 7/5*g**r + 1/3*g**3 - 1/2*g**4 - 2/3*g**6 + 0*g**2 - 3. Factor z(l).
-l**2*(l + 1)**2*(4*l - 1)
Let r(q) be the first derivative of -q**7/280 + q**6/160 + q**5/40 + q**2 + 2*q + 4. Let m(b) be the second derivative of r(b). Factor m(y).
-3*y**2*(y - 2)*(y + 1)/4
Let k be (-13 + 13)/((-8)/(-24) - 14/6). Suppose 0 = 2*b + b - 12. Let k + 0*y - 4/5*y**b + 4/5*y**2 + 0*y**3 = 0. What is y?
-1, 0, 1
Let a be (1 + -7 + 5)*0. Suppose -6*x + 176 + 40 = a. Find q such that x*q**2 + 16/3 - 18*q**3 - 24*q = 0.
2/3
Let y(c) be the third derivative of -c**5/120 + 5*c**4/48 + 7*c**2. Suppose y(v) = 0. What is v?
0, 5
Let y be 0*(-14 - (-243)/18). Factor -4/7*d**2 + 4/7*d**3 - 4/7*d**5 + 0 + 4/7*d**4 + y*d.
-4*d**2*(d - 1)**2*(d + 1)/7
Let g(a) be the third derivative of a**7/42 + 7*a**6/120 - 3*a**5/10 - 7*a**4/6 - 4*a**3/3 - a**2 - 12. Solve g(w) = 0.
-2, -1, -2/5, 2
Let p = 122/435 - -22/87. Let f(s) be the first derivative of -11/10*s**2 - 3/5*s + 1/5*s**4 - p*s**3 - 8. Determine j so that f(j) = 0.
-1/2, 3
Find a, given that 2/3*a**3 - 2/3*a + 40/3*a**2 - 40/3 = 0.
-20, -1, 1
Let t be -2*(-22)/40 - 72/144. Let u(y) be the first derivative of -t*y**5 - 1/2*y**6 + 6 + 0*y**2 + 3/4*y**4 + y**3 + 0*y. Determine a, given that u(a) = 0.
-1, 0, 1
Let p(l) be the second derivative of l**6/225 + 2*l**5/75 - 14*l**4/45 + 32*l**3/45 - 172*l. Factor p(j).
2*j*(j - 2)**2*(j + 8)/15
Let n(a) = a**3 + a**2 - a + 1. Let p = -27 + 47. Let u(t) = -t**4 + 3*t**3 + 4*t**2 - 4*t + 4. Let h(i) = p*n(i) - 5*u(i). Find v such that h(v) = 0.
-1, 0
Let h be (-3)/(-63)*28/20. Let d(t) be the second derivative of -1/15*t**4 + 2/5*t**2 + 1/50*t**5 - h*t**3 + 0 - 4*t. Factor d(v).
2*(v - 2)*(v - 1)*(v + 1)/5
Suppose 2*y + 15 = 7*y. Suppose -s + 9 = 5. Let -10*a**2 - 11*a**2 + 21*a**s - 9*a**y + 15*a**5 - 6*a + 0*a**3 = 0. What is a?
-1, -2/5, 0, 1
Let z(f) be the second derivative of -2*f**7/7 - f**6/2 + 21*f**5/20 + f**4/2 + 39*f + 6. Let z(m) = 0. What is m?
-2, -1/4, 0, 1
Let o(w) be the third derivative of -w**7/42 + 29*w**6/12 + 10*w**5 - 796*w**2. Determine q, given that o(q) = 0.
-2, 0, 60
Factor -386*r - 309*r**2 + 106*r - 4900 + 305*r**2.
-4*(r + 35)**2
Let d = 1204 - 1204. Let u(z) be the second derivative of d*z**2 - 7/20*z**4 + 1/15*z**3 - 8/15*z**6 + 18/25*z**5 - 7*z + 0. Determine p so that u(p) = 0.
0, 1/4, 2/5
Suppose 0 = -8*a + 4*a + 4*l + 1336, -5*a = -4*l - 1667. Let -331 - 3*x**5 + 6*x**2 + a - x + 10*x**4 - 12*x**3 = 0. What is x?
0, 1/3, 1
Let q = 12/31 + 33/155. Let h(b) be the second derivative of -2*b - 4*b**2 - 1/15*b**6 - 4*b**3 + 0 - 13/6*b**4 - q*b**5. Solve h(m) = 0 for m.
-2, -1
Let u = -30 - -27. Let d be (-1)/(u - -6) + (-1 - -2). Solve -8/3*g**2 + 10/3*g + d*g**3 - 4/3 = 0.
1, 2
Let q(c) be the first derivative of -13 + 1/18*c**4 - 2/3*c**3 - 6*c + 3*c**2. Factor q(v).
2*(v - 3)**3/9
Let u(n) = -4*n**2 + 90*n - 77. Let l(q) = 2*q**2 - 44*q + 38. Let o(b) = 9*l(b) + 4*u(b). Factor o(w).
2*(w - 17)*(w - 1)
Factor 5*z - 5*z**2 + 5*z**4 + 2289*z**3 - 2294*z**3 + 0*z**2.
5*z*(z - 1)**2*(z + 1)
Let d = 19164 - 19152. Let -4/3*w**2 + d*w + 40/3 = 0. What is w?
-1, 10
Let v(r) be the second derivative of 5/2*r**4 + 1/2*r**6 - 1/14*r**7 - 5/2*r**3 + 0 - 3/2*r**5 + 3/2*r**2 - 6*r. Determine q so that v(q) = 0.
1
Suppose -4 + 0 = 3*m - 4*q, m - 24 = -5*q. Suppose 3*c + m*w - 4 = 0, -6 = -4*c - w - 4*w. Factor 0 + 2*a**3 + 2/3*a + 2*a**2 + 2/3*a**c.
2*a*(a + 1)**3/3
Let i(y) be the third derivative of 1/420*y**7 - 1/120*y**6 - 1/12*y**4 - 7/120*y**5 + 0*y**3 - 14*y**2 + 0*y + 0. Find l, given that i(l) = 0.
-1, 0, 4
Let s(i) = -2*i**3 - i**2 + 2*i - 1. Suppose -5*t = -5, -3*t + 7*t = -u + 3. Let g(x) = 0*x**3 + x**3 - 2 + 3. Let v(k) = u*g(k) - s(k). Factor v(f).
f*(f - 1)*(f + 2)
Let q = 2947/2 + -1436. Factor q + 15*t + 3/2*t**2.
3*(t + 5)**2/2
Let f(s) be the first derivative of 1/16*s**2 - 1/32*s**4 - 1/8*s**3 + 3/8*s - 10. Let f(i) = 0. Calculate i.
-3, -1, 1
Let w = 124 - 124. Let q(l) be the second derivative of 0*l**3 - 1/5*l**5 + 0 + 2/15*l**6 - 2/3*l**4 + w*l**2 + 7*l. Determine j, given that q(j) = 0.
-1, 0, 2
Let k be 35/5 - (-2 + 1). Suppose -z + k = z. Find w, given that -4*w**3 + 0*w**z + 5*w**4 - 4*w**4 + w**2 + 2*w**2 = 0.
0, 1, 3
Find u, given that 62/11*u + 64/11*u**2 + 2*u**3 + 20/11 = 0.
-1, -10/11
Let d(u) be the second derivative of 0 - 2/15*u**5 - 1/45*u**6 + 2*u - 2/9*u**3 + 0*u**2 - 5/18*u**4. Factor d(x).
-2*x*(x + 1)**2*(x + 2)/3
Let w(s) = -2*s**3 + 7*s**2. Let h(g) = g**3 - 3*g**2. Suppose 0 = 2*x + 6 + 14. Let v(p) = x*h(p) - 4*w(p). Factor v(k).
-2*k**2*(k - 1)
Suppose -9*r = -13*r + 12. Let -5*c**3 - 4*c**3 + 9*c**3 + 5*c**r - 5*c = 0. What is c?
-1, 0, 1
Suppose -2*o + 16 = 4*j, -3 + 5 = j. Suppose -12*i**3 + 12*i**2 + 0 - o*i - 10 + 4*i**4 + 10 = 0. Calculate i.
0, 1
Let n = 13 + -17. Let o(r) = -5 + 5 + r - r**2. Let i(v) = -2*v**2 + 3*v - 1. Let c(h) = n*i(h) + 12*o(h). Suppose c(b) = 0. What is b?
-1, 1
Factor -3*y**3 - y**3 - 40111*y**4 + 40110*y**4 + 3*y**2 - y**2 + 3*y**3.
-y**2*(y - 1)*(y + 2)
Let q(o) be the first derivative of -o**6/24 - 22*o**5/5 - 1011*o**4/8 - 946*o**3/3 - 1849*o**2/8 + 769. Factor q(y).
-y*(y + 1)**2*(y + 43)**2/4
Let s(k) = 5*k - 10. Let l be s(10). Let r be 2*76/l + -3. Solve -2/5*c + 2/5*c**3 + r*c**2 - 4/5 = 0.
-2, -1, 1
Suppose 3*s = -g + 4*g + 18, 5*g + 10 = -5*s. Suppose -3*p - s*j - 1 = -3*j, -p - 4*j + 4 = 0. What is n in 0*n + p + 1/6*n**2 = 0?
0
Let c = 25 + -15. Suppose 30 - c = 5*h. Factor -s**3 - 9*s**3 + 0*s**3 + 3*s**5 + h*s**3 + 3*s.
3*s*(s - 1)**2*(s + 1)**2
Let c(x) = 2*x. Let r be c(4). Suppose r*s - 5*s - 9 = 0. Factor p**2 + p**3 + 18*p - s*p**2 - 17*p.
p*(p - 1)**2
Let c(q) = 3*q**2 + 177*q + 102. Let x(u) = 3*u**2 + 189*u + 102. Let y(i) = 7*c(i) - 6*x(i). Suppose y(s) = 0. What is s?
-34, -1
Factor 63*m + 60 - 2*m**2 + 23*m**2 - 6*m**2 - 11*m**2 - m**2.
3*(m + 1)*(m + 20)
Suppose -73*p + 11796 - 11650 = 0. Find f, given that 0*f + 0*f**4 - 2/3*f**5 - 4/3*f**p + 2*f**3 + 0 = 0.
-2, 0, 1
Let h(p) be the third derivative of -p**6/160 + p**5/10 - 9*p**4/32 - 9*p**3/4 + 7*p**2 - 4*p. Factor h(c).
-3*(c - 6)*(c - 3)*(c + 1)/4
Let z(d) be the third derivative of -d**9/332640 + d**8/55440 + d**5/6 - 4*d**2. Let a(u) be the third derivative of z(u). Factor a(m).
-2*m**2*(m - 2)/11
Factor 0*k + 1/10*k**5 + 0*k**2 - 3/5*k**4 - 7/10*k**3 + 0.
k**3*(k - 7)*(k + 1)/10
Let y(t) = 2*t**2 + 2*t. Let j(s) = -5*s**4 + 55*s**3 - 192*s**2 + 168*s. Let d(z) = j(z) + 6*y(z). Factor d(u).
-5*u*(u - 6)*(u - 3)*(u - 2)
Let f(o) be the first derivative of o**4/6 - 8*o**3/3 + 12*o**2 - 86. Factor f(l).
2*l*(l - 6)**2/3
Let g(b) be the second derivative of -b**9/378 - b**8/420 + b**7/210 + b**3/2 + 20*b. Let z(u) be the second derivative of g(u). Let z(x) = 0. What is x?
-1, 0, 1/2
Let z(m) be the first derivative of m**4/2 - 2*m**3/3 - 4*m**2 + 8*m + 135. Factor z(w).
2*(w - 2)*(w - 1)*(w + 2)
Let m(c) be the first derivative of c**5/15 + 11*c**4/6 + 157*c**3/9 + 66*c**2 + 108*c + 323. Suppose m(f) = 0. What is f?
-9, -2
Let b(c) be the third derivative of c**8/280 - 2*c**7/75 - c**6/60 + 245*c**2. Determine j, given that b(j) = 0.
-1/3, 0, 5
Let y(j) = -11*j**3 + 27*j**2 - 71*j + 12. Let m(v) = v**3 + v**2 + 5*v. Let p(i) = -10*m(i) - 2*y(i). Find n such that p(n) = 0.
1/3, 2, 3
Let t(b) = -2*b**4 - 6*b**3 + 10*b**2 - 2*b - 4. Let l(o) = 4*o**4 + 6*o**3 - 12*o**2 + 2*o + 6. Let c(u) = -2*l(u) - 3*t(u). Factor c(n).
-2*n*(n - 1)**3
Let b(n) be the third derivative of 0*n**3 - 1/60*n**5 + 4*n**2 - 1/120*n**6 + 0*n + 0 + 1/210*n**7 + 1/24*n**4. Factor b(p).
p*(p - 1)**2*(p + 1)
Let w be 4/12*(-3 - -3). Let f(j) be the first derivative of w*j**4 + 0*j**2 - 6 - 1/5*j**5 + 0*j + 1/3*j**3. Suppose f(s) = 0. What is s?
-1, 0, 1
Suppose 4*o + 95 - 107 = 0. Let k(c) be the first derivative of 1/3*c**o + c**2 + 3 + 0*c. What is i in k(i) = 0?
-2, 0
Suppose 35 = 3*g + m, 2*g + 3*m - 51 + 16 = 0. Factor -5*c - 35 + 43 - 11*c - g*c**2.
-2*(c + 2)*(5*c - 2)
Let z(d) = -6*d**5 + 9*d**4 + 33*d**3 - 12*d**2 - 9*d + 30. Let y(f) = 3*f**5 - 5*f**4 - 17*f**3 + 6*f**2 + 4*f - 16. Let k(c) = -9*y(c) - 5*z(c). Factor k(s).
3*(s - 1)**3*(s + 1)*(s + 2)
Let q(b) be the first derivative of b**6/24 - b**5/20 - b**4/16 + 