 8)
Let h(d) = -21*d - 19. Suppose 39*l - 9*l + 30 = 0. Let q be h(l). Determine w, given that -6/7*w**3 - 6/7*w**q + 12/7*w + 0 = 0.
-2, 0, 1
Let h(s) be the third derivative of s**6/180 + s**5/45 - 25*s**4/36 - 50*s**3/9 - 3434*s**2. Let h(a) = 0. Calculate a.
-5, -2, 5
Let z(l) be the third derivative of 2 + 0*l + 1/3*l**3 + 53*l**2 - 3/20*l**4 - 1/75*l**5. Factor z(k).
-2*(k + 5)*(2*k - 1)/5
Let c(d) = -d**3 + 3*d**2 - 3*d + 4. Let y be c(2). Let i be (632/5056)/(1/4). Factor i*s - y + 1/4*s**2.
(s - 2)*(s + 4)/4
Factor 1916*w**2 + 11263 + 1909*w**2 - 3827*w**2 - 33313 + 420*w.
-2*(w - 105)**2
Let h(c) be the second derivative of -11/120*c**6 + 0*c**2 - 3/10*c**5 + 3/4*c**4 + 0*c**3 - 256*c - 1/168*c**7 + 0. Solve h(g) = 0.
-6, 0, 1
Let p(u) = -10*u**4 + 19*u**3 - 22*u**2 - 11. Let z(r) = 9*r**4 - 18*r**3 + 23*r**2 + 10. Let w(d) = 10*p(d) + 11*z(d). Let w(i) = 0. Calculate i.
-11, 0, 3
Let v(k) be the second derivative of -228/5*k**5 - 493848*k**3 - 6498*k**4 - k - 21112002*k**2 - 2/15*k**6 - 75. Suppose v(n) = 0. What is n?
-57
Factor -43/3*m - 92/3*m**2 + 0 - 55/3*m**3 - 2*m**4.
-m*(m + 1)**2*(6*m + 43)/3
Suppose -23*g + 358 + 1574 = 0. Let n = -79 + g. Let 1/3*f + 0 - 5/6*f**4 + 5/6*f**2 + 1/2*f**n - 5/6*f**3 = 0. What is f?
-1, -1/3, 0, 1, 2
Let h be 27/30*(-8)/(-6). Let n = 1113094/5 - 222617. Factor h*f - n - 1/5*f**2.
-(f - 3)**2/5
Suppose -d + 32 = d. Let m(y) = 9*y + 29. Let j be m(-3). Factor 15*s**2 + 3 - 10*s + s - 11*s**2 - d*s**j.
-3*(s + 1)*(4*s - 1)
Let t(m) = -56*m**2 - 772*m + 38416. Let b(w) = -5*w**2 + w. Let i(j) = -12*b(j) + t(j). Find h, given that i(h) = 0.
98
Suppose -28*p - 40 = -180. Let r(q) be the third derivative of 0 - 2/15*q**4 + 0*q - 1/75*q**p - 35*q**2 - 2/5*q**3. Factor r(i).
-4*(i + 1)*(i + 3)/5
Let u(r) be the second derivative of r**6/240 + 29*r**5/20 + 841*r**4/4 - 97*r**3/3 + 16*r - 7. Let q(a) be the second derivative of u(a). Factor q(l).
3*(l + 58)**2/2
Let k(i) be the third derivative of 5*i - 1/2*i**3 + 0 + 7/60*i**4 + 1/300*i**5 - 14*i**2. Factor k(f).
(f - 1)*(f + 15)/5
Let 6/11*v**5 + 192/11*v**2 - 186/11*v - 192/11*v**4 + 0 + 180/11*v**3 = 0. What is v?
-1, 0, 1, 31
Let l(s) be the first derivative of 8*s**5/25 + 51*s**4/20 + 38*s**3/5 + 10*s**2 + 24*s/5 - 912. Solve l(i) = 0.
-2, -3/8
Let m(h) be the second derivative of h**5/4 - 85*h**4/4 - 1085*h**3/6 - 825*h**2/2 - 998*h. Find i, given that m(i) = 0.
-3, -1, 55
Suppose 8*j = 77 - 61. Factor -19*k**2 - 3 - 42 - 10*k**j + 24*k**2 + 30*k.
-5*(k - 3)**2
Let z(s) be the first derivative of 1/2*s**3 - 9/40*s**4 + 0*s + 5/4*s**2 + 1/50*s**5 + 167. Let z(f) = 0. What is f?
-1, 0, 5
Suppose -m - 28 = 5*w, 11 = -5*w + 5*m - 29. Let y be 1 - (w/(-21) - (-180)/(-140)). Factor 1/3*k**y + 1/3*k + 0.
k*(k + 1)/3
Factor 3/5*h**2 + 888/5*h - 1788/5.
3*(h - 2)*(h + 298)/5
Let v(f) be the third derivative of 0*f**3 + 2*f**2 + 19*f - 25/12*f**4 - 13/12*f**5 + 1/8*f**6 + 0 - 5/336*f**8 + 5/42*f**7. Solve v(g) = 0 for g.
-1, 0, 2, 5
Factor 0*x**3 - 4000/7*x - 4/7*x**4 + 600/7*x**2 + 7500/7.
-4*(x - 5)**3*(x + 15)/7
Let a(s) be the third derivative of -1/12*s**5 + 3/2*s**3 + 1/2*s**4 + 0 + 28*s**2 + 0*s. Factor a(j).
-(j - 3)*(5*j + 3)
Let b(o) = -443*o - 107. Let d be b(-3). Let x = -1220 + d. Factor -2/7*n**x - 162/7 + 36/7*n.
-2*(n - 9)**2/7
Let g(t) = -t**3 - 4*t**2 - 84*t - 81. Let c be g(-1). Let b(n) be the first derivative of 2/9*n**2 + 0*n**4 + c*n - 2/45*n**5 - 32 + 2/9*n**3. Factor b(k).
-2*k*(k - 2)*(k + 1)**2/9
Let u(m) be the second derivative of m**7/42 - m**6/24 - m**5/12 + 5*m**4/24 + 14*m**2 + 2*m. Let j(v) be the first derivative of u(v). Solve j(q) = 0.
-1, 0, 1
Suppose -34*s + 36 = 4*n - 35*s, 4*n - 56 = -4*s. Let y be -2 + -2 + -6 + n. What is w in 0*w + y - 8/7*w**3 + 6/7*w**2 + 2/7*w**4 = 0?
0, 1, 3
Let r = 10877/695 - 2092/139. Factor -r*l + 0 - 36/5*l**2.
-3*l*(12*l + 1)/5
Factor 3*x**2 + 2522 + 1222 - 713*x - 784*x - 381*x.
3*(x - 624)*(x - 2)
Suppose 268/5 + 2/5*v**4 - 54*v**2 - 26*v + 26*v**3 = 0. What is v?
-67, -1, 1, 2
Let g(t) = -3*t**2 - 156*t - 2035. Suppose b + w = -1, -w = 3*b - 8*b + 13. Let n(j) = -j**2 - 52*j - 678. Let o(z) = b*g(z) - 7*n(z). Solve o(s) = 0 for s.
-26
Let i(m) = -m**2 + m + 264. Let g be i(0). Solve -50*z - 264*z**2 - g*z**2 + 125 + 533*z**2 = 0.
5
Let j(a) be the second derivative of -a**5/100 + 3*a**4/40 + a**3 - 79*a**2/2 - 14*a. Let u(q) be the first derivative of j(q). Factor u(n).
-3*(n - 5)*(n + 2)/5
Let l(f) be the first derivative of -53 - 2/15*f**5 + 4*f**2 - 26/9*f**3 - 8/3*f + f**4. Factor l(x).
-2*(x - 2)**2*(x - 1)**2/3
Let g(r) = -10*r**4 - r**3 + r**2 + r - 1. Let d(n) = -28*n**4 - 295*n**3 + 10365*n**2 + 21611*n + 10949. Let p(i) = d(i) - 3*g(i). Let p(s) = 0. What is s?
-1, 74
Let h = -3951961/11 - -359271. Determine s so that -6/11*s**2 + 16/11 + 2/11*s**4 - h*s + 8/11*s**3 = 0.
-4, -2, 1
Factor -11 - 326/5*x**2 - 1/5*x**5 + 214/5*x**3 - 51/5*x**4 + 219/5*x.
-(x - 1)**4*(x + 55)/5
Suppose 2*k - 3*z - 117 = 0, -2*z - 23 = -k + 35. Suppose -10*y + 0*y = -k. Determine c, given that 51 + 4*c**3 - 55 - 2*c**3 - 2*c + y*c**2 - 2*c**4 = 0.
-1, 1, 2
Let u be (-10653)/(-6) + -5 - (-14)/(-28). Let d = u + -1766. Factor 3/2*f**d + 9/2*f - 9/2*f**3 + 3/2*f**2 - 3.
3*(f - 2)*(f - 1)**2*(f + 1)/2
Let c(p) be the first derivative of 2*p**5/35 - 39*p**4/14 + 306*p**3/7 - 1445*p**2/7 + 1758. Factor c(k).
2*k*(k - 17)**2*(k - 5)/7
Let -35*q**2 + 6*q**4 + 18*q**3 + 23*q**2 - 18*q**2 - 24*q**2 - 2*q**5 = 0. What is q?
-3, 0, 3
What is i in -2*i**2 + 12*i**3 - 26*i**2 + 19*i**3 - i**5 - 2*i**4 + 445754*i - 445754*i = 0?
-7, 0, 1, 4
Let d = 126223 - 628647/5. Let h = 496 - d. Factor 9/5*j - 3/5*j**2 + h.
-3*(j - 4)*(j + 1)/5
Let a(s) be the third derivative of -s**8/336 - s**7/56 - 41*s**3/6 - 15*s**2 - 3. Let z(x) be the first derivative of a(x). Factor z(w).
-5*w**3*(w + 3)
Let k(s) be the second derivative of 22*s + 63*s**2 + 1/4*s**4 - 43/2*s**3 - 8. Let k(z) = 0. Calculate z.
1, 42
Determine s, given that 18/7*s**4 - 57/7*s + 36 - 3/7*s**5 + 60/7*s**3 - 270/7*s**2 = 0.
-4, -1, 1, 3, 7
Let f(a) = -3*a**3 - 162*a**2 - 149*a + 533. Let c be f(-53). Suppose 2 + 98/9*o**2 - 52/3*o - 16/9*o**c = 0. Calculate o.
1/8, 3
Let u be 2/(-3) + (3 - 35/15). Let 40*b**2 - 20*b - 5*b**3 + u*b - 15*b**2 = 0. Calculate b.
0, 1, 4
Suppose 27 = -f + 3*a, 6*a - 2*a + 8 = 0. Let o = f + 39. Factor -3*z**2 + 8*z + o*z**2 + z**2.
4*z*(z + 2)
Let l(z) be the second derivative of 1/4*z**3 + 1/48*z**4 + 162*z + 1 + 9/8*z**2. Find n, given that l(n) = 0.
-3
Let o be (38/(-20) + -11 + 13)/((-1)/(-4)). Let q(l) be the first derivative of -o*l**5 - 7*l**2 - 5/2*l**4 - 6*l**3 - 5 - 4*l. Find j, given that q(j) = 0.
-2, -1
Let m = 678/4781 - -5/4781. Let z(j) be the first derivative of 1/14*j**4 - 2/21*j**3 + 2/35*j**5 - 39 + 0*j - m*j**2. Find q, given that z(q) = 0.
-1, 0, 1
Suppose -7018 = -5*t - 6*l + 2*l, 0 = -5*t - l + 7012. Let h = -9804/7 + t. Factor 16/7*a**2 + 2/7*a**4 - 8/7*a + 0 - h*a**3.
2*a*(a - 2)**2*(a - 1)/7
Let v = -245 - -247. Suppose -5*y + 4*z - 20 = 0, 15*z - 17*z + 10 = -v*y. Factor 0 + 3/8*d**4 - 3/8*d**3 - 3/4*d**2 + y*d.
3*d**2*(d - 2)*(d + 1)/8
Let -1/8*m**5 - 351/8*m**4 + 59168 - 28896*m - 26228*m**2 - 4000*m**3 = 0. Calculate m.
-172, -4, 1
Let r(q) be the third derivative of q**8/840 - q**7/175 - 7*q**6/100 + 83*q**5/150 - q**4 - 463*q**2. Determine c, given that r(c) = 0.
-5, 0, 1, 3, 4
Solve 0 + 2738/7*j**2 + 2/7*j**4 - 196*j**3 - 1368/7*j = 0.
0, 1, 684
Let z(a) = -a**3 - 17*a**2 + 258*a + 3962. Let m be z(-20). Let 2/3*y**m - 2 - 4/3*y = 0. Calculate y.
-1, 3
Find n, given that 536 - 4185*n + 1577 - 25*n**2 + 980 - 573 = 0.
-168, 3/5
Suppose -76*g + 73*g = 216. Let l = g - -75. Factor 163*a**3 + 26*a**l - 36 - 429*a**2 - 234*a**2 + 300*a.
3*(a - 3)*(7*a - 2)*(9*a - 2)
Factor -161 + 150*i**2 - 3*i**3 - 119 - 651 + 48*i - 479 - 441*i.
-3*(i - 47)*(i - 5)*(i + 2)
Let b(m) = -9*m**3 + 4*m**2 + 5*m - 4. Let u(y) = 17*y**3 - 7*y**2 - 10*y + 7. Suppose 44 = 172*r - 161*r. Let j(i) = r*u(i) + 7*b(i). Let j(c) = 0. What is c?
-1, 0, 1
Suppose 28*c = 173 - 33. Let d(x) = 10*x**2 + 20*x - 5. Let j(k) = 11*k**2 + 21*k - 8. Let t(q) = c*j(q) - 6*d(q). What is s in t(s) = 0?
-2, -1
Let k be 3/(-5) - (-2 - (3