)*(g + 3)
Factor 0 - 10/13*m**3 - 6/13*m + 14/13*m**2 + 2/13*m**4.
2*m*(m - 3)*(m - 1)**2/13
Suppose 6*v**4 - 395*v**3 + 3*v**5 + 395*v**3 = 0. What is v?
-2, 0
Let f(v) be the third derivative of v**6/360 + 98*v**5/45 + 4802*v**4/9 + 979*v**2. Factor f(g).
g*(g + 196)**2/3
Let z(i) be the second derivative of 1/14*i**7 + 2/5*i**6 - 9*i + 0 - i**4 + 9/20*i**5 + 0*i**2 - 2*i**3. Determine k so that z(k) = 0.
-2, -1, 0, 1
Let p(j) be the second derivative of -2/15*j**4 - 3/50*j**5 - 1/15*j**3 + 10*j + 0 + 0*j**2. Find u, given that p(u) = 0.
-1, -1/3, 0
Let c(f) = -4*f**2 + 23*f + 2. Let k(t) = -2*t + 2. Let g(s) = -c(s) + 5*k(s). Suppose g(d) = 0. What is d?
1/4, 8
Let k(j) be the first derivative of -j**6/60 + j**5/30 + j**4/12 - j**3/3 - 9*j**2 + 4. Let q(w) be the second derivative of k(w). Find g such that q(g) = 0.
-1, 1
Let w = 310 + -307. Let n(t) be the first derivative of 1 + 0*t**2 + 0*t + 2/27*t**w. Factor n(o).
2*o**2/9
Let c(a) be the third derivative of -a**8/560 + 3*a**7/280 - a**6/40 + a**5/40 + a**3 - 18*a**2. Let s(k) be the first derivative of c(k). Factor s(w).
-3*w*(w - 1)**3
Let v(i) be the first derivative of 3*i - 6 - 3*i**2 - 3/20*i**5 - 1/10*i**6 + 3/4*i**4 + 1/2*i**3. Let k(g) be the first derivative of v(g). Factor k(z).
-3*(z - 1)**2*(z + 1)*(z + 2)
Factor 1/2*l + 0 - 1/10*l**2.
-l*(l - 5)/10
Let w(f) = f**3 + 25*f**2 + 11*f - 45. Let m(y) = 4*y**3 + 75*y**2 + 34*y - 135. Let o(z) = 4*m(z) - 11*w(z). Suppose o(n) = 0. Calculate n.
-3, 1
Factor 3/2*q**2 + 21*q**3 + 0*q - 279/8*q**4 + 0.
-3*q**2*(3*q - 2)*(31*q + 2)/8
Suppose -13 = -5*k + 2*d, -d - d - 8 = 0. Let t be k/(4 + 15/(-4)). Factor -292*p**2 + 86*p - 16*p**4 + 138*p + 172*p**3 + 52 + t*p**5 - 28*p**4 - 116.
4*(p - 4)**2*(p - 1)**3
Let p(a) be the second derivative of a**5/30 + a**4/9 - 20*a**3/9 + 8*a**2 - 46*a + 4. Factor p(d).
2*(d - 2)**2*(d + 6)/3
Factor 1/2*t**2 + 1/6*t**4 + 0 + 5/6*t**3 - 1/6*t**5 + 0*t.
-t**2*(t - 3)*(t + 1)**2/6
Let c(y) be the first derivative of y**4/14 - 4*y**3/7 + 11*y**2/7 - 12*y/7 + 43. Factor c(a).
2*(a - 3)*(a - 2)*(a - 1)/7
Let k(u) be the first derivative of -u**6/135 - u**5/30 - u**4/18 - u**3/27 - 12*u + 12. Let y(v) be the first derivative of k(v). Factor y(d).
-2*d*(d + 1)**3/9
Let g = -3622 + 3626. Find i, given that 2 - 37/2*i**3 - 123/2*i**g - 63/2*i**5 + 14*i + 47/2*i**2 = 0.
-1, -1/3, -2/7, 2/3
Factor -2/7*h**3 + 8/7*h - 2/7*h**2 + 8/7.
-2*(h - 2)*(h + 1)*(h + 2)/7
Let d(b) = 5*b**5 + 21*b**4 - 10*b**3 - 14*b**2 + 12*b - 14. Let x(k) = 2*k**5 + 10*k**4 - 5*k**3 - 7*k**2 + 6*k - 6. Let j(o) = -3*d(o) + 7*x(o). Factor j(i).
-i*(i - 6)*(i - 1)**2*(i + 1)
Let 1/3*j**3 + j + 2*j**2 - 10/3 = 0. What is j?
-5, -2, 1
Let t = -3746 + 3750. Find h such that 343/8*h**5 - 147/4*h**t + 143/4*h**2 - 21/2*h - 259/8*h**3 + 1 = 0.
-1, 2/7, 1
Let r(x) be the first derivative of 5/4*x**4 + 1/3*x**5 + 5/9*x**3 - 2 - 5/2*x**2 - 10/3*x. Find s such that r(s) = 0.
-2, -1, 1
Factor 9/4*i**2 + 13/4*i + 1.
(i + 1)*(9*i + 4)/4
Let r(g) = g**2 + 205*g + 12769. Let j(d) = -7*d. Let h(z) = 3*j(z) - r(z). Factor h(s).
-(s + 113)**2
Let l = 265 - 265. Let b(z) be the second derivative of -z + 0*z**2 + 0 - 1/100*z**5 + 1/150*z**6 + 1/210*z**7 - 1/60*z**4 + l*z**3. Factor b(s).
s**2*(s - 1)*(s + 1)**2/5
Let f(p) = -2*p**2 - 3*p - 4. Suppose -4 = -5*l + 1. Let m(o) = -o**2 - o - 1. Let s(j) = l*f(j) - 3*m(j). Factor s(v).
(v - 1)*(v + 1)
Suppose -5*s + 156 = -w, -2*s + 4*w = 9 - 75. Factor -x**2 - 10 - s*x + 3*x**2 + 39*x.
2*(x - 1)*(x + 5)
Let a = -1373/8 - -9803/56. Solve 22/7*r**4 - 2*r**2 - 18/7*r**3 - 8/7 - 6/7*r**5 + a*r = 0 for r.
-1, 2/3, 1, 2
Let -57/2*n - 165/8*n**4 + 291/8*n**3 + 45/2*n**2 + 6 = 0. Calculate n.
-1, 4/11, 2/5, 2
Let z(x) be the second derivative of -7921*x**4/3 + 712*x**3 - 72*x**2 + 93*x. Factor z(l).
-4*(89*l - 6)**2
Let q(g) = 17*g**2 + 126*g + 1330. Let c(r) = -5*r**2 - 42*r - 443. Let w(z) = -21*c(z) - 6*q(z). Suppose w(j) = 0. What is j?
-21
Let a(d) = -4*d**3 - d - 2. Let t(x) = 10*x**3 + 26*x**2 - 99*x + 132. Let b(r) = -3*a(r) - t(r). Factor b(n).
2*(n - 7)*(n - 3)**2
Suppose -55 = -78*x + 257. Factor 6 + 3/8*z**x - 3*z**2 + 0*z**3 + 0*z.
3*(z - 2)**2*(z + 2)**2/8
Let z(b) be the first derivative of -b**7/147 + 4*b**5/35 - 16*b**3/21 - 24*b + 37. Let s(i) be the first derivative of z(i). Factor s(t).
-2*t*(t - 2)**2*(t + 2)**2/7
Factor -42*a + 18*a + 32 - 2*a**2 + 12*a.
-2*(a - 2)*(a + 8)
Let h(o) be the third derivative of o**9/3780 - o**7/315 + o**5/30 - 7*o**4/12 - 14*o**2. Let d(u) be the second derivative of h(u). Factor d(n).
4*(n - 1)**2*(n + 1)**2
Let c(o) = o**2 - 19 + 31 - 11 - o. Let f(u) = 4*u**3 - 8*u**2 - 4*u - 28. Let j(h) = -12*c(h) - f(h). Determine z, given that j(z) = 0.
-2, -1, 2
Let i(y) be the first derivative of -36 + 0*y - 1/2*y**3 - 3/2*y**2 + 3/4*y**4 + 3/10*y**5. Factor i(b).
3*b*(b - 1)*(b + 1)*(b + 2)/2
Factor -104/5 - 12*n - 4/5*n**2.
-4*(n + 2)*(n + 13)/5
Let x be (-25)/(-51) - (-21)/119. Factor 1/3*r**4 - 1/3*r**5 - 1/3*r + 1/3 - 2/3*r**2 + x*r**3.
-(r - 1)**3*(r + 1)**2/3
Suppose -2*o + 12 = 4. Let g(t) = -2*t**2 - 2*t - 4. Let j(v) = 4*v**2 + 5*v + 8. Let m(x) = o*j(x) + 7*g(x). Factor m(h).
2*(h + 1)*(h + 2)
Factor -6*o - 34*o**3 - 4*o**2 - o**3 + 5*o**3 + 9*o**4 - 2*o**4 + 33*o**2.
o*(o - 3)*(o - 1)*(7*o - 2)
Let w(m) be the second derivative of -m**4/7 + 26*m**3/21 + 20*m**2/7 - 2*m + 5. Suppose w(k) = 0. What is k?
-2/3, 5
Let b(j) = 814*j - 829*j + 2*j**2 + 3*j**3 - 9*j**2 - 5. Let n(h) = -2*h**3 + 7*h**2 + 15*h + 6. Let k(i) = -3*b(i) - 4*n(i). Let k(y) = 0. Calculate y.
-3, -1
Suppose -2*n - 1 = -5, 0 = 2*c + 3*n - 12. Let g be (c - (-15)/(-5))/2. Let 3/4*m + g + 0*m**2 - 3/4*m**3 = 0. What is m?
-1, 0, 1
Let t be 3/4 - (-260)/80. Let -10*d**3 + 8*d**3 - 6*d + 2 - 6*d**2 - t = 0. What is d?
-1
Find o such that -o**2 + 0*o**2 + 10*o**2 - 8*o**2 + 2*o + 2 + o = 0.
-2, -1
Let q(a) be the second derivative of a**5/30 - 4*a**4/3 + 64*a**3/3 - 11*a**2/2 - 7*a. Let v(l) be the first derivative of q(l). What is k in v(k) = 0?
8
Factor -60*w + 25 + 12 + 23 + 5 - 5*w**2.
-5*(w - 1)*(w + 13)
Let i(z) be the third derivative of 8*z**5/3 - 41*z**4/6 + 2*z**3/3 + 194*z**2. Factor i(v).
4*(v - 1)*(40*v - 1)
Let s = 835 + -10849/13. Determine y so that s + 2/13*y - 2/13*y**3 - 6/13*y**2 = 0.
-3, -1, 1
Let r(s) be the first derivative of -s**4/20 + 2*s**3/5 - 6*s**2/5 + 8*s/5 - 231. Find c, given that r(c) = 0.
2
Let c(a) be the third derivative of 0*a + 1/15*a**5 + 0 + 15*a**2 - 10/3*a**4 + 200/3*a**3. Factor c(y).
4*(y - 10)**2
Factor -4/3*o**3 - 96 + 40/3*o**2 - 16*o.
-4*(o - 6)**2*(o + 2)/3
Let p(y) be the second derivative of y**7/231 - 4*y**6/165 - y**5/110 + 2*y**4/33 + 12*y + 1. Let p(c) = 0. Calculate c.
-1, 0, 1, 4
Let j(t) be the first derivative of 1/3*t**6 - 6/5*t**5 - 1/2*t**4 + 14/3*t**3 + 0*t**2 + 11 - 8*t. Let j(m) = 0. Calculate m.
-1, 1, 2
Let p be (-2)/(-4) - (200/(-52))/(-2). Let j = -12/13 - p. Factor 0*t**2 - 3/2*t + j*t**3 + 1.
(t - 1)**2*(t + 2)/2
Factor 12*p + 478 + 18*p**3 + 81*p**2 - 1124 - 3*p**4 + 538.
-3*(p - 9)*(p - 1)*(p + 2)**2
Factor 25/3*t**5 - 56/3*t**3 + 0*t + 55/3*t**4 + 4*t**2 + 0.
t**2*(t + 3)*(5*t - 2)**2/3
Let g(l) be the first derivative of 19 + 1/9*l**3 - 5/6*l**2 + 2*l. Factor g(y).
(y - 3)*(y - 2)/3
Factor 47/4*r + 15/4 - 1/4*r**5 + 9/2*r**3 + 25/2*r**2 - 1/4*r**4.
-(r - 5)*(r + 1)**3*(r + 3)/4
Let c(x) = -4*x + x**2 + x**3 + 10*x - 7*x - 1. Let p(m) = -5*m**3 - 7*m**2 + m + 11. Let h(t) = 14*c(t) + 2*p(t). Let h(z) = 0. What is z?
-2, 1
Let t(v) be the first derivative of 0*v**3 + 10 + 1/6*v**4 + 1/9*v**6 - 4/15*v**5 + 0*v + 0*v**2. Factor t(f).
2*f**3*(f - 1)**2/3
Factor 0*c - 1/6*c**5 + 0*c**2 - 1/3*c**4 + 0 - 1/6*c**3.
-c**3*(c + 1)**2/6
Suppose 2*y + y + 36 = 0. Let u = 14 + y. Let 3*f**2 + 5*f**u - 6*f**2 = 0. Calculate f.
0
Determine g, given that g + g**2 - 4*g + g + 6*g = 0.
-4, 0
Suppose 3*m = 5 + 10. Suppose 3*y + y = m*k + 20, 5*y - k - 46 = 0. Factor 3*n**3 - 5*n**5 - 11*n**3 + y*n**2 + 20*n**4 - 17*n**3.
-5*n**2*(n - 2)*(n - 1)**2
Find z, given that 44*z**2 + 37*z + 289 - 22*z**2 - 21*z**2 - 3*z = 0.
-17
Let x(k) be the second derivative of k**6/90 + k**5/10 + k**4/4 - 11*k + 7. Solve x(n) = 0.
-3, 0
Let p(o) be the third der