11*k**3 = 0 for k.
0, 2
Let m(b) = -7*b**3 + 23*b**2 + 110*b + 5. Let h(t) = -22*t**3 + 70*t**2 + 348*t + 16. Let k(o) = -5*h(o) + 16*m(o). Let k(i) = 0. What is i?
-1, 0, 10
Let m be (70/4)/(8 - (-90)/(-12)). Suppose -m + 41 = 3*q. Factor -4/9 + 2/9*y**q + 2/9*y.
2*(y - 1)*(y + 2)/9
Let g = -1609437/160 - -10059. Let x(h) be the second derivative of 0 + g*h**5 + 1/4*h**4 + 3*h**2 + 5/4*h**3 - 24*h. Factor x(b).
3*(b + 2)**2*(b + 4)/8
Let x(w) be the third derivative of w**9/15120 + w**8/5040 + w**5/10 - w**4/8 + 66*w**2. Let u(c) be the third derivative of x(c). Factor u(z).
4*z**2*(z + 1)
Let o(d) = -13*d**2 + 49*d + 4. Let z(r) = -50*r**2 + 195*r + 15. Let n(q) = 15*o(q) - 4*z(q). Find y such that n(y) = 0.
0, 9
Let f be 80/(-3) + 28 - 0/1. Let v(b) be the second derivative of -f*b**3 + 0*b**2 + 1/3*b**4 - 11*b + 0. Let v(x) = 0. Calculate x.
0, 2
Let p = -1 - 24. Let v = p + 41. Factor -68 - 32 - v*u + 3*u - 4*u**2 - 27*u.
-4*(u + 5)**2
Let y(l) be the first derivative of -l**6/6 + 7*l**5/2 - 65*l**4/12 + 219*l - 5. Let q(m) be the first derivative of y(m). Factor q(w).
-5*w**2*(w - 13)*(w - 1)
Let o = -179151 + 179153. Factor -49/8 + 7/4*x - 1/8*x**o.
-(x - 7)**2/8
Let 448 - 448 - 362*f**3 + 80*f**2 + 358*f**3 = 0. What is f?
0, 20
Let w = 32304/7 - 26778/7. Let d = 790 - w. Find f, given that 2/7 - 4/7*f**3 + 0*f**2 - 2/7*f**4 + d*f = 0.
-1, 1
Let d be (-19152)/49896 - (-10)/9. Factor 2/11*c - 8/11*c**2 - 2/11*c**3 + d.
-2*(c - 1)*(c + 1)*(c + 4)/11
Suppose 36 = 4*p + 20. Let m(d) = -15*d - 2. Let l be m(-1). Factor 18 - 3*h**2 - 2*h + 14*h - 2*h**p - 4*h**3 - 8*h**3 - l*h**2.
-2*(h - 1)*(h + 1)*(h + 3)**2
Let u = 239 - 233. Factor -u*q**4 + 140*q**3 - 7*q**4 + 31*q**4 - 2450*q**2 - 20*q**4.
-2*q**2*(q - 35)**2
Let u = -733780 - -5136466/7. Factor 6/7*i + 24/7*i**2 + u*i**3 - 36/7.
6*(i - 1)*(i + 2)*(i + 3)/7
Suppose -11988*x**4 - 4*x**5 + 4000*x**2 - 12249*x**4 + 24437*x**4 - 1700*x**3 = 0. Calculate x.
0, 5, 40
Let c(s) be the second derivative of -s**5/450 + s**4/60 - 2*s**3/45 + 23*s**2 + 41*s. Let a(f) be the first derivative of c(f). Factor a(i).
-2*(i - 2)*(i - 1)/15
Let d be ((-1000)/(-336))/5 + (-76)/(-1064). Suppose d*p**5 + 62/3*p**3 + 80/3*p + 8 + 6*p**4 + 34*p**2 = 0. Calculate p.
-3, -2, -1
Let y(f) = 4*f + 71. Let v be y(-19). Let l be (4 + -2)/(v + -1)*0. Find u, given that 2/13 + l*u**2 - 2/13*u**4 - 4/13*u + 4/13*u**3 = 0.
-1, 1
Let m(g) = -5*g**3 - 185*g**2 - 198*g + 18. Let i(f) = -f**3 - 2*f**2 - 4*f + 3. Let j(w) = -6*i(w) + m(w). Factor j(y).
y*(y - 174)*(y + 1)
Suppose 4*s - x - 2 = 0, -s - 170 = -4*x - 148. Let q(v) be the third derivative of 1/8*v**4 + 0 + 1/120*v**6 + 0*v**3 + 1/15*v**5 + 0*v + 4*v**s. Factor q(i).
i*(i + 1)*(i + 3)
Let s(d) = -157*d**2 + 28168*d + 28336926. Let n(z) = -23*z**2 + 4024*z + 4048132. Let c(x) = 41*n(x) - 6*s(x). Let c(u) = 0. Calculate u.
-2012
Let v(i) = 61*i**3 - 3*i**2 + 4*i - 2. Let b be v(1). Suppose -13*t + b = -7*t. Factor 14*c - 1 + t*c + 7*c - c**2 - 29*c.
-(c - 1)**2
Let r(c) be the third derivative of c**5/120 - 107*c**4/24 - 174*c**2 + 3. Factor r(f).
f*(f - 214)/2
Let z(y) be the second derivative of 5*y**8/336 - y**6/8 - y**5/6 - 33*y**2 - 129*y. Let o(p) be the first derivative of z(p). Factor o(t).
5*t**2*(t - 2)*(t + 1)**2
Let c = 29 - -32. Factor -2147*x**2 + 12 + 1066*x**2 - 118*x - 27 + 1075*x**2 - c.
-2*(x + 19)*(3*x + 2)
Factor 3/4*x**3 - 255*x**2 + 1017/4*x + 0.
3*x*(x - 339)*(x - 1)/4
Let p = -1152 + 10370/9. Let o(d) be the third derivative of -p*d**3 + 0*d + 1/18*d**4 - 8*d**2 - 1/180*d**5 + 0. Factor o(h).
-(h - 2)**2/3
Let c(d) be the first derivative of -116*d**5/15 + 344*d**4/3 - 1792*d**3/3 + 3328*d**2/3 + 1024*d/3 - 2501. Find p such that c(p) = 0.
-4/29, 4
Let i(m) = -34 - 3*m + 92 + m + 102 + 10*m. Let l be i(-20). Let 50/13*j**5 + 2/13*j**2 + 70/13*j**4 + 0*j + 22/13*j**3 + l = 0. Calculate j.
-1, -1/5, 0
Factor -12166/23*l**2 + 314/23*l**3 + 0 - 12482/23*l - 2/23*l**4.
-2*l*(l - 79)**2*(l + 1)/23
Let h be 27/(-5) + (-94)/(-235). Let x be 1*4*h/(-140). Factor x*g**2 + 1/7*g + 0.
g*(g + 1)/7
Let -292/3 - 98*j - 2/3*j**2 = 0. Calculate j.
-146, -1
Let i(h) = 4*h**2 - 33*h - 28. Let p(x) = 9*x**2 - 69*x - 57. Let q be (3 - -2) + 9 + 0. Let f(a) = q*i(a) - 6*p(a). Suppose f(o) = 0. What is o?
-1, 25
Determine x so that 110/3 - 434/9*x + 2/9*x**3 + 34/3*x**2 = 0.
-55, 1, 3
Let c = 16 - 10. Suppose 2*a + c = -n, -2 = a + 3. Solve 11 - n*r**2 + 20*r + 0*r**2 - 26 - r**2 = 0.
1, 3
Let f(v) be the first derivative of -4*v**5/15 + 10*v**4/3 - 32*v**3/3 - 20*v**2/3 + 100*v/3 - 9288. Find r such that f(r) = 0.
-1, 1, 5
Factor 72/7*j + 38/7*j**4 + 0 + 80/7*j**2 - 134/7*j**3.
2*j*(j - 2)**2*(19*j + 9)/7
Let b(s) be the third derivative of -s**5/420 + 5*s**4/28 + 32*s**3/21 - 40*s**2. Solve b(g) = 0 for g.
-2, 32
Let z = -134 + 206. Let i = -52 + z. Solve 4*o**3 - 23*o**4 - 9*o + i*o**4 - 19*o**3 - 21*o**2 = 0.
-3, -1, 0
Let d(m) be the third derivative of 1/600*m**6 + 0*m**3 - 1/30*m**4 + 43*m**2 + 0 - 2*m - 1/100*m**5. Factor d(f).
f*(f - 4)*(f + 1)/5
Let i(u) be the first derivative of -68/3*u**2 - 135 + 140/3*u - 4/9*u**3. Find w, given that i(w) = 0.
-35, 1
Let k(s) be the second derivative of 1/33*s**4 + 1/165*s**6 + 0 + 0*s**2 - 90*s - 8/33*s**3 + 1/22*s**5. What is m in k(m) = 0?
-4, -2, 0, 1
Let h be 266/(-152) - 93/(-12). Let k be (-32)/h - (-84)/14. Suppose 0*x**2 + 0*x - 1/3*x**5 - x**4 - k*x**3 + 0 = 0. What is x?
-2, -1, 0
Let f be ((-12)/(-34))/((22620/884)/87). Let -116/15*m**2 + 128/15*m**4 + 104/15*m**3 - 4/5 - 122/15*m + f*m**5 = 0. Calculate m.
-6, -1, -1/9, 1
Let q = -153025/2 + 77606. Factor -3/2*k**2 - q + 81*k.
-3*(k - 27)**2/2
Let f(t) = -6*t**2 + 6*t + 21. Let m(a) = 13*a**2 - 13*a - 43. Let z(y) = -2*y - 7. Let q be z(-5). Let k(b) = q*m(b) + 7*f(b). Factor k(s).
-3*(s - 3)*(s + 2)
Let u(b) be the second derivative of -b**5/20 - 35*b**4/3 + b**3/6 + 70*b**2 - 121*b. Let u(y) = 0. What is y?
-140, -1, 1
Let g(l) be the second derivative of -l**5/5 - 61*l**4/3 - 236*l**3/3 - 9*l + 65. Factor g(p).
-4*p*(p + 2)*(p + 59)
Let v(k) be the first derivative of 3/4*k**4 + 0*k + 10/9*k**3 - 1/15*k**5 + 110 + 0*k**2. Factor v(y).
-y**2*(y - 10)*(y + 1)/3
Let y(c) be the third derivative of 2/75*c**5 + 0*c + 0 + 43*c**2 + 0*c**3 + 0*c**4 - 1/525*c**7 + 1/100*c**6. Determine d so that y(d) = 0.
-1, 0, 4
Let i be 3/(15/20)*((-12)/3)/(-120). Let g(c) be the first derivative of -9 + 1/5*c**2 - i*c**3 + 12/5*c. Factor g(w).
-2*(w - 3)*(w + 2)/5
Factor -30/7 - 19/7*q + 4/7*q**2.
(q - 6)*(4*q + 5)/7
Let l be 12/8*(1 + 1). Suppose -35 = -l*o - 3*c + 7, 4*o = -3*c + 51. Factor f**3 + 11*f**3 - o*f**3 - 8*f**3 + 5*f**2 + 10*f.
-5*f*(f - 2)*(f + 1)
Let z be 14 - 54*(-5)/(-30). Let q(y) be the third derivative of 0 - 2/9*y**3 + 0*y + 3*y**2 + 5/108*y**4 - 1/270*y**z. What is h in q(h) = 0?
2, 3
Let f = 270296 - 270293. Determine r, given that 0 - 2/5*r**f - 36/5*r**2 + 38/5*r = 0.
-19, 0, 1
Suppose -i + 8*i - 21 = 0. Let w(v) = -v**2 + v + 6. Let y be w(i). Solve -2*p + y*p - 3*p**2 + p + 25 - 23 + p**4 + p**3 = 0 for p.
-2, -1, 1
Suppose 4*x + 9 - 5 = d, -5*d - 76 = 4*x. Let t(u) = -u**4 + u**3 + 1. Let v(c) = -8*c**4 + 52*c**3 + 12. Let p(z) = d*t(z) + v(z). Factor p(n).
4*n**3*(n + 10)
Let w(x) be the second derivative of 5*x**7/21 + 275*x**6/2 + 21321*x**5 + 53045*x**4/3 + 2*x + 1225. Solve w(z) = 0 for z.
-206, -1/2, 0
Let q(o) = -23*o - 596. Let d be q(-26). Let x(s) be the second derivative of 0*s**d - 1/21*s**3 + 19*s + 0 - 1/105*s**6 + 1/70*s**5 + 1/42*s**4. Factor x(z).
-2*z*(z - 1)**2*(z + 1)/7
Let b be ((-5)/10)/((-2)/8) - (-207 - -209). Let x(g) be the second derivative of 0 - 2/15*g**3 + 1/10*g**4 - 1/50*g**5 - 4*g + b*g**2. Solve x(f) = 0 for f.
0, 1, 2
Let c(w) be the first derivative of -w**7/105 + 4*w**6/15 - 17*w**5/6 + 25*w**4/2 + w**2 + 31*w + 251. Let d(x) be the second derivative of c(x). Factor d(t).
-2*t*(t - 6)*(t - 5)**2
Suppose 824/3*n - 800 + 2/9*n**3 - 224/9*n**2 = 0. Calculate n.
6, 100
Suppose -32*g + 34*g - 1066 = 0. Factor -5 + g*k - 1824*k**2 - 203*k - 3293*k**2 - 328*k**2.
-5*(33*k - 1)**2
Let m(a) be the first derivative of 7*a**3/4 + 297*a**2/8 + 21*a/2 - 3764. Suppose m(r) = 0. What is r?
-14, -1/7
Let g = -2604 - 