2/17*k**3 - 6/17*k**2 + 4/17*k + 0 = 0. What is k?
-1, 0, 1, 2
Let r(k) be the second derivative of -27*k**5/20 - 61*k**4/4 - 20*k**3 + 18*k**2 + 155*k - 3. Factor r(f).
-3*(f + 1)*(f + 6)*(9*f - 2)
Suppose 441 - 5*g**2 - 5*g**3 + 5*g**4 - 441 + 5*g + 0*g**3 = 0. What is g?
-1, 0, 1
Let o = 35102/5 + -6988. Let m = o - 32. Solve 0 + 2/5*k**2 - m*k**3 + 0*k = 0 for k.
0, 1
Let o(n) be the second derivative of -n**4/4 - 12*n**3 + 53*n. Find r, given that o(r) = 0.
-24, 0
Let d = -7925 - -23791/3. Suppose -68*w**3 + 0 - d*w**5 - 20/3*w + 124/3*w**2 + 116/3*w**4 = 0. Calculate w.
0, 1/4, 1, 5
Suppose 0 = -329*r - 172*r. Factor 0 + r*x**3 + 8/15*x**2 + 0*x - 2/15*x**4.
-2*x**2*(x - 2)*(x + 2)/15
Let i(f) be the first derivative of -1/33*f**6 + 6/11*f + 28/33*f**3 + f**2 - 2/55*f**5 - 28 + 3/11*f**4. Factor i(h).
-2*(h - 3)*(h + 1)**4/11
Let i be (5 + -1)/(0 + -2). Let u(k) = 7*k**3 + 18*k**2 - 17*k - 6. Let r(b) = b**2. Let j(m) = i*r(m) + u(m). Factor j(f).
(f - 1)*(f + 3)*(7*f + 2)
Let i(k) = 100*k**3 + 26 + 20 - 3 + 125*k**2 - 8 + 170*k. Let p(l) = 11*l**3 + 14*l**2 + 19*l + 4. Let d(v) = 6*i(v) - 55*p(v). Factor d(c).
-5*(c + 1)**2*(c + 2)
Let h = -2143/7 - -307. Factor 2/7*v**3 + 0*v + h*v**2 - 8/7.
2*(v - 1)*(v + 2)**2/7
Suppose -311*c = -310*c - 4*v + 9, -15 = -5*v. Determine p so that 0*p + 2*p**4 + 1/2*p**2 - 2*p**c + 0 = 0.
0, 1/2
Factor 4*w + 0 + 50/9*w**2 - 2/9*w**4 + 4/3*w**3.
-2*w*(w - 9)*(w + 1)*(w + 2)/9
Let z(i) = -13*i**2 + 119*i - 254. Let x(h) = -4*h**2 - h + 1. Let l(k) = -4*x(k) + z(k). Solve l(s) = 0.
-43, 2
Let r = 201 + -144. Factor 26*i**3 + 32*i**3 - 40*i**3 + 18 + r*i + 57*i**2.
3*(i + 1)*(2*i + 3)*(3*i + 2)
Suppose 0 = 4*v - 9*x + 7*x - 8, -3*v - 2*x + 20 = 0. Suppose v*l - 3 = 5. Suppose 4/7 - 6/7*r + 2/7*r**l = 0. What is r?
1, 2
Let k(y) be the second derivative of 35/6*y**3 + 5*y**2 + 5/6*y**4 - 3/4*y**5 + 14*y + 0. What is i in k(i) = 0?
-1, -1/3, 2
Let b(j) be the second derivative of -3*j**2 - 28*j + 1/6*j**3 + 1/12*j**4 + 0. Factor b(q).
(q - 2)*(q + 3)
Let u(v) be the first derivative of 0*v**2 - 1/8*v**4 - 2 - 1/10*v**5 + 0*v + 1/6*v**3 + 1/12*v**6. Factor u(r).
r**2*(r - 1)**2*(r + 1)/2
Let 405/4*a + 100 + 5/4*a**2 = 0. Calculate a.
-80, -1
Suppose 0 = -j - 4*o + 11, 0*j + 4*o - 17 = -3*j. Factor 26*f**3 + 8*f**2 - 30*f**j - 32*f**4 + 0 + 0 - 20*f**5.
-4*f**2*(f + 1)**2*(5*f - 2)
Let u(y) = -10*y**4 + 65*y**3 + 130*y**2 + 70*y + 5. Let v(d) = 5*d**4 - 34*d**3 - 65*d**2 - 35*d - 3. Let t(z) = 3*u(z) + 5*v(z). Factor t(j).
-5*j*(j - 7)*(j + 1)**2
Let y(q) be the second derivative of 0 - 10/3*q**6 - 2/5*q**5 + 0*q**2 + 0*q**3 + 4/3*q**4 + 25/21*q**7 + 10*q. Let y(g) = 0. Calculate g.
-2/5, 0, 2/5, 2
Let v(o) = 2*o**5 - 25*o**4 + 12*o**3 + 31*o**2 - 20*o - 3. Let p(t) = -t**5 + 25*t**4 - 11*t**3 - 33*t**2 + 20*t + 4. Let b(w) = 3*p(w) + 4*v(w). Factor b(i).
5*i*(i - 4)*(i - 1)**2*(i + 1)
Let j(i) be the second derivative of -1/16*i**4 + 9/160*i**5 + 0 + 0*i**2 - 16*i - 1/60*i**6 + 1/48*i**3. Determine s so that j(s) = 0.
0, 1/4, 1
Let l(x) be the second derivative of -x**7/14 + 2*x**6/5 + 6*x**5/5 - 7*x**4/2 - 7*x**3/2 + 15*x**2 + 2*x + 75. Suppose l(t) = 0. Calculate t.
-2, -1, 1, 5
Let g = -16297 + 32597/2. Let y = -37 - -89/2. Factor 0 + 0*p - g*p**3 + 3*p**2 - y*p**5 - 12*p**4.
-3*p**2*(p + 1)**2*(5*p - 2)/2
Let z be -1 - 92/(-84) - (-2)/28. Let x(q) be the third derivative of 1/60*q**6 - 8*q**2 + 0 - z*q**4 + 0*q**3 + 1/30*q**5 + 0*q. Factor x(k).
2*k*(k - 1)*(k + 2)
Let a be (928/56 + -16 + 4/(-7))*-1. Let -15/7*k + a + 3/7*k**2 = 0. What is k?
0, 5
Suppose 20*x - 21*x + 2*u + 12 = 0, -5*x - 5*u = 0. Find f, given that 6/5*f**2 + 2/5*f**3 - 4/5 - 2/5*f - 2/5*f**x = 0.
-1, 1, 2
Suppose -2*r + 9 - 5 = 0. Suppose 5*u + x = 19, 4*u + r*x - 10 = u. Find v such that -15*v**2 + 15*v**u - 7*v + 4*v + 0*v + 12*v**5 + 0*v - 9*v**3 = 0.
-1, -1/4, 0, 1
Let v = -54553/2 + 27277. Suppose 0 + 1/4*t**2 - v*t = 0. Calculate t.
0, 2
Let t(x) = -9*x**3 + 5*x**2 + 9*x. Let f(s) = -5*s**3 + 3*s**2 + 5*s. Suppose -3*k = -7*k - 24. Let l(a) = k*t(a) + 10*f(a). Solve l(j) = 0 for j.
-1, 0, 1
Let g(v) be the first derivative of -7*v**5/5 + 27*v**4/2 - 68*v**3/3 - 12*v**2 + 295. Find c, given that g(c) = 0.
-2/7, 0, 2, 6
Let m(d) = 5*d**2 + 164*d + 6396. Let x(z) = 14*z**2 + 491*z + 19189. Let p(f) = -11*m(f) + 4*x(f). What is o in p(o) = 0?
-80
Let i = 45293/3 + -15095. Factor i*y - 3 + 1/3*y**2.
(y - 1)*(y + 9)/3
Let d = 11/8 - 7/40. Let w = -6/5 - -8/5. Factor -d - w*b**2 + 8/5*b.
-2*(b - 3)*(b - 1)/5
Let m(s) = 87*s + 1829. Let x be m(-21). Factor 0 + 1/2*h**3 + h + 3/2*h**x.
h*(h + 1)*(h + 2)/2
Let c be 167/15 + (-4)/30. Let z = -9 + c. Let -u**2 - 2*u**2 + 0*u**3 + u**2 - 4*u**3 - z*u**4 = 0. What is u?
-1, 0
Let b be (-2 - 46/(-25))/(4/(-10)). Let 0 - 2/5*i**3 + 0*i**2 + b*i = 0. What is i?
-1, 0, 1
Let i(m) be the first derivative of -5*m**6/6 + 14*m**5 - 305*m**4/4 + 140*m**3 - 90*m**2 + 84. Factor i(k).
-5*k*(k - 6)**2*(k - 1)**2
Let m be 8/(-176) - (-6)/11. Solve -m*p**4 + 3/2*p**2 - p + 0*p**3 + 0 = 0 for p.
-2, 0, 1
Let b = 56 + -9. Let p = 95/2 - b. Factor 0*c - 1/2*c**3 - p*c**2 + 0.
-c**2*(c + 1)/2
Factor -2 + 3/2*l + 1/2*l**2.
(l - 1)*(l + 4)/2
Let v = -20546/3 - -6850. Factor -1/3*n**5 + 0*n**2 - 4/3*n**3 + 0 - v*n**4 + 0*n.
-n**3*(n + 2)**2/3
Let g(f) = -f**2 + 4*f + 19. Let o(d) = -1. Let n(p) = g(p) - 5*o(p). Let u be n(7). Solve 5 - 85*x**2 - 5 + 139*x**u - 80*x**4 + 10*x + 61*x**3 = 0 for x.
0, 1/4, 2
Let l be -3 + 0*1*2/(-6). Let j be (35/(-70))/((-2)/(-4)*l). Factor 1/3*i**3 + 2/3*i**2 + j*i + 0.
i*(i + 1)**2/3
Let f(z) = 4*z**2 - 24*z - 93. Let o(l) = 17*l**2 - 95*l - 373. Let y(c) = 26*f(c) - 6*o(c). Let y(i) = 0. What is i?
-3, 30
Factor -70 - 274/3*d + 8/3*d**2.
2*(d - 35)*(4*d + 3)/3
Let l = 59051 + -5314687/90. Let q = 13/18 - l. Let 0*u**3 + 0 - 3/5*u**4 + q*u**2 - 6/5*u = 0. What is u?
-2, 0, 1
Let z(k) be the first derivative of k**6/720 + k**5/60 + k**4/12 - 23*k**3/3 + 23. Let y(p) be the third derivative of z(p). Factor y(i).
(i + 2)**2/2
Let b(v) = -285*v**2 + 2310*v + 63507. Let l(q) = 79*q**2 - 660*q - 18145. Let j(d) = 5*b(d) + 18*l(d). Let j(s) = 0. Calculate s.
-55
Factor -2/17*p**2 + 22/17 + 20/17*p.
-2*(p - 11)*(p + 1)/17
Let u(k) be the second derivative of -2*k**6/3 - 7*k**5/5 - 2*k**4/3 + 164*k. What is v in u(v) = 0?
-1, -2/5, 0
Factor -14/5*s**2 + 0 - 2/5*s**3 - 12/5*s.
-2*s*(s + 1)*(s + 6)/5
Let f = 9 + -7. Suppose -5*d + 4*d = -f. Find w such that -2*w**2 + w + 3*w + w**d - 3 - 1 = 0.
2
Let w(g) be the first derivative of 12/5*g + 12 + 0*g**2 - 1/5*g**3. Suppose w(f) = 0. What is f?
-2, 2
Factor 2550*o**3 + 16*o - 2438*o**3 + 36*o**4 + 4*o**5 + 144*o**2 + 48*o.
4*o*(o + 1)*(o + 2)**2*(o + 4)
Let r(i) be the second derivative of -3*i**5/20 - 3*i**4/4 + 6*i**2 - 177*i. Factor r(s).
-3*(s - 1)*(s + 2)**2
Let o(z) be the first derivative of 0*z**2 + 12*z**4 - 4/5*z**5 - 48*z**3 + 8 + 0*z. Suppose o(w) = 0. Calculate w.
0, 6
Suppose -x - 49 + 60 = 4*k, 0 = -k + 2. Let z(c) be the first derivative of 2/5*c**2 - 6 - 2/5*c**x - 1/5*c - 1/25*c**5 + 1/5*c**4. Solve z(y) = 0.
1
Let g be 2 + 0/((-4)/(-2)). Find c such that 5*c**3 - 2*c**4 - 15*c**g + 17*c**4 - 4*c - c = 0.
-1, -1/3, 0, 1
Let t(z) be the second derivative of z**6/240 - z**5/40 + z**4/16 - z**3/12 + 3*z**2/2 - 2*z. Let k(b) be the first derivative of t(b). Factor k(f).
(f - 1)**3/2
Let w(n) = -n**3 + 9*n**2 + 11*n - 8. Let k be w(10). Factor 7*f**3 + 29*f**2 + 118*f + 158*f - 72 - 115*f**k.
(f - 6)**2*(7*f - 2)
Suppose -10*n + 7*n - 6*n = 3*n. Find h such that 4/15*h**2 + 0*h - 2/15*h**3 + n = 0.
0, 2
Suppose 22/9*i**3 + 10*i**4 + 0 + 0*i + 8/9*i**5 + 0*i**2 = 0. What is i?
-11, -1/4, 0
Let d be (-21)/28*12/(-18)*0. Find k such that -1/2*k**4 + d*k**3 + k**2 + 0*k - 1/2 = 0.
-1, 1
Factor 0 + 6/7*g**2 + 0*g.
6*g**2/7
Let f(s) be the second derivative of -s**7/210 - 3*s**6/50 - 13*s**5/50 - 3*s**4/10 + 9*s**3/10 + 27*s**2/10 - s + 2. Factor f(y).
-(y - 1)*(y + 1)*(y + 3)**3/5
Let r(u) = -17*u**2 + 46*u + 38. Let p(c) = 3*c**2 - 2*c. Let j(l) = -5*p(l) - r(l). Suppose j(x) = 0. Calculate x.
-1, 19
Let q(n) = -n**3 - 6*n**2 + 6*n - 2. Let t be q(-7). Let h = 13 - t. Factor r**2 - h*r**4 + 4*r**5 - r**2 + 0*r**2 + 4*r**3.
4*r**3