 85*a**6/24 - a**5/12 + 425*a**4/24 - 119*a**2 + 5*a. Let u(p) = 0. What is p?
-1, 0, 1, 85
Let o(h) be the third derivative of -1/30*h**6 + 0*h**4 + 167*h**2 + 0 + 0*h + 0*h**3 - 2/15*h**5. Factor o(b).
-4*b**2*(b + 2)
Solve -2386*c - 220 + 1152*c - 2*c**2 + 1180*c = 0 for c.
-22, -5
Let x(d) be the first derivative of -33*d**4/20 - 2*d**3/5 + 927*d**2/10 - 1836*d/5 + 1778. Let x(a) = 0. What is a?
-68/11, 3
Suppose -10*t + 167 = -3. Suppose -2*o**4 + 20*o**3 + t*o**4 + 1720*o**2 - 1785*o**2 + 30*o = 0. What is o?
-3, 0, 2/3, 1
Let k(o) = o**3 + 43*o**2 + 479*o + 457. Let m(i) = -2*i + 8. Let y(q) = -3*k(q) + 6*m(q). Factor y(g).
-3*(g + 1)*(g + 21)**2
Let z be (-2)/(-666)*1202 - ((-5670)/(-4995))/21. Find s such that -8/3 + 2/9*s**4 - z*s - 2/9*s**2 + 8/9*s**3 = 0.
-3, -2, -1, 2
Suppose 5*s - 30 = -5*h, -3*s + 7 + 7 = 2*h. Let a = -659/3 + 1321/6. Factor -l + 0 + a*l**s.
l*(l - 2)/2
Let k(n) be the second derivative of -2*n**6/15 + 37*n**5/90 - n**4/27 - 12*n - 95. Factor k(a).
-2*a**2*(a - 2)*(18*a - 1)/9
Let g(w) be the first derivative of w**5 - 95*w**4/2 + 120*w**3 - 91. Let g(n) = 0. Calculate n.
0, 2, 36
Suppose 3*g + 3*h - 22 - 80 = 0, -3*g - 4*h = -107. Let p = -22 + g. Factor 9 - 4 + y - p*y + y**2.
(y - 5)*(y - 1)
Let v(p) be the third derivative of p**8/672 + p**7/105 - p**6/5 + 14*p**5/15 - 5*p**4/3 - 5503*p**2. Factor v(s).
s*(s - 2)**3*(s + 10)/2
Find i, given that 292*i + 689*i**2 - 342*i**2 - 345*i**2 = 0.
-146, 0
Let u(n) be the first derivative of -18*n + 3*n**3 - 15/4*n**2 + 8 - 3/8*n**4. Factor u(c).
-3*(c - 4)*(c - 3)*(c + 1)/2
Let x(u) be the third derivative of -u**6/720 + 19*u**4/144 - 5*u**3/6 - 661*u**2 + 2. Factor x(i).
-(i - 3)*(i - 2)*(i + 5)/6
Let f(m) be the first derivative of -5/6*m**6 + 21 + 0*m + 23*m**5 - 215/4*m**4 + 35*m**3 + 0*m**2. Factor f(b).
-5*b**2*(b - 21)*(b - 1)**2
Find w such that 555/2*w - 279/2 - 273/2*w**2 - 3/2*w**3 = 0.
-93, 1
Let w(b) be the first derivative of 20 + 5/14*b**2 - 1/21*b**3 + 0*b. Find u such that w(u) = 0.
0, 5
Let v(i) be the third derivative of i**5/12 + 925*i**4/12 + 171125*i**3/6 + 91*i**2 + 14*i. Factor v(a).
5*(a + 185)**2
Let z = 194 + -191. Factor z*t**2 - 121*t + 22*t + 18*t**2 - 30.
3*(t - 5)*(7*t + 2)
Let z(x) = 9*x**2 - 8*x - 31. Let r be z(-4). Factor -18*d**3 - 215*d**2 - 2 + 9 - 2*d**3 + 43 - r*d.
-5*(d + 1)*(d + 10)*(4*d - 1)
Find g, given that -10290*g - 1/4*g**3 - 67228 - 399/4*g**2 = 0.
-196, -7
Let t(c) = -c**3 + 2. Let r(o) = -11*o**3 - 6*o**2 + 18*o + 2. Let n = -203 - -197. Let h(k) = n*t(k) + 2*r(k). Suppose h(y) = 0. What is y?
-2, 1/4, 1
Factor 3*j**4 - 87 + 21*j**2 - 157 - 114 - 258 - 39*j**3 - 572 + 603*j.
3*(j - 11)*(j - 3)**2*(j + 4)
Let l be 3*2 - (-3 - -5). Factor -2*f**2 - 17*f**3 - 2*f**4 + 2*f + l*f**2 + 4*f + 11*f**3.
-2*f*(f - 1)*(f + 1)*(f + 3)
Let v(q) be the first derivative of -2*q**5/55 + 12*q**4/11 - 30*q**3/11 + 2*q**2 + 1907. Suppose v(k) = 0. Calculate k.
0, 1, 22
Let w(p) = -2*p - 20. Let u be w(-8). Let c be ((-2)/u)/(5/30). Find y such that 4*y**c + 0*y - 8*y**5 + 10*y**2 + 2*y**3 + 0*y**5 + 2*y - 10*y**4 = 0.
-1, -1/4, 0, 1
Let o(l) = 2*l**3 + l**2 - 2*l. Let w(u) = 16*u**3 + 1062*u**2 + 6116*u - 1408. Let t(c) = -10*o(c) - w(c). Factor t(k).
-4*(k + 8)*(k + 22)*(9*k - 2)
Let j(q) be the second derivative of 13*q**7/14 - 47*q**6/10 - 57*q**5/10 + 18*q**4 + 2*q + 652. Suppose j(u) = 0. Calculate u.
-18/13, 0, 1, 4
Let l(r) be the third derivative of -r**8/3192 + 8*r**7/399 - 13*r**6/380 - 10037*r**2. Determine b so that l(b) = 0.
0, 1, 39
Suppose -19*y = 26*y - 4*y - 4*y. Let s(h) be the first derivative of 0*h + h**5 + y*h**3 + 0*h**2 + 8 + 15/4*h**4. Factor s(x).
5*x**3*(x + 3)
Suppose 21 = -5*h - 4*i + 35, -h + 5 = 3*i. Factor 3*b**5 - 8*b**4 - 185*b**2 - 7*b**5 + 7*b - 3*b + 193*b**h.
-4*b*(b - 1)*(b + 1)**3
Let f be ((-19)/(-912)*-8)/(5/(-60)). Factor 8*c + 0*c**f - 32/3 - 2/3*c**3.
-2*(c - 2)**2*(c + 4)/3
Let r be (12 - 4 - -1) + 171/(-114). Solve r - 3/4*a**2 - 9/4*a = 0.
-5, 2
Let -331370*z + 5*z**3 - 4*z**3 + 330800*z + 0*z**3 + 283*z**2 = 0. Calculate z.
-285, 0, 2
Let o = 88357/4 + -22059. Let q(y) be the first derivative of -35 + 1/12*y**3 + 11/4*y**2 + o*y. Solve q(x) = 0 for x.
-11
Factor 440/3*g - 116/3*g**3 + 0 + 2/3*g**4 + 322/3*g**2.
2*g*(g - 55)*(g - 4)*(g + 1)/3
Let m(r) be the first derivative of r**5/90 - r**4/9 - 5*r**3/9 - 5*r**2/2 - 9*r + 37. Let d(k) be the second derivative of m(k). Solve d(u) = 0 for u.
-1, 5
Let u(c) be the second derivative of -c**5/100 + 11*c**4/10 - 363*c**3/10 - 820*c - 2. What is b in u(b) = 0?
0, 33
Let g(j) be the first derivative of -2*j**3/9 + 132*j**2 - 4040. Factor g(c).
-2*c*(c - 396)/3
Let h(z) = z + 10. Let q be h(-7). Find c, given that 2*c**q - 21*c - 5*c + 1912 - 1936 = 0.
-3, -1, 4
Let g(o) = -10*o**2 - 3982*o + 1140. Let h(v) = 2*v**2 - v. Let b(q) = -g(q) - 12*h(q). Factor b(c).
-2*(c - 285)*(7*c - 2)
Let q(v) = 5*v**3 - 34*v**2 + 80*v - 175. Let l be q(5). Find j, given that l + 2/3*j + 8/9*j**2 + 2/9*j**3 = 0.
-3, -1, 0
Factor -2/5*s**3 + 24/5 - 21/5*s**2 + 38/5*s.
-(s - 2)*(s + 12)*(2*s + 1)/5
Let v(k) be the first derivative of 5*k**4/12 + 20*k**3/3 + 30*k**2 + 38*k - 55. Let t(d) be the first derivative of v(d). Let t(z) = 0. What is z?
-6, -2
Let a be ((-420)/40)/(15/(-8)). Let l be 6*(328/(-120) + 3). Suppose -16/5*s**3 - a*s**2 - l*s + 4/5 = 0. What is s?
-1, 1/4
Let t = -33 - -13. Let r be t/(-7) + (-2 - (-105)/49). Factor 7/5*a + 8/5*a**2 + 3/5*a**r + 2/5.
(a + 1)**2*(3*a + 2)/5
Let u be (-8)/14 - 552/(-84). Suppose 4*r = u*r - 144. Solve -26*m**3 + 66*m + 3*m**4 + 2*m**4 + 5*m**4 + 32 - r*m**2 - 10*m = 0.
-2, -2/5, 1, 4
Let v(g) be the second derivative of -g**5/30 - 5*g**4/9 + g**3 + 30*g**2 + 635*g. Solve v(x) = 0.
-10, -3, 3
Let a(l) be the first derivative of -l**3/15 - 3*l**2/5 + 72*l/5 - 2899. Solve a(m) = 0.
-12, 6
Let o(m) be the third derivative of 3/2*m**3 + 0*m - 1/140*m**5 + 174*m**2 - 1/14*m**4 + 0. Factor o(p).
-3*(p - 3)*(p + 7)/7
Let 0*w - 3/4*w**3 + 0 - 27/4*w**2 = 0. Calculate w.
-9, 0
Let c(o) = o**2 + 13*o - 11. Let x be c(-14). Suppose -4*k = -2*r, k - 4*r + x*r = -2. Suppose 112*h**2 - 113*h**k - 14*h - 62 + 13 = 0. What is h?
-7
Let o(v) = 8*v**2 + 236*v + 3600. Let c(j) = 12*j**2 + 470*j + 7200. Let s(x) = x**2 + x. Let q(a) = c(a) + 3*s(a). Let z(l) = 7*o(l) - 4*q(l). Factor z(w).
-4*(w + 30)**2
Let p be 7 - ((-1 - -4) + -4). Suppose -3*g + 15 = 0, p*c - 2*g = 3*c. Factor 3 - 3/4*b**3 - 6*b + 15/4*b**c.
-3*(b - 2)**2*(b - 1)/4
Let h = 11962 - 59622/5. Let v = -559/15 + h. Factor 1/3*f**2 + 0*f - v.
(f - 1)*(f + 1)/3
Let v(h) = 8*h + 22. Let b be v(-3). Let o(g) = -g**3 + 4*g**2 + 2*g - 2. Let p be o(b). Factor 19*x**2 - x**2 + 4 - x + 5*x + p*x.
2*(x + 1)*(9*x + 2)
Let t be ((-24)/276 + (-2442)/1012)*((-7)/(-5) + -3). Factor 46/11*i + 2/11*i**2 + t.
2*(i + 1)*(i + 22)/11
Determine w, given that 153/2 - 23*w**3 - 1/2*w**4 + 124*w**2 - 177*w = 0.
-51, 1, 3
Factor 7/2*v**3 + 0 + 1/2*v + 4*v**2.
v*(v + 1)*(7*v + 1)/2
Let y(u) be the first derivative of u**4/10 + 82*u**3/15 + 78*u**2/5 + 8172. Determine s so that y(s) = 0.
-39, -2, 0
Factor -1381/2*u**3 + 691/2*u**2 + 0 + 0*u + 689/2*u**4 + 1/2*u**5.
u**2*(u - 1)**2*(u + 691)/2
Let l(f) = 7*f**2 - 110*f + 113. Let d(c) = 31*c**2 - 437*c + 451. Let k(p) = -2*d(p) + 9*l(p). Solve k(w) = 0 for w.
1, 115
Suppose 0 = k - 4*s - 16, -k = 2*k - 5*s - 20. Suppose 5*q + 3*q - 40 = k. Suppose q*d - 2 - d**2 + 4*d - 12*d = 0. Calculate d.
-2, -1
Solve 19*y**2 + 226*y + 1472 - 35*y**2 - 41*y + 12*y**2 - 913*y = 0 for y.
-184, 2
Factor -1/6*n**3 - 3/2*n**2 + 10 - 4/3*n.
-(n - 2)*(n + 5)*(n + 6)/6
Let g(m) be the first derivative of 36/5*m - 6/5*m**4 - 12/25*m**5 + 8/3*m**3 + 42/5*m**2 - 48 + 2/15*m**6. What is t in g(t) = 0?
-1, 3
Let d(y) = -y**2 + 15*y - 11. Let v be d(14). Suppose -420*s**3 - 66*s**2 + 428*s**v - 32 + 45*s + 99*s = 0. What is s?
1/4, 4
Let i(y) be the second derivative of -y**7/189 + 11*y**5/90 + y**4/3 + 8*y**3/27 + 35*y + 13. Find b, given that i(b) = 0.
-2, -1, 0, 4
Let q(r) = 9*r**2 + 9*r + 9. Let n be q(-1). Let -3672*j**3 + n*j**4 + 3677*j**3 - j**5 - 75*j**2 - 2*j**4 = 0. What is j?
-3, 0, 5
Let g be 5168/(-11) + 3/(-1). Let j = -471 - g. Solve 2/11*m**4 + 12/11*