)/27*-6. Factor 16/7*d - t*d**5 + 0 + 46/7*d**2 + 6*d**3 + 10/7*d**4.
-2*d*(d - 8)*(d + 1)**3/7
Let y(m) be the second derivative of -m**7/30 - m**6/25 + 23*m**5/100 + m**4/10 - 8*m**3/15 - m - 787. Find k, given that y(k) = 0.
-2, -1, 0, 1, 8/7
Let l(d) be the second derivative of 2*d**7/21 + 16*d**6/15 - 12*d**5/5 - 80*d**4/3 + 256*d**3/3 - 6730*d. Find p, given that l(p) = 0.
-8, -4, 0, 2
Let z(p) be the second derivative of -p**6/300 + 7*p**5/50 + 2*p**3/3 - 7*p**2/2 - 40*p. Let r(y) be the second derivative of z(y). Find l, given that r(l) = 0.
0, 14
Find g such that 68/13 - 96/13*g**4 + 80*g**3 - 482/13*g + 586/13*g**2 = 0.
-1, 1/4, 34/3
Let z = -229 + 230. Let y(m) = 6*m**2 - 13*m + 17. Let p(a) = -a**2 + a - 1. Let s(f) = z*y(f) + 5*p(f). Factor s(c).
(c - 6)*(c - 2)
What is h in -1/3*h**5 + h**2 + 0 + 5/3*h**3 - h**4 - 4/3*h = 0?
-4, -1, 0, 1
Let t(r) be the second derivative of -5*r**4/12 + 3755*r**3/6 + 1880*r**2 - 2200*r. What is g in t(g) = 0?
-1, 752
Suppose -r = 5*k - 1191, 1082 = 4*k - 2*r + 132. Factor 4*g**2 - 463*g + 237*g + k*g.
4*g*(g + 3)
Let z = -43532 + 43532. Factor -3/4*r**4 + 3/4*r**2 - 1/4*r**3 + 1/4*r + z.
-r*(r - 1)*(r + 1)*(3*r + 1)/4
Suppose -9*f = -5*f - 272. Factor -49*r + 80 - 4*r**3 - 127*r + 24*r**3 - f*r**2.
4*(r - 5)*(r + 2)*(5*r - 2)
Let g be 442/266 + (-2)/(-7) + 209/3971. Factor 2*u**3 + 22*u + 2/3*u**4 + 48 - 74/3*u**g.
2*(u - 3)**2*(u + 1)*(u + 8)/3
Let s(w) = -w**3 + 5*w**2 + 20*w. Let u(d) = 6*d**3 + 1838*d**2 + 211544*d - 430592. Let x(b) = 2*s(b) + u(b). Solve x(c) = 0.
-232, 2
Let x be 4846/70 + 52/(-65). Let a = x - 68. Solve 0 + a*c**3 - 9/7*c**2 + 0*c = 0 for c.
0, 3
Find r such that 30*r - 5*r**2 - 303*r**3 - 18*r - 51 + 78*r + 11 + 273*r**3 = 0.
-2, 1/2, 4/3
Suppose -1248*j + 267 - 267 = 0. Let -15/2*c + 141/4*c**2 - 27/4*c**3 + j = 0. What is c?
0, 2/9, 5
Let b(d) be the first derivative of -32 - 40*d + 1/50*d**5 - 1/15*d**3 + 0*d**2 + 0*d**4. Let u(o) be the first derivative of b(o). Solve u(w) = 0.
-1, 0, 1
Determine p so that 960*p - 33254*p**3 + 11084*p**3 + 11084*p**3 + 6800 - 12*p**2 + 11082*p**3 = 0.
-10, 17
Let d(b) be the third derivative of 20*b + 0 + 0*b**3 + 1/320*b**6 - 1/160*b**5 - 3/16*b**4 + b**2. Factor d(p).
3*p*(p - 4)*(p + 3)/8
Suppose 2*r - 4*c + 4 = 3*r, -5*r = -5*c - 45. Factor -r*o**2 - 13*o + 28*o + 3*o**2 - 10.
-5*(o - 2)*(o - 1)
Let p = 447 - 444. Suppose -854*i**3 - 20749*i - 79092 + 27728*i - 132*i**4 - 274*i**p + 27497*i - 4*i**5 + 1976*i**2 = 0. What is i?
-13, 3
Factor 2*f**4 + 1672/5*f**2 + 0 - 4184/5*f**3 + 0*f.
2*f**2*(f - 418)*(5*f - 2)/5
Find y such that -2/7*y**3 - 576/7*y - 60/7*y**2 - 256 = 0.
-14, -8
Let c = -2/61 + 250/183. Let j(k) = -k**3 + 17*k - 20. Let u be j(3). Let 0 - c*b + 28/3*b**u - 6*b**2 - 2*b**3 = 0. What is b?
-1/2, -2/7, 0, 1
Suppose -s = u - 17, -3 = u - 5*s + 2*s. Factor -13*i**2 - 13*i**2 - 8*i**2 + u*i + 31*i**2 - 12.
-3*(i - 2)**2
Suppose -5*l + 7*l = -l. Suppose 5*g - 10 - 90 = l. Let -2*w**4 + 3*w**3 - 20*w + g*w - w**4 + 6*w**2 = 0. Calculate w.
-1, 0, 2
Solve 0*z + 2/9*z**4 + 32/9 + 0*z**3 - 34/9*z**2 = 0.
-4, -1, 1, 4
Let t(a) be the first derivative of a**4/26 - 10*a**3/39 - a**2/13 + 10*a/13 - 3235. Suppose t(c) = 0. What is c?
-1, 1, 5
Let f = 361941 - 361929. Let -f - 2/3*t**2 + 22/3*t = 0. Calculate t.
2, 9
Let f(x) be the first derivative of x**3/2 - 425*x**2/2 + 283*x/2 + 3000. Factor f(z).
(z - 283)*(3*z - 1)/2
Let d(m) be the first derivative of -12/5*m**2 + 0*m - 166 - 2/5*m**3. Factor d(t).
-6*t*(t + 4)/5
Let r = 6940 - 34536/5. Let t = r + -452/15. Factor -2/3*s**3 + t*s**2 - 2*s + 0.
-2*s*(s - 3)*(s - 1)/3
Suppose -8*a = -1 - 31. Suppose -4*b + h + 105 = 0, 6*h + 115 = a*b + 3*h. Determine m, given that -12*m + b - 9*m - 5*m**2 + 3*m - 2*m = 0.
-5, 1
Let f(s) be the second derivative of -s**6/720 - s**5/40 - s**4/6 + 43*s**3/6 + 116*s. Let z(t) be the second derivative of f(t). Suppose z(x) = 0. What is x?
-4, -2
Let 0 + 54/5*a**2 + 2/5*a**4 - 24/5*a**3 + 0*a = 0. Calculate a.
0, 3, 9
Let w = -580 - -641. Factor w + 12*h - 16 - 3*h**2 + 5 + 13.
-3*(h - 7)*(h + 3)
Suppose -19*g - 4*g = -966. Let v be ((-24)/42)/(150/g - 5). Factor -18/5*f + 54/5 - 6/5*f**2 + v*f**3.
2*(f - 3)**2*(f + 3)/5
Let c(w) be the first derivative of -w**3/18 - 137*w**2/12 - 68*w/3 - 748. Find g such that c(g) = 0.
-136, -1
Let r(v) = -v**3 + 6*v**2 + 17*v - 4. Let c be r(8). Let z(i) = i**3 + i**2 - 1. Let k(l) = l**3 - l**2 - l - 3. Let g(d) = c*z(d) - k(d). Factor g(x).
(x + 1)**2*(3*x - 1)
Factor -1/3*w**2 - 148/3*w - 715/3.
-(w + 5)*(w + 143)/3
Let p(b) be the second derivative of -29*b + 1/60*b**4 - 23/30*b**3 - 6 - 5*b**2. Solve p(j) = 0.
-2, 25
Let u be ((-12)/(-216))/((-82)/(-6765)). Let h(m) be the first derivative of 24 + 55/3*m**3 - 250/3*m - 25/6*m**2 + 1/3*m**5 - u*m**4. Factor h(k).
5*(k - 5)**2*(k - 2)*(k + 1)/3
Let o(m) = -m**3 + 130*m**2 - 986*m + 1224. Let a be o(122). Factor -1/5*w**2 + 1/5*w + 1/5*w**a - 1/5*w**3 + 0.
w*(w - 1)**2*(w + 1)/5
Let a(r) be the third derivative of r**8/1512 - 11*r**7/945 - 5*r**6/108 - 13*r**5/270 - 13*r**2 + 5. Solve a(m) = 0 for m.
-1, 0, 13
Let o(z) be the first derivative of -2*z**3/15 - 578*z**2/5 - 167042*z/5 + 408. What is t in o(t) = 0?
-289
Factor -44*p - 163*p - 228*p - 594 + 21*p**2.
3*(p - 22)*(7*p + 9)
Let k(z) = 6*z - 7 - 12 + z**2 + 6. Let j be k(-8). Solve 16*i**2 - 7*i**4 - 19*i**j - 27*i**2 - 3*i**5 - 6*i**4 - 2*i = 0 for i.
-2, -1, -1/3, 0
Let a be 2/(-4)*(-257)/3855. Let x(o) be the third derivative of 0 + 0*o - a*o**6 + 0*o**5 - 13*o**2 + 0*o**3 + 1/6*o**4. Factor x(b).
-4*b*(b - 1)*(b + 1)
Let n(f) = -f - 3 + 12264*f**2 + 3 - 12269*f**2 - 4*f. Let a be n(-1). Factor 0*x + 2/7*x**5 + a*x**2 - 10/7*x**4 + 8/7*x**3 + 0.
2*x**3*(x - 4)*(x - 1)/7
What is x in 16/9 - 276*x**2 + 824/3*x + 622/9*x**3 = 0?
-2/311, 2
Let k(o) be the second derivative of 0*o**2 - 3/10*o**5 - 3*o + 4/21*o**7 - 5/6*o**4 + 1/3*o**6 + 2 - 1/3*o**3. Determine h so that k(h) = 0.
-1, -1/4, 0, 1
Let d be ((-540)/(-126))/((-3)/(-14)). Let r(c) = 2*c - 37. Let q be r(d). Factor j**3 - 6*j**4 + 0*j**4 + 5*j**q + j**4 - 8*j + 4*j**2 + j**5.
j*(j - 2)**3*(j + 1)
Let d be ((-4)/(-24)*58 - 3) + (-189 - -183). Solve 16*l - d*l**4 + 40/3*l**2 + 4/3*l**3 + 0 = 0.
-2, 0, 6
Let i be 4 + (-35 + 0)/5 + 5. Suppose 48*w + 0 - 144 = 0. Factor -2/3*g**w - 8/3 + 8/3*g + 2/3*g**i.
-2*(g - 2)*(g - 1)*(g + 2)/3
Let i(n) be the first derivative of 2*n**5/55 + 185*n**4/22 + 17296*n**3/33 + 8464*n**2/11 - 1766. Suppose i(v) = 0. Calculate v.
-92, -1, 0
Suppose -420 - 744 = -3*v. Suppose -495*q**2 + 605*q**3 + v*q + 276*q - 769*q - 5 = 0. What is q?
-1/11, 1
Let h(a) be the first derivative of -10*a**3/9 - 863*a**2/3 + 692*a/3 - 1555. Factor h(b).
-2*(b + 173)*(5*b - 2)/3
Let v(t) be the third derivative of 0 + 0*t**4 + 88*t**2 + 0*t**5 + 0*t**3 - 1/600*t**6 + 1/1050*t**7 + 0*t. What is r in v(r) = 0?
0, 1
Let a(v) be the third derivative of -v**8/42 + 39*v**7/35 - 185*v**6/12 + 168*v**5/5 - 49*v**4/3 - 27*v**2 - 1. Determine w, given that a(w) = 0.
0, 1/4, 1, 14
Solve -4*p**4 + 13 - 13287*p**5 + 297*p + 13289*p**5 - 41*p + 28*p**2 + 210 - 42*p**3 - 31 = 0 for p.
-3, -2, -1, 4
Let t = -247 + 3220/13. Let i = t - 29/117. Factor 0 + 2/9*c**2 + i*c.
2*c*(c + 2)/9
Let p(y) be the third derivative of y**6/40 + 217*y**5/60 + 95*y**4/8 + 71*y**3/6 + 97*y**2 - 23. Find l such that p(l) = 0.
-71, -1, -1/3
Suppose -142 = 11*r - 307. Let w(g) = -g**3 - 5*g**2 - 5*g - 1. Let t be w(-4). Suppose 3*l**4 + r*l**t - 222*l - 3*l**3 - 12 + 9*l**2 + 210*l = 0. Calculate l.
-2, -1, 1
Let z(q) = -q**4 - q**3 + 2*q**2 + 5. Let k(j) = -8*j**4 + 19*j**3 + 149*j**2 - 928*j + 813. Let r(w) = 4*k(w) - 36*z(w). Factor r(c).
4*(c - 3)*(c - 1)*(c + 16)**2
Let t be ((-323)/(-17))/((-2)/2 + 0). Let j = 21 + t. Determine y, given that 15*y - 12*y - y**3 + 4 - j = 0.
-1, 2
Let 58/17*a**4 - 46/17*a**2 - 12/17*a**5 + 94/17*a**3 - 82/17*a - 12/17 = 0. Calculate a.
-1, -1/6, 1, 6
Let q = -331 + 383. Suppose 4*y + 48*y**2 - q*y**2 + 4*y = 0. What is y?
0, 2
Let w be 429/(-6) - 4/((-48)/18). Let l be (-3)/6 - (3 - (-325)/w). Determine v so that -8/7*v**3 - 2/7*v**5 + 4/7*v**2 + 4/7 + 10/7*v - l*v**4 = 0.
-2, -1, 1
Let s(u) be the first derivative of 11 - 57/2*u