*3*(p - 1)*(p + 1)/2
Let r(y) be the second derivative of -y**5/80 + y**4/48 - 4*y. Determine z so that r(z) = 0.
0, 1
Suppose 0 = 3*f - 10 - 2. Let d be 1*(-2)/(-1 - 0). Factor -2 + g**3 - g + 2 + g**f - g**d.
g*(g - 1)*(g + 1)**2
Let j = -1406/6095 - 8/265. Let s = j + 35/46. What is i in -s*i**3 + 1/2*i - 1 + i**2 = 0?
-1, 1, 2
Let d(y) be the second derivative of -7*y**6/5 + 111*y**5/10 - 159*y**4/8 + 31*y**3/2 - 6*y**2 + 2*y + 17. Find u, given that d(u) = 0.
2/7, 1/2, 4
Let t(y) be the first derivative of -5*y**3/3 + 25*y**2/2 - 30*y + 60. Let t(z) = 0. Calculate z.
2, 3
Let l(w) be the third derivative of w**6/48 - w**5/15 - w**4/12 + 6*w**2. Find g such that l(g) = 0.
-2/5, 0, 2
Let z(l) = -l**4 + l**3 + l**2 - l. Let t be (-4)/6*(-6)/(-4). Let i(o) = -2*o**4 + 3*o**3 - o. Let w(a) = t*z(a) + i(a). Solve w(q) = 0 for q.
0, 1
Let u be -2 + (-2)/((-192)/206). Let n = u - -3/16. Suppose -4/3 - 4/3*x - n*x**2 = 0. What is x?
-2
Let x(w) = -w**3 - w**2. Let m(b) = 6*b**3 + 50*b**2 + 192*b + 256. Let d(r) = -m(r) - 2*x(r). Factor d(z).
-4*(z + 4)**3
Let y = 169/21 + -47/7. Factor 2/3*l**5 + 0*l**4 - y + 2*l - 8/3*l**3 + 4/3*l**2.
2*(l - 1)**3*(l + 1)*(l + 2)/3
Let s(d) = 4*d - 22. Let r(h) = 2*h - 11. Let y(g) = 13*r(g) - 6*s(g). Let a be y(8). Find l such that l**4 + 0*l**2 + 0*l + 0 + 0*l**3 + 5/2*l**a = 0.
-2/5, 0
Let f(v) = 2*v**2 - 39*v - 17. Let z be f(20). Factor -4/7*w**z + 0*w**2 + 10/7*w**4 + 0 + 0*w.
2*w**3*(5*w - 2)/7
Let q be (4/10)/((-4)/(-20)). Let 7*r**2 - 11*r**2 - 9*r + 6 + 7*r**q = 0. What is r?
1, 2
Let z = 50/3 - 16. Let p = 143 + -140. Factor 2*u + z*u**p - 2*u**2 - 2/3.
2*(u - 1)**3/3
Let x(k) be the first derivative of 8*k**5/5 + 11*k**4 - 28*k**3 + 2*k**2 + 28*k + 73. Factor x(q).
4*(q - 1)**2*(q + 7)*(2*q + 1)
Let p be 2/((6/2)/(-3)). Let r = 0 + p. Let o(v) = -v**5 - v**4 + v**2 - v. Let b(h) = h**5 + h**4 + h**3 - h**2 + 2*h. Let m(n) = r*o(n) - b(n). Factor m(j).
j**2*(j - 1)*(j + 1)**2
Let u be (-3 + (-6)/(-2))/(-1). Let b be 1/((0 - 1)/(-2)). Suppose -2*g + 5*g**2 + u*g + g**3 - 4*g**b = 0. What is g?
-2, 0, 1
Let o = -30 - -21. Let x(s) = 7*s**3 - s**2 + 2*s. Let a(l) = -27*l**3 + 3*l**2 - 9*l. Let p(b) = o*x(b) - 2*a(b). Determine i so that p(i) = 0.
0, 1/3
Let m(s) = 3*s**2 + 15*s + 30. Let r(z) = -z**2 + z - 1. Let k(j) = -m(j) - 6*r(j). Factor k(i).
3*(i - 8)*(i + 1)
Let z(r) be the second derivative of 4/9*r**2 - r + 2/15*r**5 - 4/9*r**3 + 1/54*r**4 + 4/135*r**6 + 0. Factor z(j).
2*(j + 2)**2*(2*j - 1)**2/9
Let z(j) be the first derivative of -1/4*j**2 + 0*j**3 + 1/8*j**4 + 0*j - 4. Factor z(r).
r*(r - 1)*(r + 1)/2
Suppose 3 = 2*f - 1. Factor -f + 2*y + y**2 - 3*y**2 + 5*y - 3*y.
-2*(y - 1)**2
Let z be 4/6 - (-12)/9. Let s(y) be the first derivative of -z - 4*y + 0*y**2 - 3/5*y**5 - 1/4*y**4 + 1/6*y**6 + 7/3*y**3. Let s(v) = 0. What is v?
-1, 1, 2
Let f(p) = -6*p**3 + 6*p**2 + 3. Let h(m) = m**3 + m**2 - 2*m - 1. Let n(y) = f(y) + 3*h(y). Factor n(u).
-3*u*(u - 2)*(u - 1)
Let j(x) be the third derivative of -x**7/945 - x**6/135 - 2*x**5/135 + 7*x**2. Find z, given that j(z) = 0.
-2, 0
Let u(k) = 20*k**4 - 6*k**3 - 4*k**2 + 22. Let y(t) = t**4 + 1. Let o(m) = -2*u(m) + 44*y(m). Determine a, given that o(a) = 0.
-2, -1, 0
Let u(d) = d - 1. Let n(f) = -3*f + 4. Let k(l) = -2*n(l) - 7*u(l). Let t be k(-3). Factor 4/3*s - 2/3 - 2/3*s**t.
-2*(s - 1)**2/3
Let c(v) = -v**2 + 4*v - 2. Let h be c(2). Solve h*d**4 + 3*d**2 + 2*d**4 - 3*d**3 - 7*d**4 + 3*d**5 = 0 for d.
-1, 0, 1
What is f in -4/15*f + 8/15*f**2 + 4/15*f**3 - 2/15*f**4 - 2/5 = 0?
-1, 1, 3
Let v(t) be the second derivative of t**6/50 + 3*t**5/50 - 3*t**4/20 - 2*t**3/5 + 6*t**2/5 + 8*t. Solve v(p) = 0.
-2, 1
Let w(r) be the first derivative of 2*r**5/35 - 2*r**3/7 + 2*r**2/7 - 10. Factor w(h).
2*h*(h - 1)**2*(h + 2)/7
Let n(j) = 2*j**2 - 40*j + 3. Let o be n(20). Let k(t) be the first derivative of -3 - 1/2*t + 1/4*t**2 + 1/3*t**o. Factor k(i).
(i + 1)*(2*i - 1)/2
Let h(b) = -b**4 - 30*b**3 + 22*b**2 + 11*b + 11. Let p(l) = -6*l**3 + 4*l**2 + 2*l + 2. Let j(v) = 4*h(v) - 22*p(v). Determine d, given that j(d) = 0.
0, 3
Let w(s) be the first derivative of s**4/24 - s**2/4 + 3*s + 6. Let f(i) be the first derivative of w(i). Suppose f(g) = 0. What is g?
-1, 1
Let i(p) be the third derivative of -p**5/50 + 13*p**4/60 + 2*p**3/3 - 18*p**2. Solve i(v) = 0.
-2/3, 5
Let g(c) be the third derivative of c**6/120 + c**5/60 - c**4/24 - c**3/6 + 12*c**2. Solve g(y) = 0 for y.
-1, 1
Suppose -c - 2*y = -4*c + 18, -5*c = y - 30. Suppose -2*a = -o - 9, 5*o = -6*a + 2*a + 11. Determine b, given that 2*b**3 + 5 - a*b**3 - c*b + 6*b**2 - 3 = 0.
1
Let p(a) be the third derivative of a**5/6 - a**4 + 4*a**3/3 + 4*a**2. Factor p(u).
2*(u - 2)*(5*u - 2)
Let m(l) = 1. Let w(r) = 2*r**2 + 8*r + 4. Let x be (-3 + 0 - -3)/1. Let h = -4 + x. Let v(y) = h*m(y) - w(y). Let v(u) = 0. What is u?
-2
Suppose 2*b + 9 = 3*b. Let r be -3*(-6)/b*1. Solve -2*g + g**4 - 2*g + 3*g**2 - 5*g**3 + 5*g**r + 0*g = 0 for g.
0, 1, 2
What is o in 8/3*o**3 + 16/3*o**2 - 2*o**4 + 1/3*o**5 - 16*o + 32/3 = 0?
-2, 2
Let s be (-129)/126 - (-4)/6. Let g = s - -6/7. Let k**3 - 3/2*k**4 + 0 + g*k**2 + 0*k = 0. Calculate k.
-1/3, 0, 1
Let x(o) = 13*o**3 - 7*o**2 - 19*o + 13. Let i(t) = -6*t**3 + 3*t**2 + 9*t - 6. Let g(h) = 9*i(h) + 4*x(h). Factor g(q).
-(q - 1)*(q + 2)*(2*q - 1)
Let l(s) be the third derivative of s**8/280 + s**7/56 + s**6/60 - s**3/2 - 5*s**2. Let j(y) be the first derivative of l(y). Factor j(h).
3*h**2*(h + 2)*(2*h + 1)
Let p(s) = -s**3 - s**2 - 1. Let w(v) = 73*v**3 + 67*v**2 + 20*v + 3. Let n(k) = -2*p(k) - 2*w(k). Factor n(g).
-4*(3*g + 1)**2*(4*g + 1)
Suppose -5*o = -5*y - 10, -3*y + 8 = -0*y + 4*o. Let q(r) be the second derivative of 0*r**3 + 1/6*r**4 + y - 2*r - r**2. Factor q(c).
2*(c - 1)*(c + 1)
Let l(p) be the second derivative of -p**5/90 + 5*p**4/54 - 8*p**3/27 + 4*p**2/9 + 11*p. Determine t so that l(t) = 0.
1, 2
Let c(o) be the second derivative of -3/20*o**5 + 0*o**2 + 0 - o + 1/4*o**4 - 1/9*o**3. Solve c(w) = 0 for w.
0, 1/3, 2/3
Suppose 0 = -u - 0*u - 1. Let r be (0/u)/1 + 2. Let 0*l - 4/3*l**r + 2/3*l**4 + 0*l**3 + 2/3 = 0. Calculate l.
-1, 1
Let f = 21 + -62/3. Let p be ((-4)/(-12))/((-1)/(-4)). Solve -p*b**2 - b + f = 0.
-1, 1/4
Let j(v) = -v**2 - 2. Let p(d) = -4*d**2 - 7. Let c(g) = 7*j(g) - 2*p(g). Find r such that c(r) = 0.
0
Suppose 172 = 24*q + 124. Find v, given that v**3 + 0*v - v**5 - q*v**2 + 3/2*v**4 + 1/2 = 0.
-1, -1/2, 1
Let a be (1/7*-4)/(9/(-21)). Factor 5/3*r - a*r**2 + 1/3*r**3 - 2/3.
(r - 2)*(r - 1)**2/3
Suppose 3*w - 8 = 1. Factor 2*d**w - d**3 + 2*d**2 - d - 2*d**3.
-d*(d - 1)**2
Let a(q) be the third derivative of -q**7/420 + q**6/15 - 4*q**5/5 + 16*q**4/3 - 64*q**3/3 + 5*q**2. Let a(f) = 0. What is f?
4
Let o(w) = -w**2 + 9*w - 8. Let m be o(6). Factor -10*g**2 - 6*g**2 - 8*g - 4*g**4 + 0*g**4 + 2*g**4 - m*g**3.
-2*g*(g + 1)*(g + 2)**2
Let v(a) be the second derivative of -1/9*a**4 + 0 - a - 1/45*a**6 + 0*a**2 + 1/12*a**5 + 1/18*a**3. Factor v(n).
-n*(n - 1)**2*(2*n - 1)/3
Let r(f) be the third derivative of -f**6/1440 + f**5/240 - f**4/96 + f**3/6 - f**2. Let v(a) be the first derivative of r(a). Factor v(x).
-(x - 1)**2/4
Let k = 76 + -74. Let m(u) be the first derivative of 0*u - 1/3*u**k - 5/6*u**4 + 2 - 8/9*u**3 - 4/15*u**5. Determine f so that m(f) = 0.
-1, -1/2, 0
Suppose -9*x + 13*x - 6 = 2*f, 2*x = 6. Factor 1/4 + 0*o**2 + 1/2*o - 1/4*o**4 - 1/2*o**f.
-(o - 1)*(o + 1)**3/4
Let n(b) = -b**3 + 9*b**2 - 6*b - 11. Let z be n(8). Solve 2/7*k - 4/7*k**3 + 2/7*k**z - 4/7*k**2 + 2/7*k**4 + 2/7 = 0.
-1, 1
Factor 1/9*f**2 + 64/9 - 16/9*f.
(f - 8)**2/9
Let r(j) = -j**2 - j + 1. Let g(f) = -3*f**3 - 30*f**2 - 27*f + 15. Let b(w) = -g(w) + 15*r(w). Factor b(u).
3*u*(u + 1)*(u + 4)
Let f(q) = 2*q**2 + 2 + q**2 + 3*q + 8*q**3 - 11*q**3. Let j(w) = 2*w**3 - 2*w**2 - 2*w - 2. Let p(x) = 4*f(x) + 5*j(x). Factor p(v).
-2*(v - 1)**2*(v + 1)
Let p(x) = x**2 - 11*x + 20. Let y be p(9). Find q such that 0 + 2/5*q**y - 4/5*q**3 + 2/5*q**4 + 0*q = 0.
0, 1
Let b(w) be the first derivative of -4*w**5/5 + 3*w**4 - 8*w**2 + 1. Factor b(g).
-4*g*(g - 2)**2*(g + 1)
Suppose -5*u + 1 = -19. Let i(a) be the second derivative of 0*a**2 + 2/15*a**u - 2/25*a**5 - 2*a + 0 +