5 + 0*b**3 + q*b + 0. Factor u(w).
w*(w + 1)**2
Determine a so that 3/7*a**2 + 555/7 - 558/7*a = 0.
1, 185
Let w(x) be the third derivative of -8/15*x**3 - 1/75*x**5 - 4*x**2 + 1/5*x**4 + 1/525*x**7 + 0 - 5*x - 1/100*x**6. Solve w(c) = 0 for c.
-2, 1, 2
Solve -3*v**2 - 28*v + 131*v + 101*v = 0 for v.
0, 68
Let h(b) be the second derivative of 3*b**7/35 + 16*b**6/75 - 31*b**5/50 - 11*b**4/5 - 4*b**3/3 + 8*b**2/5 + 9*b + 2. Solve h(t) = 0.
-2, -1, 2/9, 2
Let t(r) be the second derivative of -5*r**9/756 - 5*r**8/112 - r**7/14 + r**6/18 - 5*r**3/2 + 5*r. Let a(i) be the second derivative of t(i). Factor a(v).
-5*v**2*(v + 2)**2*(4*v - 1)
Let p be 10 + 143/(-11) - (-39)/9. Let a(t) be the first derivative of 10 + 12*t + 8*t**2 + p*t**3. Factor a(h).
4*(h + 1)*(h + 3)
Let x be 1118/520 - 3/(-12). What is n in x*n - 3 + 3/5*n**2 = 0?
-5, 1
Let v(r) be the third derivative of r**8/50400 + r**7/4200 - r**5/60 + 13*r**2. Let y(l) be the third derivative of v(l). Let y(h) = 0. Calculate h.
-3, 0
Let b = 47387/7 - 6769. Solve 2/7*r**2 - b*r + 2/7 = 0 for r.
1
Let g(c) be the second derivative of -c**4/78 + 4*c**3/39 - 4*c**2/13 - 11*c + 9. Suppose g(v) = 0. Calculate v.
2
Let g(u) be the third derivative of 0*u - 1/960*u**6 + 0 - 1/1680*u**7 + 0*u**3 + 1/120*u**5 - 10*u**2 + 1/48*u**4. Find n, given that g(n) = 0.
-2, -1, 0, 2
Let n(o) = 18*o**3 - 144*o**2 + 259*o - 118. Let k(c) = -28*c**3 + 216*c**2 - 388*c + 176. Let r(u) = -5*k(u) - 8*n(u). What is h in r(h) = 0?
1, 16
Let d(o) be the third derivative of o**8/672 - o**7/105 + o**6/80 + o**5/30 - o**4/12 - 228*o**2. What is n in d(n) = 0?
-1, 0, 1, 2
Determine w, given that 4*w**5 + 17*w**3 - 8*w**4 - 3*w**5 - 45*w**3 - 20*w**2 + 48*w + 3*w**5 + 52*w**2 = 0.
-2, -1, 0, 2, 3
Let h(d) be the first derivative of 3*d**2 - 2/5*d**5 - 5 - 2/3*d**3 - 3/2*d**4 + 4*d. Factor h(n).
-2*(n - 1)*(n + 1)**2*(n + 2)
What is m in 86*m**3 - 5*m**4 - 118*m**2 + 228*m**2 - 122*m**2 + 35*m**4 = 0?
-3, 0, 2/15
Let z(c) be the third derivative of -11*c**8/784 + c**7/245 - 16*c**2. Solve z(y) = 0.
0, 2/11
Let w(d) = -9*d**3 + 25*d**2 - 42*d + 21. Let n(m) = -10*m**3 + 26*m**2 - 44*m + 22. Let r(t) = 5*n(t) - 6*w(t). Factor r(x).
4*(x - 2)**2*(x - 1)
Let q = -43 - -45. Factor 2*g - g**3 + 3*g**3 - 2*g**q - 2*g**2.
2*g*(g - 1)**2
Factor 4/5*q**3 - 156/5 - 308/5*q - 148/5*q**2.
4*(q - 39)*(q + 1)**2/5
Let y(p) be the third derivative of -36*p**2 + 5/6*p**4 + 1/15*p**5 + 0*p + 0 - 4*p**3. Factor y(v).
4*(v - 1)*(v + 6)
Let b = 2511/6632 - 3/829. Let c(f) be the first derivative of 1/20*f**5 - 1/2*f + 3/16*f**4 + 3 - b*f**2 + 1/12*f**3. Factor c(q).
(q - 1)*(q + 1)**2*(q + 2)/4
Suppose 4*m = 5*l - 38, -2*l + 2*m - 4 = -20. Let j = 8 - l. Factor -2*q**3 - 2*q**2 - 12*q**j + 14*q - 28*q - 18 - 16*q.
-2*(q + 1)*(q + 3)**2
Let r(i) be the first derivative of i**4/10 + 22*i**3/15 - 5*i**2 + 26*i/5 + 283. Solve r(b) = 0 for b.
-13, 1
Let g(l) = -l**3 + 2*l**2 - 68*l - 247. Let x be g(-3). Solve 9/4*w**x - 4*w - 1 = 0 for w.
-2/9, 2
Let y(k) be the first derivative of -k**4 + 1/15*k**5 + 7 + 3*k**2 + 0*k + 6*k**3. Let x(l) be the second derivative of y(l). Factor x(q).
4*(q - 3)**2
Let o be ((-18)/33 - 4/(-22)*3) + 2. Determine d, given that -6/7*d - 3/7*d**o + 0 = 0.
-2, 0
Suppose 29 - 47 = -6*d. Let h(n) be the second derivative of -1/30*n**4 + 0 + 0*n**d - 1/25*n**6 + 0*n**2 + 6*n + 2/25*n**5. Find f such that h(f) = 0.
0, 1/3, 1
Let d be (-2 + 10/2)*1. Suppose 4*w + 20 + 14 = 5*h, -4*w = -d*h + 22. Factor -2*q**2 + 0*q**3 - 5*q**5 + 0*q**4 + 3*q**5 - h*q**3 - 6*q**4.
-2*q**2*(q + 1)**3
Let h be 2/(-5) - (-39)/60. Suppose 0 = 5*p + 10, 1 = -s + 3*p + 7. Find g, given that 0 + h*g**2 + s*g = 0.
0
Suppose -14*y - 28 = -21*y. Suppose -1368 + 1368 + 4*r**3 + 2*r**2 + 3*r**y - r**4 = 0. Calculate r.
-1, 0
Let k(j) be the third derivative of 1/45*j**3 - 1/225*j**5 - 16*j**2 + 1/1575*j**7 + 0*j**6 + 0 + 0*j**4 + 0*j. Factor k(y).
2*(y - 1)**2*(y + 1)**2/15
Let q(b) be the second derivative of b**6/240 + b**5/60 + 16*b**2 - 28*b. Let v(x) be the first derivative of q(x). Find r such that v(r) = 0.
-2, 0
Suppose 2*f**4 - 8/5 + 34/5*f**2 + 0*f - 36/5*f**3 = 0. What is f?
-2/5, 1, 2
Let d(z) be the second derivative of z**10/288 - z**9/3024 - z**8/672 - 13*z**4/6 - 41*z. Let f(o) be the third derivative of d(o). Factor f(k).
5*k**3*(3*k - 1)*(7*k + 2)
Let t be ((-12)/30)/((-1)/10). Suppose 0*u - 2*x = 2*u, -5*x = -t*u. Let -2/3*f**2 - 2/3*f + u = 0. What is f?
-1, 0
Factor -52/5*x - 24/5 - 32/5*x**2 - 4/5*x**3.
-4*(x + 1)**2*(x + 6)/5
Let u = -791/4 - -200. Let z(r) be the first derivative of 21/5*r**5 + 4 + 5/2*r**6 - 7*r**3 - u*r**4 - 3*r**2 + 0*r. Solve z(v) = 0.
-1, -2/5, 0, 1
Let o(c) be the third derivative of c**6/40 - c**4/2 - 3*c**2 + 1. Factor o(g).
3*g*(g - 2)*(g + 2)
Let c(r) be the first derivative of r**3/9 - 2*r**2/3 - 20*r + 572. Factor c(x).
(x - 10)*(x + 6)/3
Let b(k) = -2*k**2 - 2*k - 14. Let a be b(6). Let l be (-84)/a*(-7)/(-11). Determine y, given that -2/11*y**4 - l*y + 6/11*y**3 + 4/11 - 2/11*y**2 = 0.
-1, 1, 2
Let m(j) = -j**2 - 11*j + 30. Let t be m(-13). Solve 4*n**2 + n**2 - t*n**2 + n + 3*n**2 = 0.
-1/4, 0
Let z = -2/59471 - -118952/297355. Suppose 2/5*x + 0 + 1/5*x**2 - z*x**3 - 1/5*x**4 = 0. What is x?
-2, -1, 0, 1
Let d(b) = b**2 - b - 4. Let z be d(-5). Let o = 31 - z. Suppose u**2 + 0*u**2 + 5*u**3 - u**4 - 3*u**4 + u**2 - 3*u**o = 0. Calculate u.
-2, -1/3, 0, 1
Let m(r) be the first derivative of -6*r**5/5 - 21*r**4/8 - 3*r**3/2 - 195. Factor m(j).
-3*j**2*(j + 1)*(4*j + 3)/2
Factor 9*j - 3364 + 85*j + 67*j - 4*j**2 + 71*j.
-4*(j - 29)**2
Factor -3/5*l**2 + 24/5 + 6/5*l.
-3*(l - 4)*(l + 2)/5
Let m(i) = 11*i**3 - i**2 + i + 1. Let l be m(-1). Let a(c) = c**3 + 13*c**2 + 12*c + 2. Let p be a(l). Factor 2*v - 6 - 10*v + 6 + p*v**3.
2*v*(v - 2)*(v + 2)
Let b(o) = 3*o**4 - 12*o**3 + 17*o**2 - 6*o - 2. Let h = 70 - 68. Let g(p) = p**2 - 1. Let d(f) = h*g(f) - b(f). Factor d(m).
-3*m*(m - 2)*(m - 1)**2
Suppose 3*s + 19 = -4*d, -5*d + 46 = s - 5*s. Let -88/5*g**3 + 14/5*g**5 + 32/5*g**2 + 128/5*g + 32/5 - d*g**4 = 0. Calculate g.
-2, -1, -2/7, 2
Let g(t) be the second derivative of -t**5/5 + 40*t**4/3 - 874*t**3/3 + 1444*t**2 - 445*t. Let g(z) = 0. Calculate z.
2, 19
Factor 18/5*t - 8 - 2/5*t**2.
-2*(t - 5)*(t - 4)/5
Factor -2/3*o**2 - 14*o + 48.
-2*(o - 3)*(o + 24)/3
Let x(v) be the first derivative of v**5/5 - 3*v**4 + 11*v**3/3 + 81. Factor x(p).
p**2*(p - 11)*(p - 1)
Let j be (4/(-10))/(-4*9/270). Let s(g) be the third derivative of 3*g**2 + 3/40*g**4 + 0*g + 0 + 0*g**j + 1/100*g**5. Factor s(k).
3*k*(k + 3)/5
Let v(k) = 14*k**4 - 38*k**3 + 11*k**2 + 11*k. Let s(d) = 13*d**4 - 37*d**3 + 12*d**2 + 10*d - 1. Let o(l) = -2*s(l) + 3*v(l). Let o(a) = 0. What is a?
-1/4, 1, 2
What is n in 108/5*n**3 - 8/5*n + 66/5*n**2 - 486/5*n**4 - 8/15 = 0?
-2/9, 1/3
Let m = 2121 + -2121. Factor 5/2*o**3 + 0 + m*o + 5/2*o**2.
5*o**2*(o + 1)/2
Let j(r) = r**3 + 7*r**2 + 12*r + 12. Let h be j(-5). Let q(v) be the second derivative of 1/66*v**4 + 0*v**2 - 1/33*v**3 + h*v + 0. Factor q(n).
2*n*(n - 1)/11
Suppose -2*b - 6 = 0, 0 = 5*a + 2*b - 4. Factor 1340*g**4 + 30*g**3 + 50*g - 19 - 1345*g**4 + 4 - 60*g**a.
-5*(g - 3)*(g - 1)**3
Factor -93*o - 101 - 2*o**2 + 462 + 119 - 3*o**2 - 382*o.
-5*(o - 1)*(o + 96)
Find k such that 18 + 33*k - 131*k**3 + 4*k**2 + 8*k**2 + 128*k**3 = 0.
-1, 6
Let z be (-3)/7 + (-2525)/(-2625). Factor 2/15*c - 2/15*c**3 + z*c**2 - 8/15.
-2*(c - 4)*(c - 1)*(c + 1)/15
What is u in 5/4*u**2 - 25/4*u - 35/2 = 0?
-2, 7
Suppose 3*p = 8*p - 15. Factor u**4 - 2*u - 11*u**4 + 2*u + 5*u**5 + 5*u**p.
5*u**3*(u - 1)**2
Let f(q) be the first derivative of -q**5/5 - q**4/2 + q**3/3 + q**2 - 4. Suppose f(x) = 0. Calculate x.
-2, -1, 0, 1
Suppose 0 = 510*f - 533*f + 46. Solve -2/9*h**3 + 14/9*h - 4/9*h**f - 8/9 = 0.
-4, 1
Let g(r) be the second derivative of -1/4*r**4 + 3/80*r**5 + 3/2*r**2 + 0 - 1/8*r**3 + 28*r. Factor g(x).
3*(x - 4)*(x - 1)*(x + 1)/4
Let u be (1/3 + -1)/(168/(-288)). Factor -4/7*s + 8/7 - u*s**2 + 4/7*s**3.
4*(s - 2)*(s - 1)*(s + 1)/7
Let g(h) be the second derivative of -h**6/45 + 29*h**5/90 - 4*h**4/3 + 4*h**3/3 + 2*h - 80. Find a such that g(a) = 0.
0, 2/3, 3, 6
Factor -306*o + 2 + 23409/2*o**2.
(153*o