?
-1
Factor -12/5*a - 2 - 2/5*a**2.
-2*(a + 1)*(a + 5)/5
Let g(q) = q**3 + 9*q**2 - 11*q - 9. Let t be g(-10). Let b be (2 - t)/((-44)/(-8)). Factor 2/11*i**2 + b + 4/11*i.
2*(i + 1)**2/11
Let j(v) be the second derivative of v**4/15 - 2*v**2/5 + 2*v. Factor j(r).
4*(r - 1)*(r + 1)/5
Suppose -7*r + 22540 = -2*r. Let d be (-3)/2 + r/72. What is g in -16/9 - 250/9*g**4 - 140/3*g**2 - d*g**3 - 136/9*g = 0?
-1, -2/5
Let r(n) = -4*n**2 + 3*n + 3. Let z(p) = -11*p**2 + 8*p + 8. Let y(g) = -8*r(g) + 3*z(g). Let c(u) = -8*u**2 + 2. Let j(m) = c(m) - 6*y(m). Factor j(w).
-2*(w - 1)*(w + 1)
Factor 2*k**5 + 99 + 12*k**3 - 4*k**2 - 99 - 9*k**4.
k**2*(k - 2)**2*(2*k - 1)
Let q(h) be the second derivative of h**7/2520 - h**6/1080 - h**5/360 + h**4/72 - h**3/6 - 3*h. Let y(j) be the second derivative of q(j). Factor y(k).
(k - 1)**2*(k + 1)/3
Let p(z) be the second derivative of -7*z**6/10 - 3*z**5/4 + 9*z**4/4 + 5*z**3/2 - 3*z**2 + 5*z. Find l, given that p(l) = 0.
-1, 2/7, 1
Let t = 35 - 31. Let f(o) be the third derivative of 2*o**2 - 1/4*o**t + 1/3*o**3 + 0*o - 1/60*o**6 + 0 + 1/10*o**5. Find y such that f(y) = 0.
1
Let c = 26 - 23. Determine y so that 4/7*y**c + 0*y + 2/7*y**2 + 0 + 2/7*y**4 = 0.
-1, 0
Suppose -4*k - 46 = -5*o - 0*o, -k = -2*o + 16. Let y(f) be the third derivative of -f**2 - 1/90*f**5 + 0 + 0*f**3 + 1/54*f**4 + 0*f + 1/540*f**o. Factor y(m).
2*m*(m - 2)*(m - 1)/9
Let b be 1/((-4)/(-20))*4. Let l be (-10)/b - 38/(-12). Factor -l*g - 2/9 - 8*g**2.
-2*(6*g + 1)**2/9
Let y(a) be the second derivative of -3*a**8/224 - a**7/20 - a**6/15 - a**5/30 + 3*a**2/2 - 3*a. Let r(f) be the first derivative of y(f). Factor r(v).
-v**2*(v + 1)*(3*v + 2)**2/2
Let v(x) = -44*x**2 - 2*x + 11. Let w be v(-5). Let m = w - -9725/9. Determine k, given that -2/3*k - 10/9*k**4 + m*k**2 - 4/9 + 2/3*k**3 = 0.
-1, -2/5, 1
Let x(v) be the first derivative of 7/2*v**6 - 3*v**5 + 0*v**3 - 3/2*v**4 + 0*v - 2 + 0*v**2. Factor x(u).
3*u**3*(u - 1)*(7*u + 2)
Let b(u) = -3*u**2 + u. Let q(v) be the second derivative of 7*v**4/12 - v**3/3 + 2*v. Let d(z) = -15*b(z) - 6*q(z). Factor d(m).
3*m*(m - 1)
Let r be (-1)/(-1 + 0) - 1. Let z(w) be the second derivative of -1/3*w**4 + 0*w**3 - 9/10*w**5 + w + r + 0*w**2 - 7/15*w**6. Factor z(j).
-2*j**2*(j + 1)*(7*j + 2)
Let o(c) be the first derivative of 2*c**3/5 + 8*c**2/5 + 8*c/5 + 7. Factor o(h).
2*(h + 2)*(3*h + 2)/5
Let x(v) be the first derivative of 2/9*v**3 + 0*v**2 - 5/12*v**4 + 4/15*v**5 - 4 + 0*v - 1/18*v**6. Find a, given that x(a) = 0.
0, 1, 2
Let u be (48/64)/((-6)/(-40)). Suppose -5*d + d - 20 = -4*r, 5*d - u = -r. Suppose 2/11*l**3 + d*l + 2/11*l**5 + 4/11*l**4 + 0 + 0*l**2 = 0. Calculate l.
-1, 0
Let v = -57 - -61. Suppose -3/4 + 0*d**3 + 0*d - 3/4*d**v + 3/2*d**2 = 0. What is d?
-1, 1
Let l be (0*1/(-2))/(-1). Let v(s) be the first derivative of l*s + 2 - 2/25*s**5 + 1/5*s**2 + 2/15*s**3 - 1/10*s**4. Solve v(b) = 0 for b.
-1, 0, 1
Let t(w) be the second derivative of -3*w**5/20 + w**4/4 + w**3/2 - 3*w**2/2 - 6*w. Factor t(q).
-3*(q - 1)**2*(q + 1)
Determine s so that -3*s**5 + 5*s**2 - 5 - 9*s**4 - 2 + 16*s**2 + 3*s**3 - 5 = 0.
-2, -1, 1
Let z(x) = 13*x**2 - 8*x + 4. Let m = 1 + 3. Let w be 21/(-12) + (-1)/m. Let p(b) = 3*b**2 - 2*b + 1. Let d(c) = w*z(c) + 9*p(c). Factor d(u).
(u - 1)**2
Let q(t) be the third derivative of -4*t**2 - 1/90*t**5 + 0 + 1/72*t**4 + 0*t + 0*t**3 + 1/360*t**6. Factor q(r).
r*(r - 1)**2/3
Let u(t) be the second derivative of 0 - t**2 + 1/3*t**3 - 1/6*t**4 + 1/30*t**5 - 2*t. Let x(n) be the first derivative of u(n). Factor x(h).
2*(h - 1)**2
Let m = 1/3180 + 43813/1060. Let u(d) = d**2 - 12*d + 10. Let y be u(12). What is n in -8/3 - y*n**4 - m*n**3 + 100/3*n**5 + 38/3*n**2 + 8*n = 0?
-1, -1/2, 2/5, 1
Let w = -13 - -16. Determine j so that 1 + 6*j + 3*j**2 - 1 + w = 0.
-1
Determine i, given that 9/2*i**2 + 15*i - 12 = 0.
-4, 2/3
Let d = 46/5 + -133/15. Let x(f) be the second derivative of 2/9*f**3 - f - d*f**2 - 1/18*f**4 + 0. Find u, given that x(u) = 0.
1
Let w(d) = d + 29. Let n be w(0). Solve -2*g**3 + n*g**4 + 4*g**3 - 30*g**4 - g**2 = 0.
0, 1
Let 3 + 1/2*l**5 - 17/2*l - 2*l**4 + 0*l**3 + 7*l**2 = 0. What is l?
-2, 1, 3
Let k(y) be the third derivative of y**8/1008 + y**7/315 - y**6/180 - y**5/45 + y**4/72 + y**3/9 + y**2 - 19. Solve k(g) = 0.
-2, -1, 1
Let k = -3535 - -18237/5. Let d = -112 + k. Factor d*o**2 + 4/5*o + 2/5.
2*(o + 1)**2/5
Let w(h) be the second derivative of -h**5/4 - 5*h**4/12 + 5*h**3 - 14*h. Find j, given that w(j) = 0.
-3, 0, 2
Suppose b = -4*z - 3 + 5, 2*z = -b + 2. Suppose 2/3*w - 2/9*w**b - 4/9 = 0. What is w?
1, 2
Let s(o) be the third derivative of -o**6/840 + o**5/210 + o**4/24 + 2*o**3/21 + 7*o**2. Factor s(f).
-(f - 4)*(f + 1)**2/7
Let p = 2 + 0. Suppose 2 + 2 = p*i. Solve 2/7*w**i - 2/7 + 0*w = 0 for w.
-1, 1
Let c(f) be the first derivative of -f**6/21 - 6*f**5/35 + 15*f**4/14 - 34*f**3/21 + 6*f**2/7 - 8. Factor c(v).
-2*v*(v - 1)**3*(v + 6)/7
Let u = 44 + -39. Let n(f) be the second derivative of 7/12*f**u - 4/9*f**3 + 2/3*f**2 + f - 31/36*f**4 + 0. Let n(q) = 0. What is q?
-2/5, 2/7, 1
Let u(d) be the first derivative of -2*d**6/3 + d**5/5 + d**4 - d**3/3 - 22. Solve u(y) = 0 for y.
-1, 0, 1/4, 1
Let i(f) be the second derivative of -f**4/6 + 11*f**3/6 - 13*f**2/2 - 5*f. Let v(x) = x**2 - 5*x + 6. Let j(m) = -6*i(m) - 13*v(m). Factor j(t).
-t*(t + 1)
Let w = -18/11 + 83/44. Find p, given that 1/4*p**2 + 1/2*p**3 + 0*p + w*p**4 + 0 = 0.
-1, 0
Let d(l) be the second derivative of 5*l**7/84 + l**6/4 - l**5/8 - 5*l**4/8 - 5*l. Let d(w) = 0. What is w?
-3, -1, 0, 1
Let a(j) be the first derivative of -4/3*j + 1 + j**2 - 2/9*j**3. Factor a(i).
-2*(i - 2)*(i - 1)/3
Let b = -40 - -42. Determine w so that 0 - 2*w**4 + 1/2*w + 3/2*w**b + 0*w**3 = 0.
-1/2, 0, 1
Let l(d) be the first derivative of d**3/6 - 3*d**2/4 + d - 13. Solve l(q) = 0.
1, 2
Factor 2/9*a**3 + 4/9*a**2 + 0 + 2/9*a.
2*a*(a + 1)**2/9
Let z = 0 - -2. Factor -3/4*b**4 + 6*b**3 - 12 + 24*b - 18*b**z.
-3*(b - 2)**4/4
Let q(c) be the third derivative of 0*c - 1/6*c**4 + 5*c**2 + 0 + 1/90*c**5 + c**3. Solve q(v) = 0 for v.
3
Let b(c) = -4*c - 1. Suppose 3*l = 4*u + 7, u + 0 = 3*l - 4. Let v be b(u). Factor -v*z**4 - z**2 + 3*z + 5*z**5 - 7*z**3 + 2*z + 4*z**2 - 3*z.
z*(z - 1)**2*(z + 1)*(5*z + 2)
Let k(g) be the second derivative of g**10/49140 - g**9/19656 + g**8/43680 - g**4/3 + 4*g. Let a(d) be the third derivative of k(d). Let a(f) = 0. Calculate f.
0, 1/4, 1
Let m be (-5)/(-75)*33 - 2. Let p(l) be the first derivative of -1/15*l**3 + 0*l + m*l**2 + 3. Factor p(g).
-g*(g - 2)/5
Let i(y) be the third derivative of 1/735*y**7 + 0 - 9*y**2 + 0*y**4 + 0*y - 1/105*y**5 + 1/21*y**3 + 0*y**6. Factor i(w).
2*(w - 1)**2*(w + 1)**2/7
Solve -1/3*h**3 + 2/3 + 1/3*h - 2/3*h**2 = 0 for h.
-2, -1, 1
Suppose -8 + 28 = 10*p. Find u, given that 0 + 6/7*u**3 + 2/7*u + 6/7*u**p + 2/7*u**4 = 0.
-1, 0
Let j(k) be the second derivative of 7/30*k**6 + 0 + 8*k**4 - 3*k + 8*k**2 + 40/3*k**3 + 11/5*k**5. Factor j(f).
(f + 2)**3*(7*f + 2)
Let z(t) = -t**3 - 8*t**2 - 2*t - 15. Let y be z(-8). Let a = -1 + y. Factor -3/2*r**2 + 0 + a*r.
-3*r**2/2
Let i(f) be the second derivative of f**7/126 - f**6/18 + f**5/6 - 5*f**4/18 + 5*f**3/18 - f**2/6 + 17*f. Factor i(n).
(n - 1)**5/3
Let m = -2/3 + 20/21. Factor 2/7*c**3 - 10/7*c + m*c**2 + 6/7.
2*(c - 1)**2*(c + 3)/7
Let m(n) be the second derivative of -n**5/60 + n**4/12 + 3*n**2/2 - n. Let z(a) be the first derivative of m(a). Determine x, given that z(x) = 0.
0, 2
Let x(m) = -m**2 + 6*m**2 + 37*m - 31*m - 4*m**2 - 5. Let q be x(-7). Factor 1/4*o**3 + 1/2*o**4 + 0*o + 1/4*o**5 + 0 + 0*o**q.
o**3*(o + 1)**2/4
Let d(j) be the first derivative of -2*j**3/3 - j**2 + 3. Factor d(i).
-2*i*(i + 1)
Let x be (6/(-54))/((-2)/4). Let r = -20 + 182/9. Let -x*a**2 + r*a + 0 = 0. What is a?
0, 1
Let b(g) be the first derivative of g**5/5 + g**4/2 + 4. Factor b(k).
k**3*(k + 2)
Let 8*m**3 + 4*m**4 - 1411 - 12*m**2 + 1411 = 0. Calculate m.
-3, 0, 1
Suppose -24 = 6*h - 2*h. Let p = h - -11. Suppose -6*r**2 - p*r**2 - 2 + 7*r + 5*r**2 = 0. What is r?
1/2, 2/3
Let h(s) be the second derivative of -s**5/10 - 23*s**4/42 - 2*s**3/7 - 28*s. Determine z so that h(z) = 0.
-3, -2/7, 0
Let l = 176 - 98