 - 3*k - 237*k**4.
2*k*(k - 1)*(k + 1)**2
Let g(v) be the first derivative of 4*v**5 + 375*v**4/4 - 165*v**3 + 50*v**2 + 1268. Find h such that g(h) = 0.
-20, 0, 1/4, 1
Suppose -3*l + 24 - 3 = 0. Solve 16 - 28*k + k**4 + k**4 + k**3 + 6*k**2 + l*k**3 - 4*k**4 = 0 for k.
-2, 1, 4
Suppose 3*n = d + 5, 491*n - 490*n - 4*d = 20. Let r(g) be the third derivative of n + 0*g - 5/18*g**4 - 17*g**2 - 1/45*g**5 + 0*g**3. Factor r(m).
-4*m*(m + 5)/3
Factor 19/6*b + b**2 - 1/6*b**3 - 4.
-(b - 8)*(b - 1)*(b + 3)/6
Suppose -1273*f + 60*f = -43668. Determine u so that -f*u**2 - 1512*u - 21168 - 2/7*u**3 = 0.
-42
Suppose -3*y + 2*j + 106 = -3*j, 2*y = 3*j + 70. Suppose -y*h = -31*h. What is l in 3*l + 3*l**3 + h*l**2 + 5*l**2 - 2*l**2 + 3*l**2 = 0?
-1, 0
Let n(m) be the second derivative of -m**4/48 + 13*m**3/3 + 321*m**2/8 - 970*m. Factor n(h).
-(h - 107)*(h + 3)/4
Let r = 80 - 84. Let l be (-15)/(-3)*3 + r. Determine s so that -368*s + 19 + 5*s**2 + 343*s + l = 0.
2, 3
Let w(f) = f**2 + 7*f - 27. Let v be w(-13). Suppose -v + 21 = -6*h. Factor -1/3*p**h + 5/3*p**4 - 4/3*p**2 + 0 + 8/3*p - 2*p**3.
-p*(p - 2)**3*(p + 1)/3
Suppose -5 = -6*f - 125. Let q be 2/(-9) - f/90. Factor 4/11*x + 4/11*x**2 + q + 1/11*x**3.
x*(x + 2)**2/11
Let t(f) = 8*f**3 + 250*f**2 + 8316*f + 51993. Let v(c) = -14*c**3 - 498*c**2 - 16634*c - 103983. Let o(h) = -5*t(h) - 3*v(h). Let o(k) = 0. What is k?
-57, -8
Let h = -121595/2 - -60798. Factor h*a**2 + 7*a + 12.
(a + 2)*(a + 12)/2
Let k(i) be the first derivative of i**4/12 - 10*i**3 + 88*i**2/3 - 230. Factor k(c).
c*(c - 88)*(c - 2)/3
Let s(q) be the first derivative of 5/12*q**6 - 43/8*q**4 + 1/2*q**2 - 4*q + 7/10*q**5 + 43 + 37/6*q**3. Factor s(a).
(a - 1)**3*(a + 4)*(5*a + 2)/2
Let o be (60/7)/(8/84). Let p be (-15)/(-21) + 716/7. Suppose 8*k**2 - 65*k**4 + k**2 - 6*k + o*k**3 - p*k**4 = 0. Calculate k.
-1/4, 0, 2/7, 1/2
Let v(b) be the first derivative of -6 - 6/5*b**2 + 1/25*b**5 + 1/5*b**4 + 11*b - 2/15*b**3. Let n(u) be the first derivative of v(u). Factor n(a).
4*(a - 1)*(a + 1)*(a + 3)/5
Let n(p) = p**2 - 4*p. Let z(s) be the second derivative of 4*s**4/3 - 35*s**3/3 - 5*s - 19. Let r(o) = 36*n(o) - 2*z(o). Find y, given that r(y) = 0.
0, 1
Let y(d) = 20*d**2 - 120*d + 84. Let l be -5*(-4 - (-18)/5). Suppose l*m + 17 = 23. Let u(f) = 4*f**2 - 24*f + 17. Let i(p) = m*y(p) - 16*u(p). Factor i(g).
-4*(g - 5)*(g - 1)
Let n(b) be the first derivative of 3*b**5/20 - b**4/2 - b**3/2 + 3*b**2 - 93*b - 84. Let l(o) be the first derivative of n(o). Factor l(y).
3*(y - 2)*(y - 1)*(y + 1)
Let m(o) be the second derivative of o**7/21 + 2*o**6/15 - 3*o**5/2 - 6*o**4 - 36*o - 1. Factor m(c).
2*c**2*(c - 4)*(c + 3)**2
Suppose 9*t + 62 - 35 = 0. Let p(m) = 6*m**3 + 39*m**2 + 147*m. Let b(x) = -5*x**3 - 40*x**2 - 147*x. Let d(u) = t*b(u) - 2*p(u). Factor d(f).
3*f*(f + 7)**2
Suppose -2*q + 0*m - 3*m = -944, 4*q - 5*m = 1888. Let -306 + 135*u**2 + 5*u**3 + 1084*u + 36*u - q - 202 - 280*u**2 = 0. Calculate u.
1, 14
Let x(c) = c**2 - 8*c - 2. Let o be (-1 - 22/(-4))*(-66)/9. Let v(h) = 6*h**2 - 42*h - 9. Let b(g) = o*x(g) + 6*v(g). Determine p so that b(p) = 0.
-2
Factor 655 + 585 + 1088*v - 2*v**3 + 194 + 453*v**2 - 3958*v + 985*v**2.
-2*(v - 717)*(v - 1)**2
Let u = -253 + 273. Suppose c - 5*p + 20 = 0, -4*c = -6*p + 11*p - u. Let 0*o**3 + 0*o + 1/4*o**4 + 0 + 1/4*o**5 + c*o**2 = 0. Calculate o.
-1, 0
Suppose 4073*b + 18 = 4079*b. Let -6/7 + 3/7*u**5 - 6/7*u**b - 6/7*u**4 + 3/7*u + 12/7*u**2 = 0. What is u?
-1, 1, 2
Let s(m) be the second derivative of -3/4*m**3 - 3/2*m**2 + 1/20*m**6 + 0 + 54*m + 1/8*m**4 + 9/40*m**5. Find r, given that s(r) = 0.
-2, -1, 1
Let w be ((-16)/(-10)*-18)/((-8)/40). Let p = w - -5. Factor 2 + 5*g**2 - 144*g + p*g - 2.
5*g*(g + 1)
Let k(f) be the first derivative of -f**3 - 303*f**2 - 30603*f + 571. Factor k(r).
-3*(r + 101)**2
Let l(x) = 6*x**5 + 8*x**4 - 180*x**3 - 5*x + 5. Let r(d) = 7*d**5 + 9*d**4 - 180*d**3 - 6*d + 6. Let i(u) = -6*l(u) + 5*r(u). Factor i(y).
-y**3*(y - 12)*(y + 15)
Let b(n) be the third derivative of -35*n**2 + 1/4*n**5 + 0*n**3 + 5/336*n**8 + 2 - 5/24*n**6 + 1/42*n**7 + 0*n**4 + 0*n. Find m such that b(m) = 0.
-3, 0, 1
Let h be (-8)/(-36) - ((-968)/18 + 2). Factor -4*y**2 - 41*y**2 - 8 + y**2 - 26*y**2 - 49*y**3 + h*y.
-(y + 2)*(7*y - 2)**2
Let r(o) be the second derivative of o**4/4 - 7*o**3/6 - 11*o**2 + 30*o. Let c be r(9). Determine j so that 20 - 10*j + c*j**2 - 15*j - 153*j**2 = 0.
1, 4
Suppose -5*n + 5*q = -5, 22*n - 8 = 17*n + 2*q. Let a = 8 + -8. Suppose 2*k**3 - n*k - 12*k**2 + 12*k + a*k**3 + 0*k**3 = 0. What is k?
0, 1, 5
Suppose -21*c = -0*c + 105. Let l be (48/70)/(-2)*(c + -2). Factor l*t + 0 + 3/5*t**2.
3*t*(t + 4)/5
Determine c, given that -2/3*c**2 + 316/3*c - 314/3 = 0.
1, 157
Let z(a) be the second derivative of 1/4*a**5 + 165/2*a**2 - 2*a - 325/6*a**3 + 99 + 155/12*a**4. What is f in z(f) = 0?
-33, 1
Let m = -175 - -193. Factor 21*s**2 + m*s**2 - 35*s**2 + 2*s**3.
2*s**2*(s + 2)
Let r(p) be the second derivative of -p**7/42 + p**6/8 + p**5/3 + 11*p**2 - 7*p - 2. Let d(q) be the first derivative of r(q). Let d(z) = 0. Calculate z.
-1, 0, 4
Let s(z) be the second derivative of -4/3*z**3 - 63/10*z**5 + 19*z + 5*z**4 + 0 + 49/30*z**6 + 0*z**2. Determine g so that s(g) = 0.
0, 2/7, 2
Let b = 310/123 + 6/41. Suppose 61*n + 1174 - 1357 = 0. Let -8/3*o + 2/3*o**4 - b*o**2 + 0 + 2/3*o**n = 0. Calculate o.
-2, -1, 0, 2
Let j(k) be the third derivative of k**5/40 + 499*k**4/8 + 249001*k**3/4 - 3032*k**2. Solve j(d) = 0 for d.
-499
Suppose -27*q = -28*q + 60. Factor -q - 56*l + 44*l - 11 - 9 + 2*l**2.
2*(l - 10)*(l + 4)
Let p(v) be the second derivative of -v**6/60 - v**5/30 + 2*v**4/3 + 4*v**3 + 149*v**2/2 + 18*v + 1. Let h(x) be the first derivative of p(x). Factor h(l).
-2*(l - 3)*(l + 2)**2
Factor 14792/13 + 15482/13*f**2 - 29928/13*f - 348/13*f**3 + 2/13*f**4.
2*(f - 86)**2*(f - 1)**2/13
Let v be -7*(1 + (-78)/42). What is i in -14 + 4 - v + 108*i + 47*i**2 - 147*i**2 - 64*i**4 - 288*i**3 = 0?
-4, -1, 1/4
Find i, given that 205/3*i - 28/3*i**2 - 150 + 1/3*i**3 = 0.
5, 18
Suppose 6*x + 16 = y + 3*x, 2*y - 5*x - 28 = 0. Let f be -4 + (y + 4 - 3/3). Determine d so that -30*d**2 - 5*d - 15*d - 4*d**3 - 2*d**4 - 10*d**f + 2*d = 0.
-3, -1, 0
Let o = -4145 - -2945. Let d = o - -1200. Suppose 4*j**2 - 4/3*j + d - 1/3*j**5 - 13/3*j**3 + 2*j**4 = 0. What is j?
0, 1, 2
Let m = 392765/33 + -11903. Let w = -106/231 - m. Suppose -w*x - 6/7*x**2 + 2/7 = 0. Calculate x.
-1, 1/3
Let c(p) = 3969*p**3 - 710*p**2 - 424*p - 20. Let m(d) = 39690*d**3 - 7095*d**2 - 4238*d - 202. Let b(a) = 21*c(a) - 2*m(a). Factor b(h).
(9*h - 4)*(9*h + 2)*(49*h + 2)
Let a(f) = -2*f**2 - 4*f - 2. Let c be a(-4). Let u be (-20)/(-6) + (-12)/c. Factor -47*d**2 - 65*d**3 - 20*d + 19*d**2 - 30*d**u - 32*d**2 - 5*d**5.
-5*d*(d + 1)**2*(d + 2)**2
Let i(z) be the third derivative of z**7/1155 - z**6/5 + 2042*z**5/165 + 136*z**4 + 18496*z**3/33 + 2*z**2 + 1242. Factor i(p).
2*(p - 68)**2*(p + 2)**2/11
Let x(t) = -t**3 + 6*t + 2. Let p(u) = u + 1. Let g = -21 - -51. Suppose 18*w + g = 21*w. Let k(l) = w*p(l) - 5*x(l). Factor k(b).
5*b*(b - 2)*(b + 2)
Suppose -7*v = -2*v - 4*l - 31, -16 = -4*v + l. Factor 5*x**3 + 4*x + x + 8*x - 6 - 8*x**2 - 4*x**v.
(x - 6)*(x - 1)**2
Let p be (-40)/(-495)*(-15 + 24). Factor 8/11 - p*c + 2/11*c**2.
2*(c - 2)**2/11
Solve 29351*s - 2851*s + 1945 + 560*s**4 + 5295*s**3 + 17930*s**2 + 13517 - 5*s**5 - 942 = 0.
-3, -2, 121
Let m(f) be the third derivative of 0 + 112*f**2 - 11/20*f**5 + 0*f**3 + 7/4*f**4 - f. Factor m(t).
-3*t*(11*t - 14)
Let s(y) be the second derivative of y**4/36 + 5*y**3/2 + 22*y**2/3 + 492*y. Let s(m) = 0. What is m?
-44, -1
Let k be -13 + (-3255)/(-255) - 11830/(-10829). Solve 0 + 4/7*a**2 + 2/7*a**3 - k*a = 0 for a.
-3, 0, 1
Let z(d) be the second derivative of -5*d**4/12 + 140*d**3/3 - 2115*d**2/2 + 2189*d. Solve z(x) = 0.
9, 47
Let n(i) be the first derivative of -i**5 - 635*i**4/4 - 625*i**3 - 1865*i**2/2 - 620*i - 1069. Factor n(z).
-5*(z + 1)**3*(z + 124)
Let y be 220/(-25)*(-50)/4. Factor 7*f - 138 - 60*f**2 - 112 + 5*f**3 + 108*f + y*f.
5*(f - 5)**2*(f - 2)
Let p(z) be the third derivative of z**10/453600 + z**9/90720 + z**8/60480 + 26*z**5/15 - 14*z**2 - z. Let 