**6/30 - 11*m**5/15 + 4*m**4 + 24*m**3 + 514*m**2. Factor f(o).
4*(o - 6)**2*(o + 1)
Solve 18960/13*p**2 + 246400/13*p + 478/13*p**3 + 4/13*p**4 - 128000/13 = 0 for p.
-40, 1/2
Determine i, given that 1/6*i**2 + 11/6*i - 13/3 = 0.
-13, 2
Let o be 35/(-84)*9*(-1)/15. Let 1/4*v**2 - o*v**5 + 0*v + 1/4*v**3 + 0 - 1/4*v**4 = 0. What is v?
-1, 0, 1
Let z be (2 + -1 - -1) + -5. Let a(r) = -r**2 - 4*r - 3. Let k be a(z). Factor -2*y + k*y - 15*y**5 + 2*y - 50*y**4 - 30*y**2 - 5*y - 60*y**3.
-5*y*(y + 1)**3*(3*y + 1)
Let m(b) = b + 6. Let z be m(-4). Factor 9*j + 0 + 9*j - 16*j - 3 + j**z.
(j - 1)*(j + 3)
Let r be 1/((-9)/(-48))*117/861. Let d = r - 18/41. Suppose -d - 1/7*j**2 - 3/7*j = 0. Calculate j.
-2, -1
Let p be ((-312)/70)/((-30)/(-225)). Let a = 3084/91 + p. Factor -2/13 + a*m - 6/13*m**2 + 2/13*m**3.
2*(m - 1)**3/13
Let q(o) be the third derivative of -o**7/105 + o**6/60 + o**5/5 - o**4/3 - 8*o**3/3 - 6*o**2 - o. Factor q(a).
-2*(a - 2)**2*(a + 1)*(a + 2)
Let b be (5 - 4)/(1/4). Factor 4*v + 7*v + v - 6*v + 2*v**2 + b.
2*(v + 1)*(v + 2)
Let q = 40 - 38. Let z = q - 0. Factor -2/9*w + 2/9*w**3 + 0*w**z + 0.
2*w*(w - 1)*(w + 1)/9
Suppose -2*k + 48 = 4*k. Let m = -15/2 + k. Factor m*u**3 - 1/2*u**2 - 1/4*u - 1/4*u**5 + 1/4 + 1/4*u**4.
-(u - 1)**3*(u + 1)**2/4
Let s(z) = -z**4 - 15*z**3 + 9*z**2 - 5*z. Let l(u) = -u**4 - u**2. Let r(a) = -6*l(a) + s(a). Determine i, given that r(i) = 0.
0, 1
Let l(g) be the second derivative of g**5/80 + 5*g**4/16 + 25*g**3/8 + 125*g**2/8 - 115*g. Suppose l(m) = 0. Calculate m.
-5
Let b(r) be the third derivative of -r**5/15 + 31*r**4/6 - 116*r**3/3 - 23*r**2 - r. Factor b(w).
-4*(w - 29)*(w - 2)
Let k be 209/(-11) - -26 - 7. Find n such that k*n + 0 + 8/11*n**2 - 2/11*n**4 + 0*n**3 = 0.
-2, 0, 2
Suppose 32 = 11*t - 7*t. Suppose 0 + t = 4*k. Factor -16 + 48*l + 12*l**2 + 17*l**2 + 3*l**k - 4*l**2.
4*(l + 2)*(7*l - 2)
Let n(p) be the third derivative of -p**6/60 + p**5/15 + p**4/12 - 2*p**3/3 - 5*p**2 - 2*p. Determine x so that n(x) = 0.
-1, 1, 2
Let z = 147/685 + -2/137. Let x be 36 + -32 - 57/15. Factor -2/5*p + z*p**2 + x.
(p - 1)**2/5
Let a(n) = -13 - n**2 + 0*n + 14 - n. Let y(h) = -7*h**4 + 9*h**3 - 8*h**2 - 6*h + 6. Let w(c) = -6*a(c) + y(c). Determine r so that w(r) = 0.
0, 2/7, 1
Let l(w) be the second derivative of 5*w**7/84 + 3*w**6/4 + 29*w**5/8 + 215*w**4/24 + 25*w**3/2 + 10*w**2 - 247*w - 2. Factor l(c).
5*(c + 1)**3*(c + 2)*(c + 4)/2
Let n(h) = h**3 - 81*h**2 - 386*h - 329. Let g(x) = 4*x**3 - 404*x**2 - 1932*x - 1644. Let d(w) = -5*g(w) + 24*n(w). Factor d(c).
4*(c + 1)*(c + 9)**2
Let c(k) = 6*k**3 + 6*k**2 - 32*k - 8. Let q(v) = v**3 - v**2 - 4. Let w(y) = 3*c(y) - 21*q(y). What is f in w(f) = 0?
1, 2, 10
Let a be 2156/140 - ((-8)/10)/(-2). Let h be 88/275*a/2. Factor -3/5*f**2 - h*f - 12/5.
-3*(f + 2)**2/5
Let o be 9 - (-5 + 4/1 + (-88)/(-11)). Factor -24/5 + 4*j - 4/5*j**o.
-4*(j - 3)*(j - 2)/5
Suppose -21 = 5*p - r, -4 - 17 = 4*p - 5*r. Let o(b) = b + 7. Let c be o(p). Factor 10*d - c*d**2 + 6 - 3*d**4 - 9*d**3 - 6*d + 5*d + 0*d**4.
-3*(d - 1)*(d + 1)**2*(d + 2)
Let q be (4/(-10))/((-2)/20). Suppose -8 + 15 = z - 4*c, 70 = 4*z + 5*c. Factor -z*h**q + 48*h**3 - 32*h**3 - 18*h**4 - 20*h**5 + h**4.
-4*h**3*(h + 2)*(5*h - 2)
Factor -7*s**3 + 2*s**3 + 58*s**2 + 25*s + 33*s**2 - 71*s**2.
-5*s*(s - 5)*(s + 1)
Let r(j) be the third derivative of -22*j**2 + 0*j**3 + 0 + 1/60*j**5 + 0*j + 1/3*j**4. Factor r(n).
n*(n + 8)
Let w(o) = 4*o**5 + 4*o**4 - 8*o**3 - 6*o**2 + 26*o - 14. Let l(v) = -v**5 - 2*v**3 - v**2 + 1. Let z(k) = 2*l(k) + w(k). Solve z(x) = 0 for x.
-3, -2, 1
Let u(c) be the second derivative of -c**7/1365 + c**6/780 + c**5/195 - c**2/2 + c. Let v(f) be the first derivative of u(f). Factor v(k).
-2*k**2*(k - 2)*(k + 1)/13
Factor 0 + 2/9*u**2 + 12*u.
2*u*(u + 54)/9
Let x be (36/(-63))/(10/(-35)). Let k(b) be the second derivative of 1/2*b**4 + 0 + 0*b**x + 1/8*b**5 + 2*b + 1/3*b**3. Factor k(t).
t*(t + 2)*(5*t + 2)/2
Factor 3*w**3 + 5*w - 2*w - 4*w**3 + 13*w.
-w*(w - 4)*(w + 4)
Suppose 0 = 3*a + 29 - 11. Let g be (-1)/(-1) + a/(-2). Suppose 2*w + 0*w**4 + w**4 + 0*w**g + 2 - 3 - 2*w**3 = 0. Calculate w.
-1, 1
Factor 173 - 56*z - 3*z**2 - 5*z - 89*z - 20.
-3*(z - 1)*(z + 51)
Let j(c) be the second derivative of c**4/12 - 13*c**3/6 + 102*c. Find k, given that j(k) = 0.
0, 13
Let g(c) = 2*c**5 + c**3 - c**2 + c - 1. Let x(s) = 17*s**5 + 50*s**4 + 101*s**3 - 156*s**2 + 6*s - 6. Let u(o) = -6*g(o) + x(o). Suppose u(h) = 0. Calculate h.
-6, -5, 0, 1
Let l(f) be the second derivative of f**7/21 - 7*f**6/45 - 17*f**5/10 - 9*f**4/2 - 52*f**3/9 - 4*f**2 - 12*f + 1. What is r in l(r) = 0?
-1, -2/3, 6
Let i(l) be the second derivative of 0*l**2 + 1/110*l**5 - 1/22*l**4 + 12*l + 0 + 2/33*l**3. Factor i(q).
2*q*(q - 2)*(q - 1)/11
Let u(y) be the second derivative of -1/30*y**4 + 1/15*y**3 + 0*y**2 - 3*y + 0 - 1/50*y**5 + 1/75*y**6. Solve u(a) = 0 for a.
-1, 0, 1
Suppose 3 = 4*y - 3*y. Let u be 10/y + (-6)/(-9). Factor -2*p**2 + 4*p**3 - u*p**3 + 6*p**2 - 2 - 2*p**4.
-2*(p - 1)**2*(p + 1)**2
Let s(g) be the first derivative of 1/3*g**2 + 1/9*g**3 + 1/3*g + 10. Factor s(d).
(d + 1)**2/3
Let u(j) be the second derivative of -j**6/165 + j**5/55 - j**4/66 + 3*j + 13. Let u(y) = 0. What is y?
0, 1
Factor -4232/3 - 92/3*j - 1/6*j**2.
-(j + 92)**2/6
Let y = 2958 + -2955. Factor -1/4*v**y + 3/4*v**2 + 1/4 - 3/4*v.
-(v - 1)**3/4
Let g(i) be the second derivative of -i**5/20 + i**4/3 - i**3/3 - 3*i**2/2 + i. Let h be g(3). Factor 2/5*z + 2/5*z**2 + h.
2*z*(z + 1)/5
Suppose -2*y - 1089*x = -1090*x, 0 = 4*y - 3*x + 4. Factor -4/5*z**y - 2/5*z**3 + 0 + 0*z.
-2*z**2*(z + 2)/5
Let u(g) be the first derivative of g**6/30 - g**5/15 - 13*g**2 - 2. Let n(v) be the second derivative of u(v). Let n(b) = 0. What is b?
0, 1
Let r = 71/4860 + 1/486. Let f(o) be the third derivative of 0*o**4 + o**2 + 0 + 1/672*o**8 + r*o**5 + 1/48*o**6 + 1/105*o**7 + 0*o + 0*o**3. Factor f(q).
q**2*(q + 1)**2*(q + 2)/2
Let r(w) be the first derivative of -w**3 - 60*w**2 - 1200*w + 28. Find d such that r(d) = 0.
-20
Let j(m) be the first derivative of m**4/14 - 4*m**3/21 + m**2/7 - 512. Suppose j(w) = 0. What is w?
0, 1
Let q(t) be the second derivative of -14*t + 0 + 1/18*t**4 - 4/3*t**2 + 1/3*t**3. Factor q(v).
2*(v - 1)*(v + 4)/3
Let g = 917697/34 - 26994. Let r = -24/17 - g. Solve 1/2*w**3 - w + 0 + 1/2*w**5 - 3/2*w**2 + r*w**4 = 0.
-2, -1, 0, 1
Let f(x) be the first derivative of x**5/80 - x**4/48 - 5*x**3/24 - 3*x**2/8 + 20*x - 6. Let w(n) be the first derivative of f(n). Factor w(m).
(m - 3)*(m + 1)**2/4
Let i(t) = 13*t**2 + 27*t - 8. Let v(w) be the first derivative of -1/3*w**3 - 4 + 0*w**2 - w. Let u(l) = i(l) - 2*v(l). Solve u(p) = 0 for p.
-2, 1/5
Let q(r) be the third derivative of r**7/1008 + r**6/160 - r**5/120 + 5*r**4/24 - 11*r**2. Let f(p) be the second derivative of q(p). Factor f(t).
(t + 2)*(5*t - 1)/2
Let u(d) be the first derivative of 3/10*d**4 + 1/25*d**5 + d**2 + 4/5*d**3 + 3/5*d + 18. Find q such that u(q) = 0.
-3, -1
Suppose 0 = -4*m - 0*m + 3*j - 76, -5*m - 2*j - 72 = 0. Let g be m/(-5) + (-96)/80. What is z in 1/2 + 0*z**g + z - z**3 - 1/2*z**4 = 0?
-1, 1
Let f = 2257/11 - 205. Let l be (-13)/(-6) + (-30)/180. Find v, given that 0 + f*v**l + 2/11*v - 2/11*v**3 - 2/11*v**4 = 0.
-1, 0, 1
Let f(h) = 10*h**3 - 185*h**2 + 130*h + 90. Let k(i) = i**3 - 17*i**2 + 12*i + 8. Let b(r) = 4*f(r) - 45*k(r). Find a such that b(a) = 0.
0, 1, 4
Let d(k) = 8 + 24*k**2 + 2*k - 23*k**2 - 4 - 7*k. Let o be d(4). Find w such that -1/3*w**4 + o + 2/3*w**3 + 0*w - 1/3*w**2 = 0.
0, 1
Let c(v) be the third derivative of -2*v**7/105 - 17*v**6/120 + 17*v**4/24 + 2*v**3/3 - 19*v**2. Find u, given that c(u) = 0.
-4, -1, -1/4, 1
Let 17*s + 12 - 5*s**2 + 19*s + 43 + 14*s = 0. Calculate s.
-1, 11
Let o(i) = -i**5 + i**3 - i**2 - i - 1. Let d(q) = 5*q**5 - q**4 + 4*q**3 - 2*q**2 + 6*q + 6. Let m(z) = d(z) + 6*o(z). Solve m(j) = 0 for j.
-4, 0, 1, 2
Let l be -1 + 1 - ((-300)/(-54) + -6). Suppose 0 = -3*g - 5*c + 15, 3*g - 25 = -2*g + 2*c. Factor -l*p**4 + 0*p**2 + 0 + 0*p + 2/9*p**g + 0*p**3.
2*p**4*(p - 2)/9
Factor 3*a**2 + 1/3*a**3 + 8*a + 20/3.
(a + 2)**2*(a + 5)/3
Suppose k - 4*k = -57. Let i(n) = 11*n - 6*n + 14*n + 66*n**3 - 98*n**2 + k*n -