4*(s + 22)**2
Let v be -1*((-80)/6)/10. Factor 0 + 2*r**3 + 1/3*r + 4/3*r**2 + v*r**4 + 1/3*r**5.
r*(r + 1)**4/3
Let l(m) = -m**3 - 7*m**2 - 6*m - 14. Let j be l(-6). Let u be ((-9)/(-78))/(j/(-8) + -1). Factor 4/13*r - u*r**4 + 2/13 - 4/13*r**3 + 0*r**2.
-2*(r - 1)*(r + 1)**3/13
Suppose -2*m = -j - 8, 7*j - 6 = 10*j. Let b(p) be the second derivative of 0 + 1/36*p**4 + 1/60*p**5 - 2*p - 1/18*p**m - 1/6*p**2. Factor b(u).
(u - 1)*(u + 1)**2/3
Let m(a) be the first derivative of -2*a**5/9 - 3*a**4/2 + 110*a**3/27 - a**2 - 28*a/9 - 145. Suppose m(g) = 0. What is g?
-7, -2/5, 1
Let w be (20/(-875)*-7)/6. Let b(r) be the second derivative of 1/10*r**3 + 1/10*r**2 + 0 - 3/100*r**5 - 1/12*r**4 - 3*r + w*r**6. Factor b(z).
(z - 1)**2*(z + 1)*(4*z + 1)/5
Let a = -57/137 + -584157/685. Let w = -850 - a. Determine y, given that -8/5*y + 2*y**3 - 16/5 + 36/5*y**2 - 6/5*y**5 - w*y**4 = 0.
-2, -2/3, 1
Let j = 316 + -316. Let o(z) be the first derivative of j*z + 7/24*z**4 - 1/3*z**2 + 1/6*z**5 - 1 - 4/9*z**3. Factor o(y).
y*(y - 1)*(y + 2)*(5*y + 2)/6
Let 81 - 95 - 30*k + 4*k - 10*k**2 + 2*k**3 = 0. Calculate k.
-1, 7
Let d(m) be the first derivative of m**3/3 + m - 22. Let l(h) = -4*h**2 + 2*h - 4. Let t(r) = -12*d(r) - 4*l(r). Solve t(s) = 0.
1
Factor -3*n**3 - 4663*n**2 + 4573*n**2 + 3*n + 144 - 54.
-3*(n - 1)*(n + 1)*(n + 30)
Let g(i) be the first derivative of -2*i**5/5 - 11*i**4/2 - 70*i**3/3 - 25*i**2 + 75. Factor g(y).
-2*y*(y + 1)*(y + 5)**2
Factor -2/9*i**2 - 16/9 - 4/3*i.
-2*(i + 2)*(i + 4)/9
Let p be ((-13732)/(-238))/(476/28). Let b = p + 10/289. Factor b*m - 2/7*m**4 - 26/7*m**2 - 8/7 + 12/7*m**3.
-2*(m - 2)**2*(m - 1)**2/7
Let v(z) = z**3 + 11*z**2 + z + 13. Let o be v(-11). Factor -2/5*f + 0 + 2/5*f**o.
2*f*(f - 1)/5
Let x = 245/2043 + -2/227. Let g(k) be the first derivative of 1 - 2/27*k**3 - x*k**2 + 0*k. Factor g(m).
-2*m*(m + 1)/9
Suppose 0 = -12*u + 9*u + 93. Let l(m) = 4*m - 6. Let p be l(6). Suppose 4*b - 12*b**3 - p*b**4 - 6 - 15*b**3 - 48*b**2 - u*b - 15*b**3 - 3*b**5 = 0. What is b?
-2, -1
Let a(z) = -z**4 - z. Let f(c) = 5*c**4 - 13*c**3 + 11*c**2 + 7*c - 6. Let s(k) = 2*a(k) + f(k). Solve s(w) = 0 for w.
-2/3, 1, 3
Suppose 2*k + 4*g + 259 + 5 = 0, -3*g + 9 = 0. Let d = -135 - k. Solve -16/3*w**2 - 32/3*w**d - 2/3*w + 0 = 0 for w.
-1/4, 0
Let c be (-4)/(-6) + (2 - (-128)/(-72)). Let -2/3*q**2 - c*q + 4/9*q**3 + 2/9*q**4 + 8/9 = 0. What is q?
-2, 1
Suppose 2*y - 5 = -2*n + 9, -16 = 2*n - 4*y. Let l(x) be the first derivative of 0*x - n*x**2 - 4/3*x**3 + 9. Factor l(q).
-4*q*(q + 1)
Factor -2/9*m**2 + 6 - 52/9*m.
-2*(m - 1)*(m + 27)/9
Let l be (3 + 0 + -2)*-61. Let v = l + 63. Factor -2*u**v - 4/5 - 14/5*u.
-2*(u + 1)*(5*u + 2)/5
Let v(f) = f**2 + 2*f + 1. Let g be v(-3). Suppose -3*o = 8*l - 3*l - 27, g*o = 3*l + 7. Factor 4*w**o + 2*w**5 - 6*w**4 - 2*w**2 - 4*w**4 + 3*w**3 + 3*w**3.
2*w**2*(w - 1)**3
Let i(a) be the third derivative of 1/252*a**8 + 8*a**2 + 0*a**3 + 1/180*a**6 + 0*a**4 + 0*a + 0 + 0*a**5 + 1/105*a**7. Find y such that i(y) = 0.
-1, -1/2, 0
Let v(l) = -2*l**4 - 7*l**3 + 8*l**2 + 7*l - 2. Let n(s) = 5*s**4 + 21*s**3 - 25*s**2 - 21*s + 6. Let a(p) = -2*n(p) - 7*v(p). Let a(j) = 0. Calculate j.
-2, -1, 1/4, 1
Let g(s) be the first derivative of 0*s**3 - 1/9*s**2 + 1/18*s**4 + 14 + 0*s. Factor g(d).
2*d*(d - 1)*(d + 1)/9
Let z = 636 - 634. Let w = -39 + 275/7. Factor 30/7*m**3 + w*m**5 + 18/7*m**2 + z*m**4 + 0*m + 0.
2*m**2*(m + 1)*(m + 3)**2/7
Let a = -16 - -19. Suppose 4*w - 16 = -3*y + 2, -4*y - 1 = -a*w. Factor 5*t**y - t**2 - 3*t**2 + 1 + 3*t - t.
(t + 1)**2
Let w(n) be the second derivative of n**5/90 + n**4/9 + 8*n**3/27 + 2*n + 73. Factor w(q).
2*q*(q + 2)*(q + 4)/9
Let m(a) be the first derivative of a**7/105 - a**6/15 + a**5/15 + a**4/3 - a**3 - 11*a**2/2 - 2*a + 35. Let j(i) be the second derivative of m(i). Factor j(x).
2*(x - 3)*(x - 1)**2*(x + 1)
Let v be (-4)/(-15)*6/4. Let q = 66 - 64. Find k, given that v*k**3 + 0*k**q - 2/5*k + 0 = 0.
-1, 0, 1
Suppose -8*l + 13 = -3. Suppose 97*p**l + 610*p**3 + 8 + 917*p**2 + 512*p**3 + 1075*p**3 + 156*p = 0. Calculate p.
-2/13
Let c(q) be the second derivative of 0 - 10*q + 1/28*q**4 + 0*q**2 + 3/14*q**3. Solve c(x) = 0.
-3, 0
Suppose 10 = 5*d - 20. Let m(p) be the third derivative of 1/3*p**3 + 0*p**5 - 3*p**2 + 0 - 1/105*p**7 - 1/6*p**4 + 0*p + 1/30*p**d. Factor m(i).
-2*(i - 1)**3*(i + 1)
Let y be ((-72)/105)/(2 - 69/30). Factor -2/7 + y*o**2 + 4/7*o.
2*(2*o + 1)*(4*o - 1)/7
Let i(n) be the second derivative of n**6/210 - n**5/70 - n**4/84 + n**3/21 - 6*n + 1. Suppose i(a) = 0. What is a?
-1, 0, 1, 2
Let l(z) = 7*z**2 - 7*z - 2. Let s = -11 + 9. Let u(q) = -8*q**2 + 8*q + 3. Let x(b) = s*u(b) - 3*l(b). Suppose x(f) = 0. Calculate f.
0, 1
Let t(v) be the first derivative of -4*v + 1/50*v**5 - 3 + 0*v**3 + 1/10*v**4 - 4/5*v**2. Let m(c) be the first derivative of t(c). Factor m(w).
2*(w - 1)*(w + 2)**2/5
Let x(p) be the third derivative of -p**8/1512 + p**7/945 + p**6/270 - p**5/135 - p**4/108 + p**3/27 - 4*p**2. Factor x(z).
-2*(z - 1)**3*(z + 1)**2/9
Let f(o) be the first derivative of o**6/15 + 12*o**5/25 + 3*o**4/10 - 4*o**3/3 + 492. Determine n so that f(n) = 0.
-5, -2, 0, 1
Suppose 13/4*k**2 + 3/2*k**3 + 3*k + 1 + 1/4*k**4 = 0. Calculate k.
-2, -1
Let k(u) be the third derivative of -u**7/210 - u**6/120 + 2*u**5/15 + u**4/2 + 766*u**2. Factor k(d).
-d*(d - 3)*(d + 2)**2
Let w = -89 + 90. Solve 1 + 2*s**2 - w - 3*s + 2*s - s**3 = 0.
0, 1
Let o(b) be the first derivative of 3*b**4/16 - 5*b**3/4 + 21*b**2/8 - 9*b/4 + 215. Let o(s) = 0. Calculate s.
1, 3
Let z(r) be the second derivative of -2*r**7/105 - 4*r**6/25 + 8*r**5/25 + 2*r**4/5 - 14*r**3/15 - 19*r - 8. Suppose z(w) = 0. Calculate w.
-7, -1, 0, 1
Let x(m) be the second derivative of -m**7/840 + m**6/60 - 5*m**4/6 - 12*m. Let b(n) be the third derivative of x(n). Determine k, given that b(k) = 0.
0, 4
Let l(v) be the second derivative of v**5/25 + 2*v**4/15 - 26*v**3/15 + 4*v**2 - 8*v + 6. Suppose l(s) = 0. What is s?
-5, 1, 2
Let q(x) = -59*x**3 + 66*x**2 + 312*x - 62. Let w(k) = 29*k**3 - 33*k**2 - 156*k + 32. Let n(t) = 2*q(t) + 5*w(t). Suppose n(u) = 0. Calculate u.
-2, 2/9, 3
Let f(k) be the first derivative of 7*k**4/6 + 10*k**3/3 - 18*k**2 - 16*k/3 - 487. Factor f(z).
2*(z - 2)*(z + 4)*(7*z + 1)/3
Let c(o) = -31*o - 16. Let f be c(6). Let h = f + 1820/9. Factor 2/9*u**4 + 0*u - 4/9*u**2 + h + 0*u**3.
2*(u - 1)**2*(u + 1)**2/9
Let c(l) be the third derivative of -1/160*l**6 - 1/4*l**4 + 0 - 1/2*l**3 + 0*l - 1/16*l**5 - 6*l**2. Factor c(p).
-3*(p + 1)*(p + 2)**2/4
Let b(h) = h**4 - h**3. Suppose r - 9 = -6. Let w(m) = -m**4 - m**3 + m**2 + 3*m - 2. Let z(s) = r*w(s) + 6*b(s). Determine u, given that z(u) = 0.
-1, 1, 2
Suppose -9*g = -4*g + 90. Let r be g/(-2)*3/9. Factor r + 5 + 8*q**2 + 0 - 10*q**2.
-2*(q - 2)*(q + 2)
Suppose 12 = -4*v, -2*d = -4*d - 2*v - 2. Let g(f) be the first derivative of -4*f**2 - d*f + 2*f + 4*f**3 + 2. Factor g(w).
4*w*(3*w - 2)
Let -3/5*f**2 + 123/5 + 24*f = 0. What is f?
-1, 41
Let a(p) be the first derivative of 2/21*p**3 - 4/7*p**2 - 8/7*p + 1/14*p**4 + 6. Suppose a(m) = 0. Calculate m.
-2, -1, 2
Let y be (0 + (-17)/2)/(7/14). Let a be y/204*(-8 - 1). Solve a*w**2 + 0*w + 0 = 0.
0
Factor h + 112*h**2 + 16 - 108*h**2 - 17*h.
4*(h - 2)**2
Let v(g) be the third derivative of -g**7/3150 + 2*g**5/75 - g**4/12 - 6*g**2. Let y(o) be the second derivative of v(o). Factor y(a).
-4*(a - 2)*(a + 2)/5
Let h(k) = k**4 + k**3 - k**2. Let x(o) = 12*o**4 - 26*o**3 - 342*o**2 - 96*o. Let j(l) = 4*h(l) + 2*x(l). Find n such that j(n) = 0.
-4, -2/7, 0, 6
Let l(r) = r**3 - 7*r**2 + 9*r - 13. Let i be 22/(-121) + 6 - 4/(-22). Let w be l(i). Factor 2/3*a + 1/3*a**w + 0 + 1/3*a**4 - a**3 - 1/3*a**2.
a*(a - 1)**2*(a + 1)*(a + 2)/3
Find a, given that -2*a**3 + 3*a - 4*a**2 - a**5 + 0*a**2 - 11231*a**4 + 11235*a**4 = 0.
-1, 0, 1, 3
Suppose -y - 5*k + 10 = 0, -3*y - 3 = -4*k + 5. Suppose y = -a - 2 + 11. Factor -2*g**2 + 1 + a*g - 2 - g**2 - 5.
-3*(g - 2)*(g - 1)
Let k(r) be the second derivative of -69*r**5/100 - 49*r**4/10 - 58*r**3/5 - 36*r**2/5 + 296*r. Factor k(t).
-3*(t + 2)**2*(23*t + 6)/5
Let v be ((-356)/(-1335))/(1/20 - 0). Suppose -28/3*n + v*n**4 + 56/3*n**3 + 11*n**2 + 4/3 = 0.