Let k = 1 - -9. Suppose 2*n - 7*n = -k. Factor -2*t**2 + 2*t**3 + 0*t**n - 2*t**2 - 6*t**3.
-4*t**2*(t + 1)
Find i such that 38/5*i**2 + 2/5*i**3 + 42/5 - 82/5*i = 0.
-21, 1
Let x(l) be the third derivative of l**8/448 + 3*l**7/280 - 17*l**6/160 + 9*l**5/80 + l**4/2 - 3*l**3/2 + 2*l**2 + 61. Find g, given that x(g) = 0.
-6, -1, 1, 2
Factor -o - 1/2*o**2 + 3/2.
-(o - 1)*(o + 3)/2
Suppose -2*s + 37*s = 0. Factor -1/2*m**3 + 0*m + s - 2/3*m**4 + 1/6*m**2.
-m**2*(m + 1)*(4*m - 1)/6
Let v(u) be the first derivative of -3/8*u**4 - 3*u**2 - 7 - 1/40*u**6 - 3/20*u**5 - 1/2*u**3 + 0*u. Let s(x) be the second derivative of v(x). Factor s(q).
-3*(q + 1)**3
Let q(k) be the second derivative of 0*k**2 - 3*k**6 - 12/5*k**5 + 0 - 11*k + 0*k**3 - 25/21*k**7 - 2/3*k**4. Let q(f) = 0. What is f?
-1, -2/5, 0
Let u be (-60)/(-120) - (-3)/2. Let p(l) be the first derivative of 1/3*l**3 + 1/2*l**u - l - 1/4*l**4 - 3. Find x such that p(x) = 0.
-1, 1
Let y(f) be the third derivative of -f**7/70 - 3*f**6/20 - 2*f**5/5 + 3*f**4/4 + 9*f**3/2 - 181*f**2. Determine q, given that y(q) = 0.
-3, -1, 1
Suppose -4*z + z = -27. Let s(w) = -w + 9. Let g be s(z). Factor 0*q + 1/2*q**3 + q**2 + g.
q**2*(q + 2)/2
Let i(m) be the first derivative of -m**7/294 - m**6/70 - 3*m**5/140 - m**4/84 - 21*m - 13. Let z(n) be the first derivative of i(n). Factor z(p).
-p**2*(p + 1)**3/7
Let i be 1*21 - 233873/11219. Factor 4/13*o**2 - 6/13*o**3 + 0*o + 0 + 0*o**4 + i*o**5.
2*o**2*(o - 1)**2*(o + 2)/13
Suppose -302*t - 78 = -328*t. Determine y, given that -35/4*y**2 + 5/2*y**4 - 15/2*y + 0 + 5/4*y**t = 0.
-3/2, -1, 0, 2
Let s = 1079251/54 + -19985. Let f(u) be the second derivative of -3*u - 49/45*u**6 - 8/27*u**3 - 4/9*u**2 + s*u**4 + 49/45*u**5 + 0. Solve f(l) = 0.
-1/3, -2/7, 2/7, 1
Let v(l) be the first derivative of l**3/3 - l**2/2 + 2*l + 4. Let q be v(0). Suppose -2*f**q + 3*f**2 + f**2 = 0. Calculate f.
0
Suppose -5*j + 16 = -4. Determine r so that -r**3 - j*r**3 - 10*r**2 + 10*r + 5*r**2 = 0.
-2, 0, 1
Let j = 18823/4 + -4705. Factor -j*y - y**3 - 13/4*y**2 + 0.
-y*(y + 3)*(4*y + 1)/4
Let r = 692 + -692. Let l(p) be the third derivative of p**3 + 0 + r*p + 2*p**2 + 3/8*p**4 + 1/20*p**5. Find c such that l(c) = 0.
-2, -1
Let i(n) = 11*n**3 - 531*n**2 + 4899*n + 1447. Let o(q) = -23*q**3 + 1061*q**2 - 9799*q - 2893. Let v(z) = -5*i(z) - 3*o(z). Factor v(s).
2*(s - 19)**2*(7*s + 2)
Let m = -26249 + 26252. What is j in 9/2*j - 3/2 - 9/2*j**2 + 3/2*j**m = 0?
1
Let c(w) be the first derivative of 2*w**6/3 + 4*w**5/5 - 35*w**4/4 - 8*w**3/3 + 85*w**2/2 - 50*w - 510. Solve c(o) = 0.
-5/2, 1, 2
Suppose -y = 4*y - 150. Determine h so that -123*h**5 - 73*h**2 - 65*h**3 - 20*h - y*h**4 + 118*h**5 + 13*h**2 = 0.
-2, -1, 0
Suppose -400*l + 3 - 15*l**2 + 400*l + 12*l**2 = 0. What is l?
-1, 1
Let g = -467/34 - -6361/374. Solve -g*a - 2/11*a**2 - 162/11 = 0 for a.
-9
Let w = -10 - -15. Suppose -z + w = 3. Factor t**5 - 46*t**2 - 4*t**3 + t + 46*t**2 + z*t**3.
t*(t - 1)**2*(t + 1)**2
Suppose -3*d = -4*d + 4*u + 36, 3*u + 79 = 4*d. Let c be -3*d/12 + 11. Find q, given that 4*q**2 + 3*q - 8 + 2*q - c*q + 6*q = 0.
-2, 1
Let p(v) = 5*v**2 - 4*v - 8. Let y(q) = -3*q**2 + 3*q + 5. Let m(k) = 5*p(k) + 8*y(k). Let u be m(-6). Factor -u + 2*r**2 + r**2 - 4*r**2 - 2*r**2 + 12*r.
-3*(r - 2)**2
Solve 1040*r - 2021*r - 3*r**2 + 1041*r + 207 = 0.
-3, 23
Let l(y) = 2*y**2 - y - 2. Let q be l(-2). Suppose -2*x + 0*n = n - q, 5*n - 16 = -2*x. Determine k so that 0*k + 3*k**4 - 9*k**2 + 6*k + k**x - k**3 = 0.
-2, 0, 1
Let r = -1162 - -1743. Solve -7*p + 577*p**2 - 8 + 19*p - r*p**2 = 0.
1, 2
Let a be -1*(-737)/(-55) + 14. Factor a*u**3 + 0 + 3/5*u**4 - 3/5*u**5 - 3/5*u**2 + 0*u.
-3*u**2*(u - 1)**2*(u + 1)/5
Let v(n) be the first derivative of -n**6/1080 - n**5/45 - 2*n**4/9 + 12*n**3 + 10. Let i(r) be the third derivative of v(r). Factor i(t).
-(t + 4)**2/3
Solve 5*p**3 + 6*p**3 + 0*p**3 + 5*p**4 + 55*p**2 + 24*p**3 + 25*p = 0.
-5, -1, 0
Let t(g) be the third derivative of 0*g + 4/45*g**5 + 19/36*g**4 + 2/3*g**3 - 40*g**2 + 0 - 1/36*g**6. Factor t(b).
-2*(b - 3)*(b + 1)*(5*b + 2)/3
Let f(o) be the first derivative of o**8/2100 + o**7/525 - o**6/450 - o**5/75 + 2*o**3 + 20. Let s(r) be the third derivative of f(r). Factor s(w).
4*w*(w - 1)*(w + 1)*(w + 2)/5
Let g(d) = 10*d**3 - 12*d**2 - 166*d. Let a(f) = 2*f**3 - 2*f**2 - 33*f. Let j(i) = 16*a(i) - 3*g(i). Suppose j(n) = 0. Calculate n.
-5, 0, 3
Let x(a) be the second derivative of -a**4/96 - 21*a**3/16 + 203*a. Factor x(p).
-p*(p + 63)/8
Let z(s) be the first derivative of s**5/240 + s**4/48 - s**3/8 + s**2 - 14. Let b(k) be the second derivative of z(k). Find d such that b(d) = 0.
-3, 1
Let n(x) = 6*x**2 + 505*x - 8199. Let m(g) = -4*g**2 - 252*g + 4100. Let f(u) = -7*m(u) - 4*n(u). Find c such that f(c) = 0.
32
Factor 10/7*t**2 - 6/7*t**3 + 0 - 4/7*t - 2/7*t**4 + 2/7*t**5.
2*t*(t - 1)**3*(t + 2)/7
Let r(y) be the third derivative of -y**5/270 + y**4/108 + 87*y**2. Factor r(d).
-2*d*(d - 1)/9
Suppose 0 = 6*u - 13 - 5. Suppose 5*k**u + 4 + 25*k + 6 - 10*k**2 + 30*k**2 = 0. What is k?
-2, -1
Let h be 20/11 - ((-696)/(-44) - 16). Let n(i) be the first derivative of 11 + 1/7*i - 1/7*i**h + 0*i**3 + 1/14*i**4 - 1/35*i**5. Factor n(v).
-(v - 1)**3*(v + 1)/7
Let r(d) be the third derivative of d**8/43680 + d**7/16380 - d**6/4680 - d**5/780 + d**4/12 - 9*d**2. Let f(j) be the second derivative of r(j). Factor f(m).
2*(m - 1)*(m + 1)**2/13
Suppose 112 = 2*j + 3*c + 13, 5*j + 5*c - 240 = 0. Suppose -5*t = -25, -6*l + l - t + j = 0. Factor -23*m - 11*m - l - 41*m**2 + 2*m - m**2 - 18*m**3.
-2*(m + 1)*(3*m + 2)**2
Let h(v) = v**2 + v. Suppose -5*b + 3*i = -0 - 11, 2*i + 7 = 3*b. Let d be h(b). Factor -24 + 20*t**2 + 75*t**4 - 46*t**d - 52*t**2 + 18*t + 90*t - 135*t**3.
3*(t - 2)*(t + 1)*(5*t - 2)**2
Let x = 63 + -23. Suppose 11*w**2 + 11 - 425*w**4 - 430*w**3 - 11 + 9*w**2 - 105*w**5 + x*w = 0. What is w?
-2, -1/3, 0, 2/7
Solve -z**4 - 2*z**2 + 4*z**4 + 3 - 4*z**3 + 0*z**2 - 4*z**4 + 4*z = 0.
-3, -1, 1
Let m = 239 - 125. Let f be m/95 + 2/(-2). Let -1/5 - 1/5*i + f*i**3 + 1/5*i**2 = 0. What is i?
-1, 1
Let a be (5 - 5) + (1378/(-252) - -3). Let r = 2/63 - a. Factor 2*l**2 + 1 + r*l + 1/2*l**3.
(l + 1)**2*(l + 2)/2
Suppose -f = -6*u + 8*u - 6, 5*u = 10. Factor -1/5*v**f + 0*v + 1/5.
-(v - 1)*(v + 1)/5
Let f(w) = w + 4. Let o be f(-1). Let m(b) be the first derivative of 0*b + 0*b**o - 1/12*b**4 + 0*b**2 + 1/18*b**6 + 5 + 0*b**5. Let m(i) = 0. What is i?
-1, 0, 1
Suppose 5*m + 30 = 15*m. Solve 41*g**3 + 21*g**2 - 4*g**4 - 17*g + m - 25*g**3 - 19*g**3 = 0.
-3, 1/4, 1
Let q(r) be the third derivative of -3*r**6/28 + 43*r**5/210 + r**4/42 - r**2 - 69*r. Let q(x) = 0. Calculate x.
-2/45, 0, 1
Let y(m) be the first derivative of 0*m**4 - 1/20*m**5 + 1/4*m**3 - 1/4*m**2 + 0*m - 20. Factor y(h).
-h*(h - 1)**2*(h + 2)/4
Let a be (-3)/32*-8 - (-35)/28. Find g such that 8/7*g**3 + 6*g - 18/7 - 32/7*g**a = 0.
1, 3/2
Let t(g) be the first derivative of 3/2*g**2 - 3/5*g**5 - 3/2*g**4 + 1/2*g**6 - 29 - 3*g + 2*g**3. Factor t(w).
3*(w - 1)**3*(w + 1)**2
Determine h so that 13*h + 47*h**5 + 47*h**5 - 141*h**5 - 14*h**3 - 8*h**2 + 48*h**5 + 10 + h**4 - 3*h**4 = 0.
-2, -1, 1, 5
Let -8/3 - 2*j - 1/3*j**2 = 0. What is j?
-4, -2
Let v(d) be the second derivative of -1/80*d**5 + 0*d**3 + 0 + 1/168*d**7 - 1/40*d**6 - 1/2*d**2 + 5*d + 7/48*d**4. Determine g so that v(g) = 0.
-1, 1, 2
Let v be -163 + 172 - (-34)/(-6). Let f = 194/57 - 14/19. Let -f - 10*y**2 + 32/3*y + v*y**4 - 4/3*y**3 = 0. What is y?
-2, 2/5, 1
Find z, given that 2/11*z**2 - 4/11*z - 16/11 = 0.
-2, 4
Let f(d) = 12*d**4 + 8*d**3 - 22*d**2 + 4*d + 2. Let g(z) = -z**4 - z**3 - z**2 + 2*z - 1. Let p(j) = -2*f(j) - 4*g(j). Factor p(m).
-4*m*(m - 1)*(m + 2)*(5*m - 2)
Suppose -4*o = -28, 13*o + 28 = -5*t + 17*o. Solve t*q**2 + 8/5*q**3 + 0 + 12/5*q**4 + 9/10*q**5 + 0*q = 0.
-4/3, 0
Let p be -5*(-2)/345*-1. Let s = p - -73/138. What is w in -1/2*w**2 + 0 + s*w = 0?
0, 1
Let d(s) = 2*s + 1. Let c be d(2). Suppose -6*h + 10 - 4*h + 7*h - 2*h - c*h**2 = 0. What is h?
-2, 1
Suppose -71*v**2 + 37*v**2 + 42*v**2 - 14*v**5 - 40*v**3 + 46*v**4 = 0. Calculate v.
0, 2/7, 1, 2
Let v = 9339/28 + -2333/7. Factor 1/4*g**2 + v*g + 0.
g*(g + 1)/4
Let g(n) =