2*f**2*(f - 2)*(f + 1)/7
Let o(h) be the second derivative of -h**4/48 - 7*h**3/4 + 2*h - 248. Factor o(t).
-t*(t + 42)/4
Let y be 2*(-6)/15*-5. Let -j**2 - 4 + 9 - y = 0. What is j?
-1, 1
Let q = -14 + 12. Let d be q + 2/1 + 2. Factor 0*i**d + i**2 - 9*i + 9*i - i**3.
-i**2*(i - 1)
Let l(z) be the second derivative of -z**5/10 - 7*z**4/6 - 4*z**3 + 4*z + 11. Factor l(x).
-2*x*(x + 3)*(x + 4)
Let a be -1*(1 - (1 + 3)) - -61. Factor 4*b + 24*b**2 - 96*b**4 + 11*b**3 + a*b**5 + b**3 - 8*b**3.
4*b*(b - 1)**2*(4*b + 1)**2
Factor -2*y**2 - y**4 + 205*y**3 - 3*y - 405*y**3 + 3*y**2 + 203*y**3.
-y*(y - 3)*(y - 1)*(y + 1)
Suppose 3*f - 184 = -175. Suppose -3*o - 8 = 2*w, -4*o + 3*w + 16 = -w. Factor o*j + 0*j**2 + 13*j - 4*j**2 - 12 + f*j.
-4*(j - 3)*(j - 1)
Let m(u) be the second derivative of 4*u**7/63 + 5*u**6/9 + 9*u**5/5 + 26*u**4/9 + 22*u**3/9 + u**2 + 2*u + 127. Determine p, given that m(p) = 0.
-3, -1, -1/4
Let 2/11*l**5 - 6/11*l**4 + 0 + 8/11*l**2 + 0*l**3 + 0*l = 0. Calculate l.
-1, 0, 2
Let a(g) be the first derivative of 5*g**4/4 - 70*g**3/3 + 60*g**2 - 166. Solve a(v) = 0.
0, 2, 12
Let r(z) be the second derivative of 1/2*z**5 - 5/3*z**3 + 1/6*z**6 - 5/12*z**4 + 0 + 0*z**2 - 5*z. Factor r(b).
5*b*(b - 1)*(b + 1)*(b + 2)
Let q(x) = x**3 - 2*x**2 + 4*x - 2. Let o be q(-3). Let y = 61 + o. Determine a, given that 3/4*a**3 + 0 - 9/4*a**y + 3/2*a = 0.
0, 1, 2
Let x(s) = 29*s**2 + 67*s + 67. Let a(q) = -20*q**2 - 45*q - 45. Let u be 2 + (-1)/2*(-18)/3. Let m(k) = u*x(k) + 7*a(k). Factor m(g).
5*(g + 2)**2
Suppose -3*h = -3*q - 8 - 10, -18 = 3*q. Factor 0 - 4/3*f**3 - 1/6*f**4 - 8/3*f**2 + h*f.
-f**2*(f + 4)**2/6
Let v = -503 + 503. Solve 2/9*s + 4/9*s**2 + v + 2/9*s**3 = 0 for s.
-1, 0
Let m = -8 + 26. Suppose -2 = 5*z + m, 0 = 4*k - 4*z - 96. Suppose 6*u**4 + 4*u**4 - k*u**3 + 5 + 30*u**2 - 20*u - 5*u**4 = 0. What is u?
1
Let r(h) be the first derivative of -h**4/6 - 2*h**3/9 + 2*h**2/3 + 361. Factor r(s).
-2*s*(s - 1)*(s + 2)/3
Let h be (-3)/30*(22 + -27). Determine b so that 1/6*b**4 + h + 5/3*b + 2*b**2 + b**3 = 0.
-3, -1
Suppose -21 = 337*j - 342*j - 2*w, j - 18 = -5*w. Let x(m) = -m**2 + 4*m + 1. Let c be x(3). Factor 0*l**2 - 4/9*l - 2/9*l**c + 4/9*l**j + 2/9.
-2*(l - 1)**3*(l + 1)/9
Let w = 7854 + -117808/15. Suppose 2/5*k + 0 + w*k**2 = 0. Calculate k.
-3, 0
Let g(o) = 6*o**3 - 214*o**2 + 1925*o - 3057. Let p(a) = 9*a**3 - 320*a**2 + 2887*a - 4587. Let c(y) = 7*g(y) - 5*p(y). Solve c(t) = 0 for t.
2, 16
Let h(u) = 14*u**3 + 72*u**2. Let l(b) = -185*b**3 - 935*b**2. Let m(k) = 40*h(k) + 3*l(k). Factor m(t).
5*t**2*(t + 15)
Let o be (71/6)/((-644)/(-12) - 1). Let r = o + 2/79. Factor -1 - 3/2*y**3 - r*y**4 - 3*y - 13/4*y**2.
-(y + 1)**2*(y + 2)**2/4
Suppose 15*l = 112 - 82. Let a(i) be the first derivative of i - 11 - 1/3*i**3 + 0*i**l. Factor a(c).
-(c - 1)*(c + 1)
Let d(n) be the first derivative of -10 + 0*n - 1/8*n**2 + 0*n**5 + 0*n**3 + 1/8*n**4 - 1/24*n**6. Let d(r) = 0. Calculate r.
-1, 0, 1
Let v(r) be the first derivative of -3*r + 0*r**2 + 1/18*r**3 - 3 + 1/60*r**5 + 1/18*r**4. Let j(n) be the first derivative of v(n). Factor j(m).
m*(m + 1)**2/3
Factor -1/5*o**3 - 9/5*o - 6/5*o**2 + 0.
-o*(o + 3)**2/5
Let j(f) be the second derivative of -5*f**4/108 + 203*f**3/54 + 41*f**2/9 - f - 30. Suppose j(a) = 0. Calculate a.
-2/5, 41
Suppose 18 = 73*l - 128. Factor 32/5 + 24*a**l + 36/5*a**3 + 112/5*a.
4*(a + 2)*(3*a + 2)**2/5
Suppose 3*j + 47 = 2*b, 4*b = -0*b - j + 59. Suppose -5*g + 4*r + 16 = 0, 0 = -3*g - 4*r - b. Factor -3/2*i**2 + 0*i + g + 3/4*i**3.
3*i**2*(i - 2)/4
Let g(k) be the third derivative of -3*k**7/56 + 11*k**6/80 + 3*k**5/16 + k**4/16 - 2*k**2 - 57. Find p, given that g(p) = 0.
-1/3, -1/5, 0, 2
Suppose -j + 5*j = -84. Let a be (-14)/j*(-3)/(-2). Find k such that a + k - 4 - k**2 + 5 = 0.
-1, 2
Factor 0 - 32/3*n**2 - 2/3*n**3 + 2/3*n**4 - 40/3*n.
2*n*(n - 5)*(n + 2)**2/3
Let m(d) = -d**3 - 11*d**2 + 14*d + 22. Let y be m(-12). Let x be 46/(-28)*y - 1. Factor -x*w**2 - 6/7*w**3 - 4/7 - 2*w.
-2*(w + 1)**2*(3*w + 2)/7
Let s(n) = -n**3 - 5*n**2 - 2*n - 7. Let h be s(-5). Factor -18*y - 5*y**3 + 17*y**2 + y**h - 5*y**2 + 2*y**3.
-2*y*(y - 3)**2
Let n(q) = 2*q**2 + 6*q - 6. Let y be n(-9). Factor y*i - 4*i**2 - 108*i + 5*i**2.
i*(i - 6)
Let t(i) = i**3 - 2*i**2 - i - 4. Let c(p) = p**3 + p**2 - p + 1. Let d(a) = 6*c(a) + 2*t(a). Factor d(w).
2*(w - 1)*(w + 1)*(4*w + 1)
Let c(q) be the first derivative of q**4/15 - 2*q**3/5 + 4*q**2/5 + 7*q + 4. Let a(x) be the first derivative of c(x). Factor a(f).
4*(f - 2)*(f - 1)/5
Let g be (-104)/(-6)*(-2563)/(-132). Let u = 337 - g. Factor 4/9*p**2 - u + 2/9*p - 2/9*p**3.
-2*(p - 2)*(p - 1)*(p + 1)/9
Let g = 60 + -58. Suppose 9 - 13 + 7*p**4 + 8*p**3 + 3*p**3 - 13*p**g + 10*p**4 - 16*p + 5*p**5 = 0. What is p?
-2, -1, -2/5, 1
Determine v so that -36*v**4 - 5*v**2 + 3*v**4 + 38*v**4 - 5*v**3 + 5*v = 0.
-1, 0, 1
Let x(n) = 24*n**3 - 231*n**2 - 222*n + 33. Let u(v) = -3*v**3 + 29*v**2 + 28*v - 4. Let r(b) = 33*u(b) + 4*x(b). Factor r(o).
-3*o*(o - 12)*(o + 1)
Suppose 5*a = 4*a + 4. Suppose 0 = -2*u + 4*u - 2*k + a, -5*u + 30 = 5*k. What is s in 8/7*s**3 + 12/7*s - 18/7*s**u - 2/7 = 0?
1/4, 1
Let b be 32/(-12)*12/(-16). Factor 5 - j**2 + 2*j**b + 3*j**2 + 3 + 12*j.
4*(j + 1)*(j + 2)
Let l(w) = w**2 - 6*w - 5. Let c be l(9). Let r = -22 + c. Determine x so that 4*x + r - x**2 - 3 - 1 = 0.
2
Let q be 2/(-13) - 46397/(-28054). Let q + 7*r**2 + 2*r**5 - 8*r - 17/2*r**4 + 6*r**3 = 0. What is r?
-1, 1/4, 1, 3
Let o(q) = 85*q**2 - 95*q**4 + 40*q**2 + 35*q + 64*q**2 + 51*q**2. Let u(m) = -8*m**4 + 20*m**2 + 3*m. Let z(s) = 3*o(s) - 35*u(s). Factor z(x).
-5*x**2*(x - 2)*(x + 2)
Let u(c) = -6*c**4 + 42*c**3 + 63*c**2 + 39*c + 6. Let p(a) = -9*a**4 + 41*a**3 + 63*a**2 + 40*a + 6. Let q(o) = -6*p(o) + 7*u(o). Factor q(t).
3*(t + 1)*(t + 2)*(2*t + 1)**2
Suppose -9 + 3 = -n. Solve 3*f**3 - 9*f**2 - 5*f**3 - f**3 - n*f = 0 for f.
-2, -1, 0
Let d(p) = -p**2 + 85*p - 22. Let l(c) = 14*c. Let u(w) = 2*d(w) - 14*l(w). Factor u(q).
-2*(q + 2)*(q + 11)
Let c(k) be the third derivative of -1/720*k**6 + 0*k + 0 + 0*k**3 + 1/1260*k**7 - 1/180*k**5 + 0*k**4 + 34*k**2. Factor c(l).
l**2*(l - 2)*(l + 1)/6
Factor -25*g**3 - 15122 + 8*g - 3*g + 15*g**4 - 65*g**2 + 15152.
5*(g - 3)*(g + 1)**2*(3*g - 2)
Let z be ((-3)/(-5))/(-15*2/(-250)). Let t(c) be the second derivative of 0*c**2 + 0 - z*c + c**3 + 1/4*c**4. Find h, given that t(h) = 0.
-2, 0
Let i = -122638/15 - -8176. Suppose -2/15*t**4 + 0 - i*t**5 + 2/15*t**3 + 0*t + 2/15*t**2 = 0. Calculate t.
-1, 0, 1
Factor -20*m**4 + 3*m**4 + 9*m**5 - 48*m + 120*m**3 - 45*m**4 + 5*m**4 + 48 - 72*m**2.
3*(m - 2)**3*(m - 1)*(3*m + 2)
Let i(f) = -381*f**3 - 697*f**2 - 380*f - 52. Let o(t) = t**3 + 2*t**2 + 2. Let y(q) = -i(q) + 4*o(q). Factor y(h).
5*(h + 1)*(7*h + 2)*(11*h + 6)
Let i(r) be the first derivative of -r**5/5 + 2*r**3/3 - r - 77. Let i(u) = 0. What is u?
-1, 1
Let x = -47 + 51. Factor 33*p**x + 40*p**3 - 8*p**4 - 15*p**5 + 20*p**5 + 20*p**2.
5*p**2*(p + 1)*(p + 2)**2
Let h = -21139/9 - -2349. Factor 0 + h*c + 2/9*c**3 - 4/9*c**2.
2*c*(c - 1)**2/9
Factor -5/6*d**3 + 5/2*d**2 - 175/6 + 55/2*d.
-5*(d - 7)*(d - 1)*(d + 5)/6
Let k = -1321 - -1324. Let p(l) be the third derivative of -3/56*l**4 + 0 + 1/70*l**5 + 0*l**k - 4*l**2 - 1/840*l**6 + 0*l. Let p(j) = 0. What is j?
0, 3
Let j(l) = l**4 - 6*l**3 - 12*l**2 + 14*l - 9. Let y(k) = 3*k**4 - 17*k**3 - 35*k**2 + 41*k - 26. Let t(c) = -17*j(c) + 6*y(c). Suppose t(v) = 0. Calculate v.
-3, 1
Let c(q) be the third derivative of 0 + 1/84*q**8 - 1/6*q**4 + 2/15*q**5 - 42*q**2 - 4/105*q**7 + 0*q**3 + 0*q + 0*q**6. Factor c(n).
4*n*(n - 1)**3*(n + 1)
Let f(q) = q**2 + 13*q - 13. Let i be f(-14). Let r be (-35)/(-147) + i/3. Factor r + 2/7*m - 6/7*m**2 + 2/7*m**4 - 2/7*m**3.
2*(m - 2)*(m - 1)*(m + 1)**2/7
Let a(m) be the third derivative of -2/27*m**4 - 1/168*m**8 - 4/27*m**3 - 1/315*m**7 - 41*m**2 + 0 + 7/270*m**5 + 17/540*m**6 + 0*m. Solve a(s) = 0 for s.
-1, -2/3, 1
Determine l, given that -34*l**2 + 21*l - 118 - 25*l**3 - 163*l + 23*l**3 + 8 = 0.
-11, -5, -1
Let o(f) be the second derivative of -f**8/8400 + f**7/4200 + 6*f**3 + 22*f. Let a(b) be the second derivative of o(b). Determine r so that a(r) = 0.
0, 1
What is p i