uch that h(y) = 0.
-190, 0
Let m(i) be the first derivative of -i**4/48 + 2*i**3/9 - 19*i**2/24 + i - 4139. Determine y so that m(y) = 0.
1, 3, 4
Factor 0 - 6/7*l**2 + 4/7*l**3 + 2/7*l**4 + 0*l.
2*l**2*(l - 1)*(l + 3)/7
Let d = -2/226437 + 2264384/1585059. Let -d - 3/7*l + 1/7*l**2 = 0. Calculate l.
-2, 5
Let v = 86/1249 - -1208/18735. Solve -8/15*q - 2/5 - v*q**2 = 0 for q.
-3, -1
Let l(z) be the first derivative of -z**6/2 - 78*z**5/5 + 363*z**4/4 + 26*z**3 - 180*z**2 - 1079. Determine b, given that l(b) = 0.
-30, -1, 0, 1, 4
Let i = 847231/3 - 282407. Suppose i*n + 0 + 2/9*n**2 = 0. What is n?
-15, 0
Factor 2/7*p**4 + 138338/7*p**2 - 1052/7*p**3 + 0*p + 0.
2*p**2*(p - 263)**2/7
Suppose -99*k + 325*k = 182*k + 88. Factor -1/2*t**k + 0 - 32*t.
-t*(t + 64)/2
Let n(m) be the third derivative of -m**6/6 + 1117*m**5/15 - 778*m**4/3 + 296*m**3 + 852*m**2. Factor n(i).
-4*(i - 222)*(i - 1)*(5*i - 2)
Let a = -4699/20 + 1176/5. Factor 21/2*k**3 + a*k**4 + 0 + 0*k + 441/4*k**2.
k**2*(k + 21)**2/4
Let b(k) = -22*k**2 + 180*k - 339. Let i be b(3). Suppose -4*s**4 + 36/11*s**i + 10/11*s**5 - 46/11*s + 12/11 + 32/11*s**2 = 0. What is s?
-1, 2/5, 1, 3
Determine u so that 35/6*u - 152/3 - 1/6*u**2 = 0.
16, 19
Let g(y) be the second derivative of y**5/60 - y**4/9 - 7*y**3/18 + 5*y**2/3 + 1121*y. Factor g(l).
(l - 5)*(l - 1)*(l + 2)/3
Let w be (336 - 336)*(-1)/(-3). Factor -7/3*i**4 + 23/3*i**3 - 2*i**2 + 0*i + w.
-i**2*(i - 3)*(7*i - 2)/3
Let z(d) = -6*d**2 + 11*d + 23. Let r(l) = -5*l**2 + 12*l + 29. Let t(b) = -5*r(b) + 4*z(b). Let c be t(19). Factor c*k**2 - 44/5*k + 8/5.
4*(k - 2)*(5*k - 1)/5
Let o(w) be the first derivative of -w**3/9 - 825*w**2 - 2041875*w - 8240. What is p in o(p) = 0?
-2475
Let q(i) be the second derivative of -2*i**6/135 + 64*i**5/45 - 416*i**4/9 + 14336*i**3/27 - 25088*i**2/9 - 989*i. Factor q(w).
-4*(w - 28)**2*(w - 4)**2/9
Let o(h) = -82*h - 2865. Let l be o(-35). Let g(m) be the third derivative of 1/20*m**l + 5/2*m**3 + 0 + 3/4*m**4 + 0*m - 10*m**2. Solve g(a) = 0.
-5, -1
Suppose p = 13 + 59. Let g be 6 + p/(-42) + (-4)/14. Solve g*l**4 - 8/9*l**3 + 0 - 4*l**2 + 8/9*l = 0.
-1, 0, 2/9, 1
Let u = 28933/5 - 115727/20. Suppose -9/4*n - u*n**2 - 2 = 0. Calculate n.
-8, -1
Solve 243*c**4 + 225/2*c**3 + 73/4*c**2 + 0 + c + 54*c**5 = 0 for c.
-4, -1/6, 0
Let h be (-2 - 128/(-70))*(11 - (-32)/(-2)). Let q = 125 - 873/7. Factor 0 + q*g**2 + h*g.
2*g*(g + 3)/7
Let z(v) be the first derivative of 22*v**3 + 23*v + 5*v**4 + 34*v**2 - 1/5*v**5 - 114. Let z(n) = 0. What is n?
-1, 23
Let g(m) be the third derivative of m**5/10 - 37*m**4/8 - 19*m**3/2 - 484*m**2. Suppose g(t) = 0. Calculate t.
-1/2, 19
Suppose -5*i = -7*x + 8*x + x, 2*x + 3*i - 4 = 0. Determine o, given that 0 - 3/4*o**2 + 0*o + 7/8*o**4 + 3/4*o**x - 7/8*o**3 = 0.
-3/2, -2/3, 0, 1
Let o(r) be the first derivative of -r**3/3 + 24*r**2 - 47*r - 859. Factor o(k).
-(k - 47)*(k - 1)
Let u(o) = o**2 + 6*o + 12. Let y be u(-2). Suppose 17 = 5*x + 2*d, -13*x = -12*x + 4*d - 7. Factor 1/3*g**2 + 0*g + 0 - 1/3*g**x + 1/3*g**5 - 1/3*g**y.
g**2*(g - 1)**2*(g + 1)/3
Let u = 14044/2877 + -206/959. Determine o, given that -4/3*o**3 - 14/3*o**2 - 4/3 - u*o = 0.
-2, -1, -1/2
Factor 1/2*p**2 - 1/6*p**4 - 101/6*p + 11/2*p**3 + 11.
-(p - 33)*(p - 1)**2*(p + 2)/6
Suppose -57 = 2*n - 0*n + 3*k, 0 = -2*k - 2. Let y = -20 - n. Factor -37*w**2 + 32*w + y*w**2 - 18*w**2 + 18*w**3 - 2*w**4.
-2*w*(w - 4)**2*(w - 1)
Suppose -2*r + 4 = -4. Let f be 27*(-110)/(-198) - (19 - 4). Determine c so that 24/5*c + 44/5*c**2 + 24/5*c**3 + 4/5*c**r + f = 0.
-3, -2, -1, 0
Factor -8/9*c + 1/9*c**2 + 5/3.
(c - 5)*(c - 3)/9
Let h = 1627/12270 + 3/4090. Let j(v) be the third derivative of -1/90*v**6 + 16/9*v**3 + 0*v + h*v**5 + 0 - 7*v**2 + 5/6*v**4. Factor j(f).
-4*(f - 8)*(f + 1)**2/3
Let z(m) be the first derivative of 9*m**4/4 + 518*m**3 - 2075*m**2/8 + 173*m/4 + 4022. Let z(g) = 0. Calculate g.
-173, 1/6
Let k(o) = -2*o**3 + 2*o**2 + 5*o + 3. Let r = 716 - 717. Let n be k(r). What is h in 0 - 16/3*h**n - 7/3*h**3 - 4/3*h = 0?
-2, -2/7, 0
Let a be (-20)/(-170) + (-457)/(-17). Suppose -8 = -2*n - 2*n. Determine m, given that 6*m**4 - 108 + a*m - n*m**2 + 72*m**5 - 99*m**3 + 114 - 10*m**2 = 0.
-1, -1/2, -1/4, 2/3, 1
Let m = -28744 - -28750. Let a(y) be the first derivative of 6 - 12/5*y**5 + 0*y + 1/2*y**m + 3/2*y**2 - 4*y**3 + 9/2*y**4. Factor a(k).
3*k*(k - 1)**4
Suppose 40*r**2 + 99*r**2 - 11*r**2 - 15*r**2 + 3*r**3 + 19*r**2 = 0. What is r?
-44, 0
Let a(v) = -2*v**3 - 73*v**2 + 1075*v - 3000. Let r(s) = 7*s**3 + 218*s**2 - 3225*s + 9000. Let f(d) = 8*a(d) + 3*r(d). Find l such that f(l) = 0.
-24, 5
Suppose -102 = n - 53*n + 314. Let b(q) be the first derivative of -2*q**3 - 1/2*q**4 - 2*q - 3*q**2 - n. Factor b(j).
-2*(j + 1)**3
Let x(u) be the second derivative of -u**6/60 + 103*u**5/20 - 11209*u**4/24 + 5150*u**3 - 22500*u**2 + 25*u + 95. Let x(f) = 0. What is f?
3, 100
Let g(z) be the first derivative of -201 - 16*z - 10/3*z**3 + 41*z**2. Factor g(w).
-2*(w - 8)*(5*w - 1)
Let f(c) = -2*c**2 + c + 2. Let z(h) = 18 - 23*h + 102*h**2 - 94*h**2 - 6*h. Let s(l) = -6*f(l) - 2*z(l). Factor s(t).
-4*(t - 12)*(t - 1)
Let o be 2/(-6)*-3 + (31 - 27). Solve -5*z**3 - o*z**3 + 29*z**2 + z**4 - 7*z - 15*z - 10*z + 12 = 0 for z.
1, 2, 6
Let y(g) be the first derivative of g**6/6 - 4*g**5/5 - 7*g**4/4 + 22*g**3/3 + 12*g**2 - 119. Solve y(w) = 0.
-2, -1, 0, 3, 4
Let u be 100/(-40)*64/(-80). Let w(t) be the second derivative of -1/5*t**5 + 21*t + 4*t**3 + 5/3*t**4 + 0 + 0*t**u. Factor w(n).
-4*n*(n - 6)*(n + 1)
Let j(z) be the second derivative of 7*z**5/20 - 1151*z**4/3 + 3283*z**3/6 + 657*z**2 + z + 3066. Factor j(o).
(o - 657)*(o - 1)*(7*o + 2)
Let u = 1337/4 - 3991/12. Let h(j) be the second derivative of -10*j + 0*j**2 - 1/2*j**6 + 5/12*j**4 + 0 - u*j**3 + j**5. Solve h(y) = 0.
-2/3, 0, 1
Suppose -153*h = -152*h - 3. Let x(k) be the second derivative of -1/15*k**4 + 0*k**6 - 3/50*k**5 + 1/105*k**7 - 16*k + 0*k**h + 0 + 0*k**2. Factor x(f).
2*f**2*(f - 2)*(f + 1)**2/5
Find f, given that 0 - 2/17*f**2 + 730/17*f = 0.
0, 365
Let i = -2 + 3. Suppose 5 - 5 = 68*p. Factor -1 + p*w - w**2 - 4*w - i - 1.
-(w + 1)*(w + 3)
Let i = -1608 - -80401/50. Let z(u) be the second derivative of 0 + 2/5*u**2 + 2/15*u**4 + 1/3*u**3 + 13*u + i*u**5. Determine h so that z(h) = 0.
-2, -1
Let h(y) = y**2 - 163*y + 6488. Let g be h(69). Solve 12/5 + 2/5*i**2 - g*i = 0.
2, 3
Let t(r) = -2*r**3 + 4 + 8*r - 3*r**2 + r**3 - 4*r**2 + 0*r**3. Let k be t(-8). Factor 0 + k*q - 12*q**2 + 4*q**3 + 0 + 4*q**2.
4*q*(q - 1)**2
Let y(o) be the third derivative of o**7/945 - 11*o**6/270 - 289*o**5/270 + 155*o**4/54 + 11680*o**2. Determine m, given that y(m) = 0.
-10, 0, 1, 31
Let z be (-83 - 34608/(-420))/((-2)/5). Factor 2*n - 1/2*n**3 + 0 + z*n**2.
-n*(n - 4)*(n + 1)/2
Let l(n) = n**5 - n**4 - n**3 - 3*n**2 - n. Let p(r) = 11*r**5 + 28*r**4 - 131*r**3 - 84*r**2 + 106*r. Let z(b) = 14*l(b) - p(b). Find v, given that z(v) = 0.
-1, 0, 1, 4, 10
Let y(j) be the first derivative of -3*j**4/14 + 34*j**3/7 + 114*j**2/7 + 944. Suppose y(x) = 0. What is x?
-2, 0, 19
Let x be (-1)/4*0 - (-8)/2. Let n be x/(-3*20/(-45)). What is c in -c**4 + 9*c**3 - 8*c - 2*c**4 - n*c**3 + 5*c**4 = 0?
-2, 0, 1
Let a(d) be the second derivative of d**7/315 + 7*d**6/75 - 14*d**5/75 - 22*d**4/15 + 829*d. Suppose a(w) = 0. What is w?
-22, -2, 0, 3
Let x(s) be the second derivative of -3/14*s**3 + 11/140*s**5 + s + 0*s**2 + 1/7*s**4 + 9 + 1/105*s**6. Solve x(i) = 0 for i.
-3, 0, 1/2
Let o(x) be the first derivative of 5*x**4/4 + 17*x**3 + 5*x**2 + 3*x - 367. Let f be o(-10). Solve -49/2*p**f - 2*p + 0 + 14*p**2 = 0.
0, 2/7
Let n(w) = -12*w**2 - 19*w + 110. Let a(s) = s**2 - 2. Let l(t) = -65*a(t) - 5*n(t). Factor l(d).
-5*(d - 12)*(d - 7)
Suppose -1396 = 8*k - 1412. Let j(z) be the third derivative of 1/90*z**5 + 1/2*z**4 + 0 + 9*z**3 + 0*z + 26*z**k. Suppose j(l) = 0. Calculate l.
-9
Let g(k) = 2*k**5 - k**4 - k**3 + k + 1. Let p(o) = 5*o**5 + 44*o**4 - 248*o**3 + 452*o**2 - 353*o + 104. Let i(n) = 2*g(n) - p(n). Factor i(m).
-(m - 2)*(m - 1)**3*(m + 51)
Suppose -31*n - 1/2*n**2 - 468 = 0. What is n?
-36, -26
Let f(s) be the second derivative of -25*s**7/42 - 19*s**6/24 + 141*s**5/8 + 2335*s*