + 466 + 631 + 19*m - 1648 + 20*m. Let l be a(15). Factor 5/3*n**3 - 3*n**2 - 9/2*n + 1/6*n**5 + 7/6*n**l + 9/2.
(n - 1)**2*(n + 3)**3/6
Let q(h) be the second derivative of -5/147*h**7 + 158*h + 5/7*h**5 + 0 - 15/7*h**3 + 18/7*h**2 - 10/21*h**4 + 2/105*h**6. Suppose q(a) = 0. Calculate a.
-3, -1, 2/5, 1, 3
Suppose 3*z + 5*h + 3 = -6, 25 = 5*z - 5*h. Let 5*u**4 - 20*u**z - 38 + 5*u**5 - 44 - 20*u**3 + 82 = 0. What is u?
-2, -1, 0, 2
Let n(w) be the first derivative of w**6/3 - 3*w**5/5 - 4*w**4 + 3*w**3 + 16*w**2 + 12*w + 102. Solve n(u) = 0 for u.
-2, -1, -1/2, 2, 3
Suppose -5*k - 10 = w - 11, 2*w = -4*k + 2. Let p be (-4)/(-54) + k + 11094/6966. Factor 8/3 - p*s**2 + 6*s.
-(s - 4)*(5*s + 2)/3
Let q be 2/(-12 - -5 - -1)*12/(-5). Let z(b) be the first derivative of -2/5*b**2 - q*b - 1/15*b**3 - 25. Factor z(h).
-(h + 2)**2/5
Let n(v) be the third derivative of -v**5/20 - 95*v**4/8 + 48*v**3 + 517*v**2. Factor n(a).
-3*(a - 1)*(a + 96)
Let w(b) be the first derivative of -b**3 + 1950*b**2 - 1267500*b - 13599. Find d such that w(d) = 0.
650
Let p = 460 - 455. Determine w, given that 120*w - 320 + 85*w**3 - 20*w**4 + 340*w**2 + p*w**5 - 10*w**5 - 200*w = 0.
-4, -1, 1, 4
Let a be 6 + ((49 - 5)/11 - 6). Let l(h) be the third derivative of 0 + 5*h**2 + 0*h - 1/12*h**a + 0*h**3 + 1/90*h**5. Factor l(k).
2*k*(k - 3)/3
Let m(u) = 7*u**2 + 4322*u - 4515. Let k(v) = 36*v**2 + 21548*v - 22576. Let g(i) = -3*k(i) + 16*m(i). Factor g(h).
4*(h - 1)*(h + 1128)
Suppose 2*j - 3*d = -8*d + 31, -4*j - 3*d + 55 = 0. Factor 2*c**2 - j*c + 4*c + 40 + 0*c + 52*c - 11*c - 2*c**3.
-2*(c - 5)*(c + 2)**2
Suppose 0 = -q + u - 1, -2*q + 3 + 4 = u. Determine f so that 7*f + 6 - 62*f**q + 2*f + 65*f**2 = 0.
-2, -1
Let b = -44 - -486/11. Let f be (2/(-132))/(14/(-84))*(-4 + 8). Factor f*q**2 + 0*q**3 - b + 0*q - 2/11*q**4.
-2*(q - 1)**2*(q + 1)**2/11
Solve -20 - 29/7*i**4 + 197/7*i**3 + 416/7*i - 443/7*i**2 - 1/7*i**5 = 0 for i.
-35, 1, 2
Let u(h) be the third derivative of -3*h**8/280 + 4*h**7/35 - 29*h**6/60 + h**5 - h**4 + 8*h**3/15 - 471*h**2 - 2*h. Solve u(s) = 0.
1/3, 2
Let y(d) be the second derivative of 2*d**7/21 - 2*d**6/15 - 12*d**5/5 + 28*d**4/3 - 32*d**3/3 + 4*d + 121. Factor y(k).
4*k*(k - 2)**2*(k - 1)*(k + 4)
What is q in 9/4 + 25921/4*q**2 + 483/2*q = 0?
-3/161
Let q be