c + 4)
Find i, given that -65536/3 + 2039/6*i**3 - 294400/3*i - 42923*i**2 - 2/3*i**4 = 0.
-2, -1/4, 256
Suppose -12*f - 12*f + 96 = 0. Let -3*y**2 - 75*y**4 - 83*y**f + 162*y**4 + 7*y**2 + 8*y**3 = 0. What is y?
-1, 0
Let k(x) be the third derivative of -x**6/10 - 1892*x**5/15 + 211*x**4/2 + 2524*x**3/3 - 27*x**2 - 5*x + 17. What is q in k(q) = 0?
-631, -2/3, 1
Let m(y) be the first derivative of -y**4 - 112*y**3/3 + 120*y**2 + 2548. Factor m(n).
-4*n*(n - 2)*(n + 30)
Let s(l) be the second derivative of -l**7/168 + 13*l**6/60 - 11*l**5/40 - 5*l**4/3 + 127*l**3/24 - 25*l**2/4 + 74*l + 2. What is j in s(j) = 0?
-2, 1, 25
Let o be ((-60)/100)/((-588)/10). Let w = 43/98 - o. Find d such that -9/7*d**4 + 9/7*d**2 + 0 - 3/7*d**3 + w*d = 0.
-1, -1/3, 0, 1
Let u = 206 + -202. Factor 4*n - 4*n**3 - u*n**3 - 2*n**2 + 3*n**4 - n**4 + 4*n**3.
2*n*(n - 2)*(n - 1)*(n + 1)
Suppose 24*b - 5*b - 228 = 0. Let 4*x**2 - b*x**3 + 66*x + 9*x**3 - 15 - 57 + 5*x**2 = 0. Calculate x.
-4, 1, 6
Let k(a) be the second derivative of -9*a**3 - 27/2*a**2 - 2*a - 3*a**4 - 1/30*a**6 + 49 - 1/2*a**5. Factor k(c).
-(c + 1)*(c + 3)**3
Suppose 4*r = -8*m + 5*m + 6, 0 = 4*r + 5*m - 2. Suppose 5*s = -r*w + 999, 0*w + 601 = 3*s + w. Factor s*t**2 + 10 - 181*t**2 + 49*t - 4*t.
5*(t + 2)*(4*t + 1)
Suppose -749*c + 754*c - 154 = -29. Let n(s) be the first derivative of -s**5 - 20*s + 32 + 35/4*s**4 - c*s**3 + 65/2*s**2. Factor n(p).
-5*(p - 4)*(p - 1)**3
Suppose k = 2*y - 3, -200*k + 198*k + 9 = y. Suppose -5*p - 5*r + 30 = 0, -7*r + 26 = y*p - 2*r. Factor 144/5 + 72/5*v + 2/15*v**3 + 12/5*v**p.
2*(v + 6)**3/15
Let m(i) be the first derivative of 3*i**5/35 + 159*i**4/28 + 88*i**3 - 504*i**2 - 6490. Solve m(v) = 0 for v.
-28, 0, 3
Let c(p) be the first derivative of p**5/80 - 47*p**4/32 - 6*p**3 - 20*p**2 - 29. Let f(s) be the second derivative of c(s). Factor f(g).
3*(g - 48)*(g + 1)/4
Let z = 174 - 66. Factor -1024 - 156*o + 136*o - 4*o**2 - z*o.
-4*(o + 16)**2
Let h(s) be the first derivative of -s**7/70 - s**6/5 + s**5/20 + s**4 - 17*s**2 + 71. Let y(n) be the second derivative of h(n). Solve y(q) = 0.
-8, -1, 0, 1
Let c(b) be the first derivative of -2*b**4/7 - 2*b**3/3 + 2*b**2/7 + 918. Factor c(p).
-2*p*(p + 2)*(4*p - 1)/7
Let x(p) = -p - 7. Let h be x(1). Let o(f) = -2*f**3 - 16*f**2 - f + 9. Let u be o(h). Factor 5*t + u*t**2 - 13*t**2 + 0*t - 9*t**2.
-5*t*(t - 1)
Find v, given that -19/2*v**3 + 39/4*v - 43/2*v**2 + 23/4*v**4 - 1/4*v**5 + 63/4 = 0.
-1, 1, 3, 21
Factor -29*z**2 - 91*z**2 - 40*z**2 + 2*z**4 - 42*z**3 + 356*z**2.
2*z**2*(z - 14)*(z - 7)
Suppose 6040 + 8468 = 578*z - 520. Let 2/13*i**2 - 4*i + z = 0. What is i?
13
Suppose 70*y + 230*y + 3*y**4 + 1794 - 80*y**3 - 1182 - 615*y**2 - 220*y**3 = 0. What is y?
-2, -1, 1, 102
Let x be 2/(-5) + -2 + (-3)/5. Let i(v) = v**2 + v - 2. Let b be i(x). Factor 0*q - 2*q**3 + 4*q - 2*q**3 - 4*q**4 + b*q**2.
-4*q*(q - 1)*(q + 1)**2
Let z(k) = -9*k**2 - 2004*k - 332667. Let s(u) = -u**2 - u. Let g(x) = -6*s(x) + z(x). Let g(j) = 0. What is j?
-333
Suppose 13 = 4*w + 1, -w = 3*x - 15. Let m(i) be the third derivative of 1/96*i**x + 12*i**2 - 1/480*i**6 + 0 + 0*i**3 + 0*i**5 + 0*i. Factor m(v).
-v*(v - 1)*(v + 1)/4
Let x(a) be the first derivative of -a**6/72 - a**5/18 + 55*a**4/72 + 10*a**3/3 - a**2 + 36*a + 237. Let k(y) be the second derivative of x(y). Factor k(l).
-5*(l - 3)*(l + 1)*(l + 4)/3
Let l(c) = -3*c**5 + 15*c**3 + 8*c**2 + 2*c + 2. Let z(n) = -n**5 + n**2 - n - 1. Let i(o) = -l(o) - 2*z(o). Factor i(r).
5*r**2*(r - 2)*(r + 1)**2
Let f(x) be the third derivative of -x**5/12 - 25*x**4/8 - 35*x**3/3 + 3584*x**2. Factor f(o).
-5*(o + 1)*(o + 14)
Factor 13*q**2 - 16 + 26 - 14*q**2 - 157*q - 10.
-q*(q + 157)
Let v(b) be the third derivative of -1/2*b**4 - 151/50*b**7 + 0*b - 9/28*b**8 + 152*b**2 + 0 - 829/200*b**6 + 0*b**3 - 56/25*b**5. Let v(m) = 0. Calculate m.
-5, -2/5, -1/4, -2/9, 0
Let u be 1 - 1 - (-25 - (-6 + -19)). Let l(r) be the second derivative of -3/8*r**2 + u + 0*r**3 + 1/16*r**4 + 15*r. Factor l(n).
3*(n - 1)*(n + 1)/4
Let h(t) be the second derivative of t**4/4 + 393*t**3 + 463347*t**2/2 + 335*t. Determine s so that h(s) = 0.
-393
Let z(u) be the first derivative of 21/4*u**2 - 441/4*u - 163 - 1/12*u**3. Factor z(r).
-(r - 21)**2/4
Let r(y) be the third derivative of 59*y**2 + 0*y**3 - 1/150*y**5 + 0*y + 11/60*y**4 + 0. Factor r(p).
-2*p*(p - 11)/5
Let j be -3 - 1 - -4 - (15 + -19). Let p be 4 - ((-3)/3 - -2). Factor 0*d + 1/6*d**2 + 1/3*d**p + 0 + 1/6*d**j.
d**2*(d + 1)**2/6
Let n(m) be the first derivative of -m**5/20 + 15*m**4/2 - 958*m**3/3 + 1740*m**2 - 3364*m - 4308. Let n(y) = 0. What is y?
2, 58
Let t(d) be the second derivative of -d**5/4 + 10*d**4 - 120*d**3 + 640*d**2 + 820*d. Factor t(y).
-5*(y - 16)*(y - 4)**2
Let q(t) be the third derivative of -t**6/40 + 7*t**5/12 - 31*t**4/8 - 35*t**3/6 + t**2 - 28*t. Determine v, given that q(v) = 0.
-1/3, 5, 7
Solve -225/7*d**2 + 0 - 12/7*d**5 - 66/7*d + 186/7*d**3 + 117/7*d**4 = 0 for d.
-2, -1/4, 0, 1, 11
Suppose -2 = -6*q - 14. Let w be 9/(-12) - (q - 54/(-56)). Suppose 0 + 2/7*d**2 + w*d = 0. Calculate d.
-1, 0
Let s be 232 + (-28 - 2/(16/(-168))). Factor -162 - 3/4*b**3 + 53/2*b**2 - s*b.
-(b - 18)**2*(3*b + 2)/4
Let l(m) be the first derivative of -m**9/12096 + m**8/1344 - m**7/840 + 47*m**3/3 - m**2 - 76. Let p(h) be the third derivative of l(h). Factor p(t).
-t**3*(t - 4)*(t - 1)/4
Suppose 0 = 49362*v - 49409*v + 141. Suppose -v*u**3 + 14/3*u**2 - 4/3 - 1/3*u = 0. Calculate u.
-4/9, 1
Let y = 10286 - 10286. Let z(o) be the third derivative of y*o - 1/60*o**5 + 0*o**3 + 0*o**4 + 0*o**6 + 0 - 25*o**2 + 1/840*o**7. Let z(j) = 0. What is j?
-2, 0, 2
Let p = 2421317/120 - 163603/8. Let g = p - -273. Factor 0 + 14/15*k**2 - 8/15*k**3 - 8/15*k**4 - g*k.
-2*k*(k + 2)*(2*k - 1)**2/15
Let u(q) be the second derivative of q**6/180 - q**5/20 + q**4/6 - 47*q**3/6 - 30*q. Let w(x) be the second derivative of u(x). Factor w(h).
2*(h - 2)*(h - 1)
Solve -187*y**3 + 30 + 177*y**3 - 32*y**2 + 4*y + y + 0*y - 28*y**2 + 30*y**4 + 5*y**5 = 0.
-6, -1, 1
Let k(f) be the second derivative of -6*f**7/7 + 143*f**6/10 - 309*f**5/20 - 219*f**4/4 + 235*f**3/2 - 66*f**2 - 2105*f. Solve k(j) = 0.
-4/3, 1/4, 1, 11
Let a(u) be the second derivative of 1 + 27*u - 205/3*u**3 + 46*u**2 - 3/2*u**4. Factor a(p).
-2*(p + 23)*(9*p - 2)
Suppose -3*q - 3 = 5*h, q + 150 = 3*h + 135. Let b(f) be the third derivative of 0*f + 0*f**h - 1/160*f**5 - 21*f**2 - 1/32*f**4 + 0. Factor b(m).
-3*m*(m + 2)/8
Let m be 7 - ((-2)/(-30))/((-519)/1557). Factor -2/5*w**3 - m*w**2 - 32/5 - 66/5*w.
-2*(w + 1)**2*(w + 16)/5
Let w = 296 - 3846/13. Let l = 47/17 - 475/221. Solve 8/13*a**2 - l*a + 0 - w*a**3 = 0.
0, 2
Let k = -461 - -463. Find d, given that -252*d + k + 133*d - 2*d**2 + 119*d = 0.
-1, 1
Let t(z) be the first derivative of -27 + 9/5*z**2 + 17/5*z + 1/15*z**3. Solve t(l) = 0 for l.
-17, -1
Let c(g) be the third derivative of g**7/42 - 67*g**6/120 + 34*g**5/15 - 11*g**4/6 + 20*g**2 - 42. Factor c(u).
u*(u - 11)*(u - 2)*(5*u - 2)
Let n(w) be the third derivative of w**7/1050 - 239*w**6/200 + 143*w**5/20 - 2143*w**4/120 + 119*w**3/5 - 41*w**2 - 2. Factor n(i).
(i - 714)*(i - 1)**3/5
Let m be (-2)/(-1) - 2/(-2). Let y = -11463 + 11465. Determine h so that -4*h**3 - 6*h - 53*h**y + 4*h**3 - 2*h**m + 45*h**2 = 0.
-3, -1, 0
Find c such that 1120/3*c - 6272/3*c**2 - 50/3 = 0.
5/56
Suppose 0 = 8*c + 31730 - 31770. Let m(u) be the third derivative of -u**2 + 1/105*u**7 + 0*u + 0*u**4 + 0 + 0*u**6 - 1/30*u**c + 0*u**3. Factor m(l).
2*l**2*(l - 1)*(l + 1)
Let b(w) be the first derivative of w**6/780 - w**5/390 + 57*w**2 - 46. Let s(d) be the second derivative of b(d). Factor s(h).
2*h**2*(h - 1)/13
Let x(j) be the third derivative of -j**7/5670 - j**6/540 - j**5/135 - 17*j**4/8 - j**3/6 + 148*j**2. Let m(a) be the second derivative of x(a). Factor m(d).
-4*(d + 1)*(d + 2)/9
Let q(l) be the third derivative of -l**5/480 - 53*l**4/192 + 9*l**3/8 - 1150*l**2. Factor q(t).
-(t - 1)*(t + 54)/8
Let l(w) be the second derivative of -w**5/12 - 5*w**4/24 - 36*w**2 - 5*w + 17. Let v(s) be the first derivative of l(s). Find a such that v(a) = 0.
-1, 0
Let n(p) be the first derivative of -20*p**2 + 17/6*p**3 + 1/8*p**4 