2)). Let f(i) be the second derivative of -1/20*i**4 + 0*i**m + 0*i**3 + 0 + 8*i - 1/100*i**5. Let f(r) = 0. What is r?
-3, 0
Let b(q) be the third derivative of q**6/200 + 3*q**5/20 - 53*q**4/20 - 12*q**3 - 8563*q**2. Factor b(h).
3*(h - 6)*(h + 1)*(h + 20)/5
Suppose -104*j + 1777 = -4047. Let t be 8/j*49/21. Factor -t*g**3 + 1/3*g**5 + 0*g - 1/3*g**2 + 1/3*g**4 + 0.
g**2*(g - 1)*(g + 1)**2/3
Suppose 78*b = -46*b + 97*b + 135. Let r = 1/6 - -1/3. Determine k, given that -r*k**b + k**4 - k**2 + 0 + 1/2*k + 0*k**3 = 0.
-1, 0, 1
Suppose -3*x = -6*l + 10*l + 3281, -2*l + 3*x - 1627 = 0. Let q = -818 - l. Factor q + 0*s + 2/3*s**2 - 7/3*s**4 - 5/3*s**3.
-s**2*(s + 1)*(7*s - 2)/3
Let q(z) be the first derivative of -z**3/18 - 677*z**2/12 + 113*z - 12402. Factor q(s).
-(s - 1)*(s + 678)/6
Let h = 48748 - 975743/20. Let t = -192/5 - h. Factor -t*z - 1/2 - 1/4*z**2.
-(z + 1)*(z + 2)/4
Factor 253*j - j**2 - 124*j - 18 - 120*j.
-(j - 6)*(j - 3)
Let -18*x**2 - 19179492*x**5 - 6*x**4 + 19179493*x**5 - 16*x**3 - 9*x**3 = 0. Calculate x.
-2, -1, 0, 9
Let f(b) be the first derivative of -2*b + 12 + 1/3*b**3 - 1/2*b**2. Suppose f(u) = 0. Calculate u.
-1, 2
Let x = -87818 - -1141636/13. Factor 2400/13*z - 120/13*z**2 - 16000/13 + x*z**3.
2*(z - 20)**3/13
Let f(l) be the first derivative of 1/3*l**3 - 8*l - l**2 + 80. Let f(w) = 0. What is w?
-2, 4
Determine r, given that 57/2*r**2 + 33*r - 21/2*r**4 + 0 - 15*r**3 = 0.
-2, -1, 0, 11/7
Suppose -378*y**2 + 14*y**5 + 52900 + 100*y**5 - 13672*y**3 - 9726*y**2 + 340*y**4 + 156860*y + 45*y**5 + 141*y**5 = 0. What is y?
-5, -1/3, 23/5
Let f(t) = -t + 4. Let a be f(0). Suppose 0 = a*n + 2*n - 6. Solve -5 - 2 - 16*m - 4 - 4*m**2 - n = 0.
-3, -1
Suppose 23*n - 534 = 87. Factor 4*v**2 + 55*v + 20 - 2*v - 6*v**3 - n*v + 4*v**3.
-2*(v - 5)*(v + 1)*(v + 2)
Let n(w) = 95*w**3 + w**2 + 2*w. Let y be n(-1). Let s be ((-4)/(-5))/(y/(-30) + -3). Factor -24*q - 44*q**2 - 726*q**3 + 774*q**3 + 11*q**s + 9*q**4.
4*q*(q - 1)*(q + 3)*(5*q + 2)
Let n(k) = -36*k + 616. Let o be n(17). Let m(t) be the third derivative of 15/2*t**3 + 0*t + 1/3*t**5 + 35/16*t**o + 1/48*t**6 + 0 + 12*t**2. Factor m(h).
5*(h + 2)*(h + 3)**2/2
Determine p so that 343*p**2 + 94*p**2 + 8*p**2 + 77*p - 175*p**2 + 455*p + 2*p**3 = 0.
-133, -2, 0
Let q(a) be the third derivative of -a**6/30 - 4*a**5/35 - a**4/14 + 4*a**3/21 + 7*a**2 + 1. Factor q(l).
-4*(l + 1)**2*(7*l - 2)/7
Let z(b) be the third derivative of -b**5/12 + 835*b**4/24 - 415*b**3/3 - 19*b**2 - 4*b. Factor z(x).
-5*(x - 166)*(x - 1)
Let o(v) be the second derivative of 66*v + 5/21*v**3 + 0 - 3/70*v**5 - 1/21*v**4 + 0*v**2. Determine a so that o(a) = 0.
-5/3, 0, 1
Suppose 5*l - 230 = -3*w, 2*l - 142 = -l - w. Solve 6*r + 7*r**3 + r**3 - 47*r**4 - 5*r - 21*r + 16 - 6*r**2 + l*r**4 = 0.
-4, -2, 1
Suppose 61 = 4*v + k, -14*v - 3*k + 71 = -9*v. Determine s, given that -122*s - 11*s**2 - 128 - 2*s**3 - v*s**2 + 26*s - 5*s**2 + 8*s**2 = 0.
-4
Let y(g) be the second derivative of g**6/90 - 4*g**5/15 + 3*g**4/4 + 8*g**3/9 - 14*g**2/3 + 501*g. Find o such that y(o) = 0.
-1, 1, 2, 14
Suppose -304*q + 21 = -307*q + 3*z, 2*z - 39 = -3*q. What is l in 0 + 0*l + 2/3*l**3 - 2/3*l**4 + 0*l**2 + 1/6*l**q = 0?
0, 2
Factor 328 - 176*u - 625*u**2 - 154*u + 627*u**2.
2*(u - 164)*(u - 1)
Let h(b) be the first derivative of 2*b**6/3 + 28*b**5/5 + 2*b**4 - 160*b**3/3 - 204. Suppose h(u) = 0. What is u?
-5, -4, 0, 2
Suppose 0 = 27*m - 32*m. Let t be (m - -1)/(25/50). Factor 9*c**4 + 12*c**3 - c**2 - 8 + 5*c**t - 5*c**4 + 0*c**2 - 12*c.
4*(c - 1)*(c + 1)**2*(c + 2)
Let c(q) be the third derivative of 2*q**7/105 + 6*q**6 + 71*q**5/3 - 30*q**4 - 712*q**3/3 - 9*q**2 + 2*q - 166. Solve c(j) = 0 for j.
-178, -2, -1, 1
Let q(z) = 5667*z - 136006. Let g be q(24). Find l, given that 15/4 - 3/8*l**g + 9/8*l = 0.
-2, 5
Let r be 135/5 - (-8 + 2)/(-2). Let s(x) = x**2 - 24*x + 11. Let w be s(r). Factor 0*b + 10*b**2 + 5*b**3 - 4*b - w - b + 1.
5*(b - 1)*(b + 1)*(b + 2)
Let a(p) be the second derivative of 3*p**5/10 + 5*p**4/12 - 16*p**3/3 + 21*p**2/2 + 5164*p. Factor a(y).
(y - 1)*(y + 3)*(6*y - 7)
Let 42*h - 27*h**4 - 185*h**2 + 2054*h**2 - 1089*h**3 + 65 + 61 - 921*h = 0. What is h?
-42, 1/3, 1
Let b = -3/6673 - -233573/40038. Find z such that 85/6*z**2 + 0 + 15/2*z + b*z**3 - 5/6*z**4 = 0.
-1, 0, 9
Let a = -478 + 503. Let n be 37/2 - 12/8. Find z such that z**2 + n + 60*z + 7*z**2 - a*z**3 + 7*z**2 + 3 = 0.
-1, -2/5, 2
Let n be (-36)/96 - (-207946)/112. Let z = -1856 + n. Find r such that -6/7*r + 0*r**2 - 4/7 + z*r**3 = 0.
-1, 2
Let v(w) = -2*w**2 + 13*w + 36. Let j be v(8). Let g be (3/(-5))/((-18)/j). Factor g*h**3 + 2*h**2 + 0 + 8/5*h.
2*h*(h + 1)*(h + 4)/5
Let x(y) be the first derivative of y**4/14 - 16*y**3/7 - 27*y**2/7 + 100*y/7 - 10452. Factor x(z).
2*(z - 25)*(z - 1)*(z + 2)/7
Let s(j) be the second derivative of -31*j**6/45 - 22*j**5/3 - 7*j**4/6 + 141*j - 17. Solve s(i) = 0 for i.
-7, -3/31, 0
Let r(n) = -2*n**2 + 1135*n + 1110. Let l(t) = -5*t**2 + 3415*t + 3330. Let j(m) = 3*l(m) - 10*r(m). Factor j(k).
5*(k - 222)*(k + 1)
Let g(a) = 2*a**2 + 41*a + 216. Let j be g(-10). Let x(h) = -h - 4. Let f be x(-6). Find i, given that -2*i**2 - 2*i**2 + i**2 - 5*i + j + 4*i**f = 0.
2, 3
Let k(m) = -9*m + 138. Let w be k(15). Find y such that -6*y**w - 6*y**3 + 26*y**3 - 5*y**3 - 4*y**4 - 5*y**3 + 24*y**2 = 0.
-2, 0, 3
Let -364/5*b + 176/5*b**2 + 184/5 + 4/5*b**3 = 0. What is b?
-46, 1
Let h(w) be the first derivative of w**5/15 + 11*w**4/6 - 100*w**3/9 + 52*w**2/3 - 2400. Factor h(g).
g*(g - 2)**2*(g + 26)/3
Let t(q) = -112*q**3 + q + 1 + q**2 + 113*q**3 + 0*q**2. Let u(h) = 3*h**3 - 35*h**2 - 195*h + 5. Let s(j) = -10*t(j) + 2*u(j). Factor s(i).
-4*i*(i + 10)**2
Let o = 50 + -46. What is s in -32*s**2 - 83*s - 4*s**5 - 7*s**3 - 49*s + 13*s**3 - 72 + 34*s**3 + 8*s**o = 0?
-2, -1, 3
Let c = 40/253 - 24947/159390. Let x(w) be the third derivative of 0*w + 12*w**2 + 0 - c*w**5 + 0*w**3 + 0*w**4. Factor x(g).
-2*g**2/21
Let x(t) = -2*t**5 - 34*t**4 - 40*t**3 + 4*t**2 + 4. Let s(w) = -4*w**5 - 66*w**4 - 81*w**3 + 7*w**2 + 7. Let b(a) = 4*s(a) - 7*x(a). Factor b(o).
-2*o**3*(o + 2)*(o + 11)
Find v such that -48/5 + 444/5*v**2 - 16*v - 32/5*v**5 - 216/5*v**4 - 68/5*v**3 = 0.
-6, -2, -1/4, 1/2, 1
Suppose 3*g - 2*b + 2 = 1, b - 8 = -g. Let x(f) = 3*f**2 - 7*f - 4. Let z be x(g). Let 2/17*n**z - 2/17 + 2/17*n**3 - 2/17*n = 0. Calculate n.
-1, 1
Let j = 51 - 509/10. Let u(p) be the first derivative of 0*p**3 + 0*p**2 - j*p**4 + 0*p - 2/25*p**5 + 13. Determine m so that u(m) = 0.
-1, 0
Let d be (5/6)/(1/6) - 5. Suppose -4 = -4*f + c, 3*c + d = -3*f + 18. Let -9/5*o**4 + 0 - 3/5*o + 9/5*o**f + 6/5*o**5 - 3/5*o**3 = 0. Calculate o.
-1, 0, 1/2, 1
Let k be (-11)/(5/((-105)/(-22)) - 1). Let s = k + 234. Determine j so that 1/3*j**2 + 0*j + 0 + 1/6*j**s = 0.
-2, 0
What is g in 335*g + 281*g**2 - 165 + 5*g**3 - 354*g**2 - 102*g**2 = 0?
1, 33
Let n be 2/(-3) + 28/6. Let d = 3096 - 3093. Factor 341*o**2 - 343*o**2 + 2*o**3 + 2*o**d - 2*o**n.
-2*o**2*(o - 1)**2
Suppose 32/19*z**2 - 2/19*z**5 - 32/19 + 0*z**4 + 26/19*z**3 - 24/19*z = 0. What is z?
-2, -1, 1, 4
Let q be (-9)/(-30)*(9/117 + 555/10530). Let b(j) be the third derivative of 1/2*j**3 + 0*j - 1/360*j**6 - 33*j**2 + 0 + 17/72*j**4 + q*j**5. Factor b(g).
-(g - 9)*(g + 1)**2/3
Let w = 1550 - 1542. Let u be -16 + 15 + w + (0 - 2). Let -2/9*f + 0 + 7/9*f**2 - 1/9*f**u - f**3 + 5/9*f**4 = 0. What is f?
0, 1, 2
Let l(s) = s**3 + 11*s**2 + 3. Let a be l(-9). Determine b, given that -4*b**3 + a*b - b**2 + 17*b**2 - 165*b = 0.
0, 4
Let u be 40/(-30)*6/(-4). Suppose 3*p - 77 = 5*x, -54 = -4*p - 2*x + 40. Factor 12*w**u + 2*w**3 + w**3 + 16 - w**3 - p*w - 4*w**3.
-2*(w - 2)**3
Factor -4/3*k**2 + 5120/3*k - 1638400/3.
-4*(k - 640)**2/3
Let m(u) = -11*u**2 - 73*u + 80. Let h(t) = 13*t**2 + 74*t - 82. Let p(j) = 4*h(j) + 5*m(j). Factor p(y).
-3*(y - 1)*(y + 24)
Factor 17781 - 3*b**5 + 7*b**5 - 160*b**4 - 10504*b**2 + 4913*b - 181*b + 2176*b**3 - 205.
4*(b - 13)**3*(b - 2)*(b + 1)
Let w = 1185/496 - -55/496. Solve -5/2 - 1/2*p + 1/2*p**3 + w*p**2 = 0.
-5, -1, 1
Suppose -6*s + 3*v = -60, -1554*s = -1552*s + 4*v - 60. Suppose -2/5*r**3 + 2*r**4 - 58/5*r**2 - 24/5 - s*r = 0. Calculate r.
-1, -4/5, 3
Let y be