4*x + 5*x**2.
x*(x + 1)**2*(x + 2)
Let z(d) be the second derivative of -3*d**6 + 91*d**5/10 - d**4/3 - 313*d. Factor z(u).
-2*u**2*(u - 2)*(45*u - 1)
Let u(y) be the first derivative of y**3/2 - 27*y**2/2 + 243*y/2 - 183. Factor u(s).
3*(s - 9)**2/2
Let v = -128 - -131. Suppose -2*k + 4*y = 6, -v*y = 2*k - 4 - 11. Factor 0 + 2/9*f + 32/9*f**k - 16/9*f**2.
2*f*(4*f - 1)**2/9
Let r = 59 + -57. Let u(h) be the second derivative of 0 - 1/2*h**3 - 2*h + 1/2*h**4 + 0*h**r. Determine n so that u(n) = 0.
0, 1/2
Factor -426*a**2 + 0*a**3 + a**4 + 429*a**2 - a - 3*a**3.
a*(a - 1)**3
Let p = -109 - -63. Let b be p/3*5/(-20). Suppose -b*g**2 - 3/2*g**3 + 2/3 + 0*g + 5/3*g**4 = 0. What is g?
-1, -1/2, 2/5, 2
Let c(k) = 2*k + 16. Let q = -21 + 13. Let n be c(q). Determine s so that 1/2*s**3 + 0 + n*s + 0*s**2 + 1/2*s**4 = 0.
-1, 0
Let v(z) be the first derivative of 2*z**2 - 1/20*z**5 - 1/4*z**4 + 0*z**3 - 4 + 3*z. Let j(f) be the first derivative of v(f). Factor j(b).
-(b - 1)*(b + 2)**2
Suppose -5*m - 15 + 30 = 0. Find j, given that -1 + m - 8*j + 64*j**3 - 12*j**2 + 24*j**5 - 101*j**4 + 31*j**4 = 0.
-1/3, 1/4, 1
Let c(w) be the first derivative of w**4 + 28*w**3/3 + 20*w**2 + 216. Factor c(g).
4*g*(g + 2)*(g + 5)
Factor -1/5*x**2 + 0 + 6/5*x**3 - 6/5*x + 1/5*x**4.
x*(x - 1)*(x + 1)*(x + 6)/5
Suppose -5 + 1 = 4*u, -s - 12 = 2*u. Let w be (34/s - -3)*-10. Find m, given that -4*m**4 - 5*m**2 - m**4 + 14*m**3 - w*m**3 = 0.
0, 1
Let -5*u + 1/2*u**2 + 21/2 = 0. What is u?
3, 7
Let k(o) be the second derivative of 5*o**4/12 + 10*o**3/3 - 5*o**2/2 - 34*o. Let n(s) = -2*s**2 - 10*s + 3. Let m(t) = 3*k(t) + 5*n(t). Factor m(j).
5*j*(j + 2)
Let x(p) = -2*p**2 - 14*p - 9. Let a(m) = 2*m**2 + 16*m + 10. Let w(r) = 3*a(r) + 4*x(r). Factor w(t).
-2*(t + 1)*(t + 3)
Let r = 925/2 - 462. Solve -1/2*j**2 + 0*j - r*j**4 + j**3 + 0 = 0 for j.
0, 1
Let x(h) = 3*h**3 + 87*h**2 + 12. Let j(u) = -4*u**3 - 88*u**2 - 14. Let z(t) = -6*j(t) - 7*x(t). Factor z(k).
3*k**2*(k - 27)
Suppose -23*p**4 + 4*p**5 + 4*p - 16*p**2 + 5*p**4 - 3*p**4 + 24*p**3 + 2*p**4 + 3*p**4 = 0. Calculate p.
0, 1
Let h(p) be the third derivative of p**8/112 + 3*p**7/70 - p**6/8 - 3*p**5/20 + p**4/2 - 31*p**2. Factor h(k).
3*k*(k - 1)**2*(k + 1)*(k + 4)
Let w(p) be the third derivative of -1/3*p**5 + 2/21*p**7 + 0*p - 4*p**2 - 5/6*p**4 + 5/336*p**8 + 1/8*p**6 + 0*p**3 + 0. Solve w(i) = 0.
-2, -1, 0, 1
Let h(w) be the first derivative of 9*w**2 - 1/3*w**3 + 25 - 81*w. Factor h(d).
-(d - 9)**2
Let i(o) = -o**2 - 9*o + 8. Let b be i(-10). Let j be (32/6)/(-4)*3/b. Factor -1/2*q**2 - j + 2*q.
-(q - 2)**2/2
Let n = 17 - 15. What is k in 0*k**2 + 2 - k**2 + 2*k**n + 0*k**2 + 3*k = 0?
-2, -1
Let a(j) be the third derivative of j**7/70 - 23*j**6/240 + 7*j**5/60 + j**4/16 - 361*j**2. Factor a(b).
b*(b - 3)*(b - 1)*(6*b + 1)/2
Let m(d) be the first derivative of 3*d**5 - 35/4*d**4 - 10*d + 21 + 5*d**3 + 15/2*d**2. Let m(n) = 0. What is n?
-2/3, 1
Let r(x) be the third derivative of x**8/112 - 11*x**7/70 + 13*x**6/20 - 4*x**5/5 + 478*x**2. Let r(q) = 0. Calculate q.
0, 1, 2, 8
Let w = -2839 - -2842. Factor 0 + 0*u**2 - 5/4*u**w + 0*u.
-5*u**3/4
Let h(v) be the third derivative of v**5/450 + 11*v**4/180 + 34*v**2. Factor h(q).
2*q*(q + 11)/15
Let m(c) = 7*c**2 - 198*c + 12. Let z(t) = -6*t**2 + 198*t - 9. Let j(r) = 3*m(r) + 4*z(r). Solve j(x) = 0 for x.
0, 66
Let c(k) be the second derivative of -159*k**5/20 + 13*k**4 + k**3/2 - 408*k. Solve c(y) = 0 for y.
-1/53, 0, 1
Let u be 2/(-1)*15/(-10). Factor 5*c**u - 10*c + 3*c - 2*c**3 - 5*c.
3*c*(c - 2)*(c + 2)
Let d = -43 - -87/2. Let m(z) be the second derivative of d*z**3 + 0 + 0*z**2 + 3/40*z**5 - 2*z + 3/8*z**4. Factor m(u).
3*u*(u + 1)*(u + 2)/2
Suppose -5/3*u**3 + 17/3*u + 1/3*u**4 - 10/3 - u**2 = 0. What is u?
-2, 1, 5
Let b(t) = -t**2 - 10*t - 3. Let a be b(-9). Let j = a + -2. Find w, given that 2*w**5 - w**4 - w**2 - w**4 - j*w**4 - w**2 + 6*w**3 = 0.
0, 1
Let i(o) = -1181*o - 4722. Let q be i(-4). Factor 0 - 2/9*h**3 + 2/3*h + 4/9*h**q.
-2*h*(h - 3)*(h + 1)/9
Let l be -8*-2*6/(-8). Let h be -2*((-2)/(-10) + l/10). Factor 0 + 1/3*n + 1/3*n**3 + 2/3*n**h.
n*(n + 1)**2/3
Suppose 5*t - 4 = 4*d - d, 0 = t + d - 4. Let 2*u + 8 + 6*u**2 - 14*u - 2*u**t = 0. Calculate u.
1, 2
Let p(w) = 5*w**2 - 290*w + 4205. Let d(n) = -5*n**2 + 290*n - 4205. Let o(x) = 5*d(x) + 4*p(x). Let o(q) = 0. What is q?
29
Suppose -o + 544 + 1121 = 0. Factor o*z - 1665*z - 3 + 3*z**2.
3*(z - 1)*(z + 1)
Let r(p) = 2*p**3 + p**2 - 2*p - p + 2*p. Let i(o) be the first derivative of o**4/4 - o**2/2 + 7. Let w(v) = i(v) - r(v). Factor w(t).
-t**2*(t + 1)
Solve 31*d - 19*d**3 - d**4 + 4*d**4 - 61*d + 51*d**2 - 5*d**3 = 0 for d.
0, 1, 2, 5
Let q(u) be the third derivative of -u**8/2856 + 11*u**7/1785 + 13*u**6/1020 - 11*u**5/510 - u**4/17 - 602*u**2 - u. Let q(j) = 0. What is j?
-1, 0, 1, 12
Let v = 48 + -48. Suppose 0 = -r - 4*c - 4, v = -5*r - 5*c + 10. Find d such that 0*d + d**2 - 7/2*d**r - 5/2*d**3 + 0 = 0.
-1, 0, 2/7
Let q(p) = -2*p**4 - p**3 - 2*p**2 + p - 1. Let i(k) = 7*k**4 + k**3 - 6*k**2 - 17*k - 2. Let z(m) = i(m) + 3*q(m). Factor z(u).
(u - 5)*(u + 1)**3
Let h(u) be the third derivative of -u**8/8 - 121*u**7/105 - 509*u**6/420 + 89*u**5/70 + 2*u**4/3 - 20*u**3/21 - 209*u**2 - 3. Suppose h(g) = 0. Calculate g.
-5, -1, -1/3, 2/7
Let z(f) be the first derivative of f**5/5 - 11*f**4/4 + 8*f**3 + 2*f**2 - 32*f + 406. What is c in z(c) = 0?
-1, 2, 8
Let i(a) be the first derivative of -11*a**4/4 - a - 2. Let h be i(-1). Let 4*w**3 - 14*w - 12*w + h*w = 0. What is w?
-2, 0, 2
Suppose 26/17*j**4 + 100/17*j + 0 + 2/17*j**5 + 190/17*j**2 + 114/17*j**3 = 0. Calculate j.
-5, -2, -1, 0
Let t be 3 - (35/5 - 0). Let o be 4/(t/(-2)) - (3 + -3). Let -2/3*q**o + 0 + 8/9*q**5 + 2/9*q + 2/3*q**4 - 10/9*q**3 = 0. What is q?
-1, 0, 1/4, 1
Suppose 4*b + 345 = 3*z, 3*z + 2*b = -b + 345. Find t such that -25*t**5 - 58*t**3 + z*t**4 + 4*t - 117*t**3 + 85*t**2 + 22*t - 6*t - 20 = 0.
-2/5, 1, 2
Let g = -49 + 56. Solve 9*k - 256*k**3 + 252*k**3 + g*k = 0.
-2, 0, 2
Let v be 4 - (-9)/((-27)/6). Factor -10*b + 3*b**2 + 9 + 13 - b**v - 10.
2*(b - 3)*(b - 2)
Let x(c) = c**4 - c**3 + 1. Let t(h) = 15*h**4 - 10*h**3 - 5. Suppose -2*w - 3*w = 25. Let u(j) = w*x(j) - t(j). Factor u(r).
-5*r**3*(4*r - 3)
Let d = 3629/286 - 140/11. Let u = 15/52 + d. Solve 1/2*o - u - 1/4*o**2 = 0.
1
Let m = -10555 + 73893/7. Find g, given that 0*g**4 - m*g**2 + 0 + 4/7*g**5 + 0*g - 12/7*g**3 = 0.
-1, 0, 2
Let t(x) = 4*x**2 - 38*x + 30. Let d(n) = -2*n**2 - n - 1. Let p(f) = -6*d(f) - t(f). What is c in p(c) = 0?
-6, 1/2
Let v = 3187/6 - 2156/3. Let u = 192 + v. Suppose 1/2*f**2 - 3*f + u = 0. What is f?
3
Let d(q) be the second derivative of -q**5/20 - q**4 + q**3/6 + 6*q**2 - 242*q. Determine b so that d(b) = 0.
-12, -1, 1
Let c(n) be the second derivative of 0*n**2 + 0 + 0*n**3 + 23*n + 4/3*n**4 - 1/15*n**6 - 7/10*n**5. Let c(y) = 0. Calculate y.
-8, 0, 1
Let g(o) = o**5 + 13*o**4 + 68*o**3 + 106*o**2 - 6. Let n(x) = x**4 + 2*x**3 + x**2 + 3. Let r(y) = -g(y) - 2*n(y). Let r(h) = 0. What is h?
-6, -3, 0
Factor -162*l + 71*l + 71*l - 4 - 23*l**2 + 0 - 40*l**3 - 17*l**2 - 4*l**5 - 20*l**4.
-4*(l + 1)**5
Suppose -4*t + 15 = -y, -t + 6 = 2*y - 0*y. Suppose c - 2*j = -3 + 4, 4*c = -t*j + 16. Factor -8*i**c + 4*i - 2*i + 2*i**2 + i**5 - 5*i + 1 - 3*i**4 + 10*i**3.
(i - 1)**4*(i + 1)
Solve 16*v**2 - 349*v + 2141 - 43*v - 28*v**2 + 7463 + 16*v**2 = 0 for v.
49
Suppose 4*m + 8 = 0, -3*m + 7*m + 8 = 3*g. Suppose g = -9*d + 2*d + 14. Factor 2/3*j**3 + 2/9*j**d + 0 - 4/9*j.
2*j*(j + 1)*(3*j - 2)/9
Let x(o) be the second derivative of -49*o**4/54 + 112*o**3/27 - 64*o**2/9 - 27*o. Let x(v) = 0. What is v?
8/7
Let d be 32/30 - 2/5. Let k = 3494/5259 - -4/1753. Determine v, given that -k + 0*v + d*v**2 = 0.
-1, 1
Let c(n) = 69*n**5 + 6*n**4 + 6*n**3 + 27*n**2 + 15*n - 18. Let l(o) = -5*o**5 - o**4 - o**2 - o + 1. Let a(d) = c(d) + 15*l(d). Let a(g) = 0. What is g?
-1, 1/2, 1
Let u(h) be the second derivative of -3*h**7/133 + 29*h**6/95 - 16*h**5/19 - 44*h**4/57 + 208*h**3/57 + 112*h**2/19 + 211*h. Determine t so that u(t) = 0.
-2/3, 2, 7
Let s = -6238 - -6240. Factor -2*b**s + 1/2*b**3 + 0 + 0*b.
b**2*(b - 4)/2
Solve -33*a**2 + 28663 + 228*a + 372*a