7
Let v(p) be the first derivative of -p**4/2 - 34*p**3/3 - 11*p**2 + 1210*p - 109. Find c such that v(c) = 0.
-11, 5
Let i be 14/3*(-27)/(-63). Let p(s) be the second derivative of -1/120*s**6 + 0*s**3 + 1/48*s**4 + 0 + 0*s**i + s + 0*s**5. Factor p(a).
-a**2*(a - 1)*(a + 1)/4
Let u = -36 + 39. Suppose -2*o = -u*o + 3. Solve 0 + 0*i - 1/2*i**4 + 0*i**2 + 1/2*i**5 + 0*i**o = 0 for i.
0, 1
Let d be (3 - 3)*(-3)/6. Factor 1/6 - 1/6*j**2 + 1/3*j**3 - 1/4*j + d*j**4 - 1/12*j**5.
-(j - 1)**3*(j + 1)*(j + 2)/12
Let r(l) be the third derivative of l**6/210 - l**4/42 - 306*l**2. Find d such that r(d) = 0.
-1, 0, 1
Let p = -6 - -8. Let i = 356/5 - 71. Let -i*f**p + 2/5 + 1/5*f = 0. Calculate f.
-1, 2
Let l(h) be the first derivative of -7/12*h**3 + 1/2*h**2 + 1/4*h**4 + 1 + h. Let r(j) be the first derivative of l(j). Factor r(z).
(2*z - 1)*(3*z - 2)/2
Solve -34*f - 25*f - 18*f**2 - 9076*f**3 + 23*f + 9074*f**3 = 0 for f.
-6, -3, 0
Let d(h) be the third derivative of -h**5/15 - h**4 + 14*h**3/3 - 67*h**2 + h. Factor d(c).
-4*(c - 1)*(c + 7)
Let v(u) = 5*u**3 + u**2 - u. Let y = 2 - 1. Let s be v(y). Find c such that s*c**2 + 4*c - 2*c**2 - 10*c + 3 = 0.
1
Factor -3*u**2 - u + u - 6*u - 165 + 162.
-3*(u + 1)**2
Let g(u) be the third derivative of -u**5/12 - 85*u**4/12 + 175*u**3/6 + 190*u**2. Factor g(c).
-5*(c - 1)*(c + 35)
Let p(n) be the second derivative of n**4/60 - n**3/15 - 23*n. Determine y so that p(y) = 0.
0, 2
Let q(v) = v**3 + 6 - 10 + 7*v**2 + 3 - v. Let h be q(-7). Suppose h*r**3 + 7*r**2 - 3*r**2 + 4*r**3 = 0. What is r?
-2/5, 0
Let 15/2*q**2 - 115/2*q - 20 = 0. Calculate q.
-1/3, 8
Let q = -149 + 154. Let w(j) be the second derivative of 49/135*j**6 - 8/27*j**3 + 4*j + 0*j**2 + 10/9*j**4 - 7/5*j**q + 0. Factor w(m).
2*m*(m - 2)*(7*m - 2)**2/9
Let s(a) be the third derivative of a**7/105 + 13*a**6/240 + a**5/24 - 13*a**4/48 - 3*a**3/4 - 208*a**2. Factor s(k).
(k - 1)*(k + 1)**2*(4*k + 9)/2
Let g = -3 + 5. Suppose -2*s + 3*d = s - 6, 4*s = d + 11. Factor -5*t**3 + t**3 + 4 + s*t**3 + 5*t**3 - 4*t**g - 4*t.
4*(t - 1)**2*(t + 1)
Let f(g) = -11*g**2 - 4*g - 5. Let l(y) = -2*y**2 + 2*y. Let s(w) = f(w) - 3*l(w). Factor s(v).
-5*(v + 1)**2
Let 35*f**4 + 149 + 70*f**3 - 238*f**2 + 107 + 1103*f**2 + 800*f + 128*f**3 + f**5 + 157*f**3 = 0. What is f?
-16, -1
Let k(d) be the third derivative of d**7/10 + 19*d**6/40 + 2*d**5/5 - d**4/2 - 54*d**2. Solve k(x) = 0 for x.
-2, -1, 0, 2/7
Factor 0*m - 2/7*m**5 - 26/7*m**4 + 384/7*m**2 + 0 - 32/7*m**3.
-2*m**2*(m - 3)*(m + 8)**2/7
Suppose -4*q - 6 = -2*q. Let x(d) = d + 6. Let c be x(q). Factor -5 + 11*w**3 - w**c - 10*w + 0 + 5*w**4.
5*(w - 1)*(w + 1)**3
Let p = -276611/20 - -13834. Let w(l) be the second derivative of -45/4*l**4 + 1/28*l**7 + p*l**5 - 6*l - 81/4*l**2 - 11/20*l**6 + 81/4*l**3 + 0. Factor w(n).
3*(n - 3)**3*(n - 1)**2/2
Let u(w) = 2*w**3 + 44*w**2 - 16*w - 10. Let v(t) = -3*t**2 - 1. Let a(i) = 2*u(i) + 28*v(i). Suppose a(c) = 0. What is c?
-2, 3
Let q(b) = -10*b**2 + 16. Let c(x) = 18*x**2 + x - 30. Let m(j) = 6*c(j) + 11*q(j). Factor m(f).
-2*(f - 2)*(f - 1)
Let x(b) be the first derivative of 45 - 5/4*b**4 - 35/3*b**3 + 0*b + 0*b**2. Suppose x(y) = 0. What is y?
-7, 0
Let i(w) be the second derivative of -w**8/3360 + w**7/420 - w**6/120 + w**5/60 - 7*w**4/12 + 27*w. Let j(q) be the third derivative of i(q). Factor j(a).
-2*(a - 1)**3
Let i(v) be the third derivative of v**6/40 - 3*v**5/20 - v**4/8 + 3*v**3/2 - 285*v**2. Factor i(o).
3*(o - 3)*(o - 1)*(o + 1)
Let x(t) be the third derivative of t**6/40 - 4*t**5/5 + 5*t**2 + 9*t. Factor x(i).
3*i**2*(i - 16)
Suppose -145*a - 144 = -193*a. Let w(k) be the first derivative of 5 + 3/14*k**2 - 6/7*k + 1/7*k**a. Factor w(j).
3*(j - 1)*(j + 2)/7
Let l(g) be the first derivative of 30 + 0*g**2 + 0*g + 2/21*g**3. Find f, given that l(f) = 0.
0
Let r(n) be the second derivative of 1/40*n**5 - 7*n + 25/4*n**3 - 5/8*n**4 - 3/2*n**2 + 0. Let c(k) be the first derivative of r(k). Let c(m) = 0. What is m?
5
Suppose 4*o + m = 7, -o + 3*m + 17 = -1. Let x(w) be the second derivative of -8*w + 1/16*w**4 - 3/8*w**2 + 0 - 3/80*w**5 + 1/8*w**o. Factor x(l).
-3*(l - 1)**2*(l + 1)/4
Let a(k) be the first derivative of -k**5/15 + k**4/3 - 2*k**3/3 + 11*k**2/2 - 11. Let v(y) be the second derivative of a(y). Factor v(s).
-4*(s - 1)**2
Let k(f) be the second derivative of 2/21*f**7 - 3/10*f**5 + 4/3*f**4 + 2*f + 0 + 0*f**2 - 1/3*f**6 + 4/3*f**3. Solve k(y) = 0.
-1, -1/2, 0, 2
Let x(j) be the first derivative of 5*j**4/4 - 70*j**3/3 + 285*j**2/2 - 360*j - 122. Factor x(s).
5*(s - 8)*(s - 3)**2
Factor -128/3 + 14/3*y**2 + 32*y.
2*(y + 8)*(7*y - 8)/3
Find m, given that -2116/3 - 184/3*m - 4/3*m**2 = 0.
-23
Suppose 3*b**2 - 12*b**3 + 9 - 4*b**2 + 36*b + 19*b**3 - 11*b**3 = 0. Calculate b.
-3, -1/4, 3
Let k(x) be the second derivative of -x**7/1260 - x**6/90 - x**5/20 + 23*x**4/12 - 22*x. Let n(l) be the third derivative of k(l). Factor n(i).
-2*(i + 1)*(i + 3)
Suppose 9*t = 8*t + 3. Let d be 38/10 - 2/(-30)*t. Determine z so that 3/2*z**d + 3/2 - 3*z**2 + 3*z + 3*z**5 - 6*z**3 = 0.
-1, -1/2, 1
Find m, given that 2/9*m**4 + 14/9*m**3 + 40/9*m + 16/9 + 4*m**2 = 0.
-2, -1
Determine u, given that -6828*u + 1323 - 1923*u - 753*u**2 - 7*u**3 - 11*u**3 + 939*u = 0.
-21, 1/6
Let d(f) = -45*f**2 + 75*f + 216. Let s(q) = 37*q**2 - 76*q - 216. Let n(t) = -5*d(t) - 6*s(t). Determine u, given that n(u) = 0.
-24, -3
Let b(o) = 2*o**2 + o - 3. Let v(m) be the third derivative of m**5/15 + m**4/24 - 5*m**3/6 - 9*m**2. Let x(g) = 5*b(g) - 3*v(g). Factor x(u).
-2*u*(u - 1)
Solve -4827/10*c**2 - 1145/2*c - 125 - 7/10*c**4 - 359/10*c**3 = 0 for c.
-25, -1, -2/7
Suppose 169*d + 4 = 167*d. Let w be ((-230)/(-161))/(-2*2/d). Factor 1/7*g**3 - w*g - 3/7 - 1/7*g**2.
(g - 3)*(g + 1)**2/7
Let m(u) = -2*u**3 - 6*u + 2. Let a(p) = p**4 - p**3 - p**2 - 3*p + 1. Let l(j) = -4*a(j) + 2*m(j). Factor l(q).
-4*q**2*(q - 1)*(q + 1)
Factor 6*f - 21*f**2 - 5*f**2 + 19*f - 9*f**2 + 15*f**3 - 5.
5*(f - 1)**2*(3*f - 1)
Let x(h) = h**2 + h - 12. Let k(t) = 2*t**2 + 86*t - 12. Let c(v) = -2*k(v) + 2*x(v). Factor c(a).
-2*a*(a + 85)
Suppose 1355*v - 1351*v = -q + 10, -5*q + 6 = -2*v. Factor -h**5 + 1/3*h - 14/3*h**3 + 11/3*h**4 - 1/3 + 2*h**q.
-(h - 1)**4*(3*h + 1)/3
Let n(z) be the first derivative of 2*z**3/3 - 3*z**2 + 81. Factor n(i).
2*i*(i - 3)
Suppose -19 = -2*x - 5*q - 5, 4*x = 2*q + 4. Suppose c + 4*u - 3 = -10, -57 = -5*c + 3*u. Solve -3 + c*w - 3*w**2 - 15*w + 0*w**x = 0.
-1
Let n = -92/15 + 229/30. Let x(d) be the first derivative of -d**3 + 3 - d + n*d**2 + 1/4*d**4. Suppose x(h) = 0. Calculate h.
1
Factor 24/5 + 18/5*s**2 + 8*s + 2/5*s**3.
2*(s + 1)*(s + 2)*(s + 6)/5
Let r(v) be the third derivative of -v**8/168 + v**7/15 - 4*v**6/15 + 2*v**5/5 + 702*v**2. Suppose r(z) = 0. What is z?
0, 2, 3
Let x(u) = u**2 - 20*u + 94. Let t be x(13). Let z = -1 + 1. Suppose z - 8/7*w**2 - 8/7*w - 2/7*w**t = 0. What is w?
-2, 0
Let i(k) be the third derivative of k**9/7560 - k**7/1260 + 3*k**4/8 - 2*k**2. Let c(o) be the second derivative of i(o). Factor c(w).
2*w**2*(w - 1)*(w + 1)
Suppose -10*f + 66 - 16 = 0. Let k(b) be the first derivative of 2/15*b + 8/15*b**2 + 34/75*b**f + 1 + 4/45*b**6 + 44/45*b**3 + 14/15*b**4. Factor k(d).
2*(d + 1)**4*(4*d + 1)/15
Let g(z) = -z**5 - z**4 - z**3 - 1. Let n(l) = -63*l**5 + 144*l**4 - 141*l**2 + 57*l - 9. Let p(d) = 3*g(d) - n(d). Suppose p(f) = 0. What is f?
-1, 1/5, 1/4, 1, 2
Let j(f) = -3*f**2 + 1. Let y be j(3). Let t be 2/(-10) + y/(-5). Factor -6*n**3 - n**t - n**5 + 8*n**3 + n**5 - n.
-n*(n - 1)**2*(n + 1)**2
What is l in -l - 4 + 1/4*l**3 + l**2 = 0?
-4, -2, 2
Let x(w) be the third derivative of 0*w + 0*w**3 - 1/240*w**6 + 0*w**5 + 0 + 1/48*w**4 - 17*w**2. Factor x(i).
-i*(i - 1)*(i + 1)/2
Let c(z) be the first derivative of z**5/160 - z**3/48 - 15*z - 19. Let g(n) be the first derivative of c(n). Suppose g(h) = 0. What is h?
-1, 0, 1
Suppose -10*c + 24 = -6*c. Suppose -11*b + 5 = -c*b. Factor 4*w**3 + 2*w**4 - 4*w + 2 - b + 0*w**4 - 3.
2*(w - 1)*(w + 1)**3
Let d(v) be the second derivative of -v**7/5880 + v**6/840 - v**5/280 + v**4/168 - v**3/3 - 21*v. Let p(t) be the second derivative of d(t). Factor p(s).
-(s - 1)**3/7
Let s(x) be the first derivative of