42
Let r = 393 - 1959/5. Let k = 9/52 - -787/260. Factor -k - r*g**2 - 28/5*g.
-2*(g + 4)*(3*g + 2)/5
Suppose -5*v + 3*x - 9 = 0, -4*v - 7*x - 13 + 81 = 0. Let 98/15*w + 2/15*w**4 + 0 + 2*w**v + 42/5*w**2 = 0. What is w?
-7, -1, 0
Let l(i) = 4*i - 7. Let z be l(3). Let r(b) be the third derivative of 0*b - 1/36*b**4 - 1/45*b**z + 0*b**3 - 1/180*b**6 + 0 + 2*b**2. Let r(h) = 0. What is h?
-1, 0
Let j = -13 - -13. Factor 4*m**2 + j*m - 6*m + 0*m**2 - 6*m + 8.
4*(m - 2)*(m - 1)
Let u = 119 - 122. Let n be 7/(-21) + ((-74)/30 - u). Solve -2/5*d - 1/5 - n*d**2 = 0.
-1
Let v be (-6)/96 + (1270/(-160) - -10). Let -3/2*a**3 + 3/2*a**4 + 0*a - 3*a**v + 0 = 0. Calculate a.
-1, 0, 2
Let h(d) be the third derivative of d**6/1260 - d**5/70 - 11*d**4/126 - 336*d**2. Factor h(f).
2*f*(f - 11)*(f + 2)/21
Let u(l) be the second derivative of l**4/24 + 5*l**3/3 - 69*l. Factor u(q).
q*(q + 20)/2
Let u(y) = -2*y**3 - 10*y**2 + 4*y + 30. Let x(d) = d**2 - d - 1. Suppose 0 = -3*g - a + 10, -5*g = -a - 0*a - 6. Let z(i) = g*u(i) + 44*x(i). Factor z(b).
-4*(b - 4)*(b - 1)**2
Suppose -202*w = -171*w - 31. Factor n**2 - 1/2*n + 1/2*n**3 - w.
(n - 1)*(n + 1)*(n + 2)/2
Suppose -o + 6 + 2 = 2*y, 0 = -3*o - 4*y + 18. Suppose o = 55*z - 54*z. Find g, given that -2/9*g**4 + 14/9*g**3 - 10/3*g**2 + 0 + z*g = 0.
0, 1, 3
Let k be ((-40)/(-105))/((264/(-28))/(-11)). Factor k*w + 2/3 - 2/9*w**2.
-2*(w - 3)*(w + 1)/9
Let j(s) = s**2 + 454*s + 17326. Let w(r) = -12*r**2 - 5901*r - 225237. Let v(y) = -27*j(y) - 2*w(y). Factor v(b).
-3*(b + 76)**2
Let x(v) be the first derivative of -23 - 7/8*v**2 + 1/2*v - 1/3*v**3. Determine j, given that x(j) = 0.
-2, 1/4
Let h(y) be the third derivative of 2/15*y**3 + 1/15*y**4 + 1/75*y**5 + 0*y + 0 - 4*y**2. Factor h(b).
4*(b + 1)**2/5
Suppose 213 = 5*i + 178. Let o(f) be the third derivative of 0*f**3 + 1/392*f**8 + 0*f**5 + 3*f**2 - 1/84*f**4 + 8/735*f**i + 0*f + 0 + 1/70*f**6. Factor o(y).
2*y*(y + 1)**3*(3*y - 1)/7
Suppose -1/5*m**2 + 1/5 + 0*m = 0. Calculate m.
-1, 1
Let q(y) = -2*y**2 - 13*y - 17. Let w be q(-4). Let r(v) be the first derivative of 0*v**2 - 1/3*v**4 + 4/9*v**w + 0*v - 6. Determine j so that r(j) = 0.
0, 1
Let z be 10/(-15)*(-1)/7. Let b(i) be the first derivative of 0*i + 1/7*i**2 - 1 + z*i**3. Factor b(o).
2*o*(o + 1)/7
Let p(i) be the second derivative of i**5/10 - i**4/6 - 4*i**3/3 + 4*i**2 + 215*i. Solve p(t) = 0 for t.
-2, 1, 2
Let z(f) = -38*f**3 - 724*f**2 - 40*f - 36. Let p be z(-19). Factor 1/4*x**4 - x**3 + 0 - 11/4*x**p - 3/2*x.
x*(x - 6)*(x + 1)**2/4
Factor -6/5*r + 0*r**2 + 2/5*r**3 + 4/5.
2*(r - 1)**2*(r + 2)/5
Let l(c) = c**3 + 2*c**2 + c + 2. Let v be l(-2). Suppose v = -13*z + 9*z. Factor z - 1/4*t**2 - 1/4*t**3 + 1/4*t**4 + 1/4*t.
t*(t - 1)**2*(t + 1)/4
Let m be -1*3*((-880)/60 + 14). Suppose 12*c**m - 32/3*c - 20/3*c**4 - 16/3 + 32/3*c**3 = 0. What is c?
-1, -2/5, 1, 2
Let y be (-21 - 1038/(-54))*(-3)/4. Solve 26/3*o**2 + 0 - y*o = 0 for o.
0, 2/13
Let m(p) be the first derivative of p**6/3 - 26*p**5/5 + 55*p**4/2 - 142*p**3/3 - 40*p**2 + 200*p - 278. Find c such that m(c) = 0.
-1, 2, 5
Let b be 2/13 + 50/13. Suppose b*i - 5 = 7. Factor -2*q - 6 - i*q**2 + q - 8*q.
-3*(q + 1)*(q + 2)
Let t(f) be the third derivative of -f**6/360 + 7*f**4/72 + f**3/3 + 19*f**2. Determine u so that t(u) = 0.
-2, -1, 3
Suppose -5*j + k + 20 = 0, -3*j + 6 + 6 = 5*k. Let y(l) be the first derivative of j*l**3 + 15/2*l**2 + 3/4*l**4 + 6*l - 3. Solve y(z) = 0 for z.
-2, -1
Let u(d) be the second derivative of -d**4/6 - 256*d**3/3 - 16384*d**2 + 175*d. What is g in u(g) = 0?
-128
Let l = 6430 + -44998/7. Let -l + 9/7*p + 3*p**2 = 0. What is p?
-1, 4/7
Let n be 14/6 + (-4)/(-6). Let u(x) = x**2 + x. Let v be u(-1). Factor -n*k**2 + k**2 + 7*k + k + v - 8.
-2*(k - 2)**2
Let m(v) be the second derivative of -12*v + 0 + 0*v**2 - 1/30*v**4 + 0*v**3. Factor m(a).
-2*a**2/5
Let g(f) be the first derivative of f**4 + 4*f**3 - 20*f**2 + 40. Factor g(d).
4*d*(d - 2)*(d + 5)
Let t be (-8 - -8)*((1 - 1) + 1). Let p be 0/(t + -1 + -1). Find n such that 2/7*n**5 + p*n - 2/7*n**2 + 2/7*n**4 - 2/7*n**3 + 0 = 0.
-1, 0, 1
Let q(o) be the first derivative of 2/15*o**3 - 1/5*o**2 - 2/25*o**5 + 0*o + 1/10*o**4 - 5. Let q(f) = 0. Calculate f.
-1, 0, 1
Let l(u) = -3*u**4 + u**3 + 24*u**2 - 28*u + 7. Let b(z) = -2*z**4 + z**3 + 16*z**2 - 20*z + 5. Let s(x) = 7*b(x) - 5*l(x). Factor s(m).
m**2*(m - 2)*(m + 4)
Let y = -7854/19 - -39289/95. Find f such that -1/5*f + 4/5*f**2 - 6/5 - y*f**3 = 0.
-1, 2, 3
Suppose -8*c + 25 = -3*c. Factor -14*n**2 + c - 5 + 12*n**2.
-2*n**2
What is g in 2/5*g**5 + 24642/5*g**3 - 444/5*g**4 + 0*g**2 + 0*g + 0 = 0?
0, 111
Determine y, given that 15/7*y**3 - 3/7 + 3/7*y**2 - 15/7*y = 0.
-1, -1/5, 1
Let w(y) be the first derivative of -y**4/4 + 13*y**3/3 - 20*y**2 + 36*y + 153. Suppose w(a) = 0. Calculate a.
2, 9
Let v(g) be the second derivative of -g**6/15 + 11*g**5/10 - 19*g**4/3 + 52*g**3/3 - 24*g**2 - 50*g. Factor v(l).
-2*(l - 6)*(l - 2)**2*(l - 1)
Let d(a) be the second derivative of -2*a**6/15 + 3*a**5/5 + a**4/3 - 2*a**3 + 100*a. Solve d(s) = 0 for s.
-1, 0, 1, 3
Let j(d) be the second derivative of -d**7/672 + d**6/72 - d**5/24 - d**3/2 - 10*d. Let p(b) be the second derivative of j(b). Factor p(v).
-5*v*(v - 2)**2/4
Let m(t) be the third derivative of -t**9/18144 + t**8/3360 - t**6/540 - 5*t**3/3 - 17*t**2. Let g(v) be the first derivative of m(v). Let g(d) = 0. What is d?
-1, 0, 2
Let h(p) = -p**2 - 114*p + 979. Let v be h(8). Factor 180/7*y + 354/7*y**2 + 180/7*y**v + 27/7 + 27/7*y**4.
3*(y + 3)**2*(3*y + 1)**2/7
Suppose -12 = 3*n + 4*j, n - 31*j + 36*j + 26 = 0. Solve 0 - 6/7*m**2 + 3/7*m**3 + 3/7*m**n + 0*m = 0 for m.
-2, 0, 1
Let n = 204/5 + -40. Let h(b) be the first derivative of -2 - n*b + 3/5*b**2 - 2/15*b**3. Factor h(v).
-2*(v - 2)*(v - 1)/5
Let t(j) = j**2 - 46*j - 6. Let l(b) = 5*b**2 - 186*b - 26. Let u(m) = 6*l(m) - 26*t(m). Factor u(k).
4*k*(k + 20)
Let x = 2281 - 6835/3. Find u, given that 12*u**2 - 24*u + 2/9*u**4 - x*u**3 + 18 = 0.
3
Let m(g) = -7*g**5 - 17*g**4 + 20*g**2 + 6*g + 2. Let h(l) = l**5 + 2*l**4 - l**3 - l + 1. Let d(b) = 6*h(b) - 3*m(b). Suppose d(u) = 0. Calculate u.
-2, -2/3, 0, 1
Let r(y) = y - 5. Let d be r(7). Factor -2*x**2 + 98 - 71 - 18*x - d*x**2 + 7*x**2.
3*(x - 3)**2
Solve -184/9*h**3 - 2/9*h**4 - 559682/9 - 97336/9*h - 2116/3*h**2 = 0 for h.
-23
Let x(p) be the first derivative of 2*p**5/5 + 341*p**4/4 + 6441*p**3 + 360639*p**2/2 - 185193*p - 160. Factor x(a).
(a + 57)**3*(2*a - 1)
Factor 5*o**4 - 1/5*o**5 - 23*o**3 - 101*o**2 - 112*o - 196/5.
-(o - 14)**2*(o + 1)**3/5
Let 9/5 + 9/5*y**4 - 6*y**3 + 3*y + 3*y**5 - 18/5*y**2 = 0. Calculate y.
-1, -3/5, 1
Suppose 7*n = 5*n - 2*s + 2, s = 5*n - 23. Find y, given that 1/2*y**2 + 0*y + 0 + 0*y**3 - 1/2*y**n = 0.
-1, 0, 1
Let g be -1 - -1 - 5/(-5). Find i such that 0*i**2 + 8*i + 4*i**2 - g + 5 = 0.
-1
Let a(v) be the first derivative of -v**5/10 + 5*v**4/8 + 7*v**3/6 - 5*v**2/4 - 3*v - 47. Solve a(t) = 0.
-1, 1, 6
Let h(r) = -2*r**3 - r. Let b be h(-1). Suppose -1 = -2*l + 3. Factor y - y**l + b*y - 5*y.
-y*(y + 1)
Let p(l) = l**2 - 18*l + 4. Let t be p(18). Suppose t*n + n = 10. Factor 5*c**2 + 2*c**2 - 2 - 4*c - 9*c**n.
-2*(c + 1)**2
Let b(x) = 5*x + 5. Let h be b(-3). Let s = h + 13. Determine m so that 8*m**s - 9*m**4 + m + m + 9*m**2 - 7*m**5 + 0*m**5 - 3*m**3 = 0.
-1, -2/7, 0, 1
Let w(k) be the first derivative of -2/3*k - 1/9*k**3 + 1/2*k**2 + 11. Factor w(a).
-(a - 2)*(a - 1)/3
Let u(p) = -5*p**2 - 27*p - 48. Let h(n) = 60*n**2 + 325*n + 575. Let r(b) = 3*h(b) + 35*u(b). Let r(t) = 0. Calculate t.
-3
Let j be (-1)/(-10 + (-136)/(-17)). Determine y so that -1/4*y**2 + 0 + 1/4*y**4 - j*y**3 + 1/2*y = 0.
-1, 0, 1, 2
Let u(l) = -2*l**2 + 17*l - 21. Let s be u(7). Let z be (s/(-1))/(3 + -2). Determine j, given that z*j + 0 - j**2 - 1/2*j**3 = 0.
-2, 0
Suppose 2*n - 8 = -5*a + n, -a + 5*n + 12 = 0. Factor h**2 - 9*h**4 - 5*h**a + 12*h**4 - 5*h**4 - 6*h**3.
-2*h**2*(h + 1)*(h + 2)
Factor 1/7*m**3 - 3/7*m - 4/7*m**2 + 18/7.
(m - 3)**2*(m + 2)/7
Let u = -5101/2 + 2552. Factor -3/2 - u*j**2 + 3*j.
-3*(j - 1)**2/2
Find j, given that 2805/7*j**2 - 6050/7*j + 1/7*j**4 + 0 + 108/7*j**3 = 0.
-55, 0, 2
Let a(y) be the first derivativ