*(a + 2)
Let r(c) = c**3 + 12*c**2 + 3. Let a be r(-12). Let f(p) = -p**2 + p + 1. Let w(t) = t**2 + 5*t - 9. Let s(h) = a*f(h) + w(h). Let s(n) = 0. Calculate n.
1, 3
Suppose g - 12 = -v - 4*g, v - 12 = 5*g. Suppose 3*l = -l + v. Suppose -6*k**3 - k**3 - 45*k**2 + 4*k**5 + 13*k**2 + 16*k**4 + 16 - k**l + 4*k = 0. Calculate k.
-4, -1, 1
Let v(a) = a**5 + a**4 + a**3 + a. Let o(q) = 6*q**5 - 24*q**4 + 132*q**3 - 128*q**2 - 508*q + 1024. Let g(h) = o(h) - 4*v(h). Factor g(s).
2*(s - 4)**4*(s + 2)
Let x(n) be the third derivative of -n**8/2520 + n**7/630 - n**5/90 + n**4/36 + 10*n**3/3 + 2*n**2. Let p(t) be the first derivative of x(t). Factor p(k).
-2*(k - 1)**3*(k + 1)/3
Let k be 4/26 - (-3)/(117/(-6)). Determine s so that k*s - 4*s - 66*s**3 + 6*s**2 + 64*s**3 = 0.
0, 1, 2
What is h in 0 + 1/6*h**3 - 1/2*h**2 + 0*h + 1/3*h**4 = 0?
-3/2, 0, 1
Let k = -2629/5 + 526. Let r(m) be the second derivative of k*m**5 + 4/3*m**3 + 0*m**2 - 8*m + 0 - m**4. Factor r(g).
4*g*(g - 2)*(g - 1)
Let f(m) = -m**2. Let s(j) = 4*j**2 - 20*j + 100. Let w(c) = -3*f(c) - s(c). Let h(r) = r**2 - 20*r + 100. Let t(k) = -7*h(k) - 6*w(k). Factor t(l).
-(l - 10)**2
Suppose 0 = 17*j - 13*j - 72. Suppose -7*z = -j*z. Let z - 1/4*l - 1/2*l**3 - 3/4*l**2 = 0. Calculate l.
-1, -1/2, 0
Let o(g) = -2*g + 12. Let j be o(5). Suppose 0 = 2*l + 2, l = 4*x - j*l - 15. Determine r so that -13*r + 14*r**3 - 9*r**2 - 2 + x*r - 20*r**3 - 5*r**2 = 0.
-1, -1/3
Let n(j) be the third derivative of -5*j**8/336 - j**7/21 + 5*j**6/24 + 5*j**5/6 - 5*j**4/6 - 20*j**3/3 - 185*j**2. What is w in n(w) = 0?
-2, -1, 1, 2
Let o(q) = 2*q**2 + 24*q - 52. Let z(g) = -3*g**2 - 24*g + 55. Let t(a) = 5*o(a) + 4*z(a). Factor t(k).
-2*(k - 10)*(k - 2)
Let z(k) = -k**3 + 5*k**2 + 5*k + 7. Let p be z(6). Let i(c) = 35*c**2 - 60*c + 45. Let j(f) = -f**2 + f. Let w(a) = p*i(a) + 30*j(a). Factor w(s).
5*(s - 3)**2
Let z(f) be the third derivative of -f**5/80 - 89*f**4/16 - 177*f**3/8 + 853*f**2. Let z(j) = 0. Calculate j.
-177, -1
Let i(y) be the second derivative of y**9/12096 + y**8/6720 - y**7/840 - y**6/360 + 8*y**3/3 + 10*y - 2. Let b(k) be the second derivative of i(k). Factor b(r).
r**2*(r - 2)*(r + 1)*(r + 2)/4
Let w(c) be the first derivative of 0*c + 0*c**2 + 0*c**3 + 19 + 1/50*c**5 - 1/40*c**4. Factor w(v).
v**3*(v - 1)/10
Let n(m) = -m**3 + m**2 + 3. Let l(u) = -72*u**2 - 120*u - 12. Let t(w) = l(w) + 4*n(w). Factor t(g).
-4*g*(g + 2)*(g + 15)
Let x(j) = -10*j**2 + 34. Suppose -3*y = -9*y - 42. Let f(s) = 9*s**2 - 33. Let h(d) = y*f(d) - 6*x(d). Determine m so that h(m) = 0.
-3, 3
Let i(s) be the first derivative of -s**4/132 + s**3/33 - s**2/22 + 2*s - 14. Let d(l) be the first derivative of i(l). Suppose d(o) = 0. Calculate o.
1
Let c(w) be the third derivative of w**6/40 + 11*w**5/10 + 12*w**4 + w**2 - 272. Factor c(m).
3*m*(m + 6)*(m + 16)
Let c(l) = -4*l**3 - 2*l**2 + 55*l + 5. Let h(o) = 4*o**3 + 4*o**2 - 54*o - 6. Let p(d) = -6*c(d) - 5*h(d). Factor p(b).
4*b*(b - 5)*(b + 3)
Suppose 0 = 5*s + 5 - 0. Let h be s/4 + (-104)/(-32). Factor 0*n**2 - 3*n**2 + n + 13*n**3 - n**4 - 10*n**h.
-n*(n - 1)**3
Let s(j) be the first derivative of -j**4/2 - 118*j**3/3 - 58*j**2 - 25. Let s(f) = 0. Calculate f.
-58, -1, 0
Let f(a) be the second derivative of 2*a**7/147 + 4*a**6/35 + 11*a**5/35 + 2*a**4/21 - 8*a**3/7 - 16*a**2/7 - 2*a + 27. Factor f(s).
4*(s - 1)*(s + 1)*(s + 2)**3/7
Let s(k) = 9*k - 28. Let m be s(10). Let x = m - 58. Factor 0 + 1/3*z**5 + 1/3*z**3 + 0*z**2 + 0*z - 2/3*z**x.
z**3*(z - 1)**2/3
Let o(j) be the third derivative of j**6/360 + 5*j**5/36 + 17*j**4/18 + 22*j**3/9 - 50*j**2. Factor o(r).
(r + 1)*(r + 2)*(r + 22)/3
Let t = 309 - 138. Let i = t - 1535/9. Factor 0 + 2/9*c + i*c**2 - 2/9*c**5 + 0*c**3 - 4/9*c**4.
-2*c*(c - 1)*(c + 1)**3/9
Let b(m) be the third derivative of -m**9/756 - m**8/420 + m**7/210 + m**6/90 + 31*m**3/6 + 5*m**2. Let n(y) be the first derivative of b(y). Factor n(d).
-4*d**2*(d - 1)*(d + 1)**2
Suppose -3*j - j = 8. Let n be j/(-6)*2*3. Factor -n + 5*s**2 + 2*s**3 - 11*s**2 + 7*s - s + 0*s.
2*(s - 1)**3
Let f(q) be the first derivative of 4*q**3/9 + 32*q**2/3 - 48*q + 92. Let f(g) = 0. Calculate g.
-18, 2
Let u(w) be the first derivative of 2*w**6/7 + 9*w**5/35 - 51*w**4/28 - 12*w**3/7 + 6*w**2/7 - 83. Suppose u(y) = 0. Calculate y.
-2, -1, 0, 1/4, 2
Suppose 0 = -28*a + 32*a + 28. Let o be ((-1)/a)/(12/14). Solve 0 - o*u**2 - 1/3*u = 0.
-2, 0
Let b(a) be the third derivative of -a**5/80 - 17*a**4/32 - 2*a**3 - 58*a**2. Factor b(c).
-3*(c + 1)*(c + 16)/4
Let r be -7 - ((-42)/7 + 11). Let i be r/15 + (-140)/(-50). Factor -4/5*z + 0*z**i - 2/5 + 4/5*z**3 + 2/5*z**4.
2*(z - 1)*(z + 1)**3/5
Determine x so that 2*x**4 - 5*x**3 - 10*x**2 - 5*x + x**5 + 15*x - 2*x + 4*x - 8*x + 8 = 0.
-2, -1, 1, 2
Suppose 16*r + 23 = 5*s + 15*r, 0 = 2*s - 5*r - 46. Factor 48 - 44/3*w**2 + 32*w + 4/3*w**s.
4*(w - 6)**2*(w + 1)/3
Let b be 3 + -1 + 8/4. Suppose -2*c = -0*c - b. Determine o, given that 0 - o - 4*o**c - 7/4*o**3 = 0.
-2, -2/7, 0
Suppose 0 = n + 3*n - 8. Suppose n*j + 10 = 7*j. Factor 3/2*i**2 - 4*i + j.
(i - 2)*(3*i - 2)/2
Factor -288 - 10/3*y**4 + 864*y + 184/3*y**3 - 384*y**2.
-2*(y - 6)**3*(5*y - 2)/3
Let k(x) be the first derivative of -9*x**5/5 + 15*x**4/4 + 74*x**3 + 36*x**2 - 153. What is r in k(r) = 0?
-4, -1/3, 0, 6
Let m = 28 - 26. Let p(j) be the second derivative of 3*j**5/10 + j**4/6 - j**3/3 - 2*j. Let v(z) = z**3 - z**2 - z. Let g(y) = m*v(y) - p(y). Factor g(b).
-4*b**2*(b + 1)
Let f be 11 + (-288)/27 - (-5)/(-35). Solve 2/21*g**4 + 2/21*g**5 - 4/21*g**3 - f*g**2 + 2/21*g + 2/21 = 0 for g.
-1, 1
Let -1/7*w**3 - 40/7*w - 48/7 - 11/7*w**2 = 0. What is w?
-4, -3
Factor 2/15*t**5 + 0 + 0*t**4 - 2/15*t**3 + 0*t + 0*t**2.
2*t**3*(t - 1)*(t + 1)/15
Determine p, given that 24*p - 3*p**3 - 15/2*p**4 + 45/2*p**2 + 6 = 0.
-1, -2/5, 2
Determine l, given that 53/5*l**2 + 82/5*l - 17/5*l**4 - 1/5*l**5 - 13/5*l**3 + 32/5 = 0.
-16, -1, 2
Let p(f) = 85*f**4 + 25*f**3 - 10*f**2 - 20*f. Let n(c) = 3*c**4 - c**3 + c**2 + c. Let t(o) = 20*n(o) - p(o). Factor t(d).
-5*d*(d - 1)*(d + 2)*(5*d + 4)
Let v = -1608 - -1610. Factor -9/2*a**v + 9*a + 3/4*a**3 - 6.
3*(a - 2)**3/4
Let j(w) = w**2 - 8*w - 6. Let b be j(9). Determine s so that -10*s + 5*s**b + 10*s**3 - 5*s**3 - 5*s**2 + 5*s**4 = 0.
-2, -1, 0, 1
Let d = 66 - 61. Suppose -d*h = 32 - 32. Factor -1/4*g**3 + h + 0*g - 1/4*g**2.
-g**2*(g + 1)/4
Find t, given that -31/4*t - 1/2 + 4*t**3 + 17/4*t**2 = 0.
-2, -1/16, 1
Let p(q) be the second derivative of -q**8/3360 - q**7/840 - q**6/720 + q**3/6 + 14*q. Let f(b) be the second derivative of p(b). Solve f(w) = 0 for w.
-1, 0
Let h(c) be the second derivative of 2*c**7/7 + 4*c**6/15 - 6*c**5/5 - 4*c**4/3 + 2*c**3 + 4*c**2 - 60*c + 2. Solve h(x) = 0.
-1, -2/3, 1
Let q be (-40)/(-24) + 213/180. Let c = q - 9/4. Let 3/5*h - 3/5*h**3 - c*h**2 + 3/5 = 0. Calculate h.
-1, 1
Let x(d) be the third derivative of d**8/560 + d**7/25 + 6*d**6/25 - 7*d**5/50 - 49*d**4/40 + d**2 + 24. Determine y, given that x(y) = 0.
-7, -1, 0, 1
Let o(q) = -5*q - 10. Let g be o(-6). Factor -4*f**2 + 0*f**2 - 35*f + 15*f + 4 - g.
-4*(f + 1)*(f + 4)
Let b(c) be the third derivative of -c**7/1050 + c**6/75 - 23*c**5/300 + 7*c**4/30 - 2*c**3/5 - 2*c**2 + 9. Factor b(x).
-(x - 3)*(x - 2)**2*(x - 1)/5
Let a = 85 + -55. Let f be 10/a + (-14)/6. Let x(l) = -2*l**3 - 6*l**2 - 4*l - 3. Let k(d) = 2*d**3 + 6*d**2 + 4*d + 2. Let h(w) = f*x(w) - 3*k(w). Factor h(o).
-2*o*(o + 1)*(o + 2)
Let t(p) be the third derivative of p**7/42 - 2*p**6/3 + 71*p**5/12 - 35*p**4/3 - 605*p**2. Factor t(u).
5*u*(u - 8)*(u - 7)*(u - 1)
Let p be (6/(-231))/(60/(-105)). Let c(j) be the first derivative of -5/11*j**2 + p*j**4 + 4/11*j - 8 - 2/55*j**5 + 2/11*j**3. Let c(h) = 0. What is h?
-2, 1
Let y(r) = r**2 - 22*r - 238. Let x be y(-8). Suppose 2/5*m**3 + 4/5*m - 6/5*m**x + 0 = 0. What is m?
0, 1, 2
Let k(s) be the first derivative of 4 - 2/27*s**3 + 4/9*s**2 - 8/9*s. Let k(f) = 0. What is f?
2
Solve -2*f - 1/2*f**2 + 21/2 = 0 for f.
-7, 3
Let j(o) be the third derivative of 0*o + 0*o**4 + 0*o**6 + 0*o**5 + 0 + 2/2205*o**7 + 1/3528*o**8 + 0*o**3 - o**2. Factor j(k).
2*k**4*(k + 2)/21
Suppose 7 - 175 = -7*r. Solve -8*t + r*t**3 - 6*t**5 + 4 + 4*t**4 - 