late g.
0, 2/5
Let g(a) be the third derivative of -a**8/504 + 2*a**7/315 - a**5/45 + a**4/36 - 7*a**2. Let g(i) = 0. What is i?
-1, 0, 1
Factor 3/4*u**4 + 9/4*u**2 + 9/4*u**3 + 3/4*u + 0.
3*u*(u + 1)**3/4
Let k(h) be the first derivative of -1/12*h**3 + 0*h - 1/8*h**2 - 9. Let k(n) = 0. What is n?
-1, 0
Let w(x) be the second derivative of -1/30*x**6 + 0*x**4 - 1/40*x**5 + 0 - 1/84*x**7 + 0*x**3 + 0*x**2 + 3*x. Factor w(k).
-k**3*(k + 1)**2/2
Determine y, given that -1/6*y**2 - 4/3*y + 10/3 = 0.
-10, 2
Let u(f) = -f**3 - f**2 - 3*f - 3. Let t(x) = 19*x + 15*x - 35*x - 1. Let o(p) = -3*t(p) + u(p). What is a in o(a) = 0?
-1, 0
Let b = -234 + 3745/16. Let h(u) be the second derivative of 0 - b*u**4 - u + 0*u**3 + 0*u**2 + 3/80*u**5. Determine a, given that h(a) = 0.
0, 1
Let q(d) be the second derivative of -d**7/280 - d**6/10 - 6*d**5/5 - 8*d**4 - 3*d**3/2 + 6*d. Let a(l) be the second derivative of q(l). What is j in a(j) = 0?
-4
What is g in -2/3*g**2 + 0 + 0*g + 1/3*g**5 + 5/3*g**3 - 4/3*g**4 = 0?
0, 1, 2
Let p(z) = z**2 + z. Let o(a) = 4*a**2 + 6*a + 2. Let u(n) = 2*o(n) - 6*p(n). Solve u(r) = 0.
-2, -1
Let n = -12 + 20. Let f be 18/(-12)*n/(-3). Let -4 - 8*p**f + 6*p**3 + 3*p**5 + 4 - p = 0. Calculate p.
-1/3, 0, 1
Let d(z) be the second derivative of z**4/30 + 2*z**3/15 + z**2/5 + 3*z. Let d(q) = 0. What is q?
-1
Let o(w) = -w**5 + 3*w**4 - 2*w**3 - 3. Let n(q) = q**5 - q**4 + 1. Let p(h) = 6*n(h) + 2*o(h). What is j in p(j) = 0?
-1, 0, 1
Suppose 18 = 5*j + 3*v, v - 4*v = -j. Suppose 0*f = j*f + 4*g + 17, -3*f - 2 = g. Factor -3*n**2 + 5*n**2 - f + 1 - 2*n.
2*n*(n - 1)
Suppose -3*u - 6 = -6*u. Solve -1/3*h**u + 0 - 1/3*h = 0.
-1, 0
Let o(h) be the third derivative of -h**7/1680 + 7*h**6/960 - h**5/32 + 13*h**4/192 - h**3/12 - 27*h**2. Factor o(r).
-(r - 4)*(r - 1)**3/8
Suppose -4 = 3*u - 5*u. Suppose 5*c - u*c - 3*c - 3*c**2 = 0. What is c?
0
Let x(f) be the first derivative of -f**4/12 + 2*f**3/9 - 20. Let x(v) = 0. What is v?
0, 2
Find q such that -3 - 39/4*q**2 + 12*q + 9/4*q**3 = 0.
1/3, 2
Suppose -11*q + 6*q = -20. Let r(m) be the second derivative of -2*m**2 + 7/6*m**q + m + 0 + 5/3*m**3. Find v such that r(v) = 0.
-1, 2/7
Let i(v) = -11*v**2 + 21*v - 19. Let a(b) = -5*b**2 + 10*b - 9. Let z(p) = 13*a(p) - 6*i(p). Let k be z(-5). Let 8*o - 10*o**3 - 8*o - 4*o**k = 0. Calculate o.
-2/5, 0
Solve 0*n**3 + 0*n + 1/2 - n**2 + 1/2*n**4 = 0.
-1, 1
Let -6 + 5*a**4 + 5*a**3 + 4 + 2 = 0. Calculate a.
-1, 0
Suppose 0 = l + 25 - 26. Let s(h) be the first derivative of -6/13*h**2 - 2/39*h**3 - 18/13*h - l. What is v in s(v) = 0?
-3
Let b(d) be the third derivative of 1/300*d**6 + 0*d**4 + 0*d**3 + 0*d + 0 + 1/150*d**5 - 6*d**2. Factor b(k).
2*k**2*(k + 1)/5
Factor 1/3*f**2 + 10/3*f + 25/3.
(f + 5)**2/3
Find a, given that 0 + 1/6*a**2 + 0*a = 0.
0
Let d = -21/4 + 23/4. Let w(o) = -11*o + 88. Let b be w(8). Determine x so that 0 + d*x**2 + b*x = 0.
0
Let l(a) = -a + 1. Let j be l(-1). Factor 10*p - 9*p - 5*p**3 - 5*p**j - 3*p**4 - 2*p - 2*p**3.
-p*(p + 1)**2*(3*p + 1)
Let b = -323 - -327. Factor 1/2*t**3 + 1/2*t**2 + 0 + 0*t - 1/2*t**b - 1/2*t**5.
-t**2*(t - 1)*(t + 1)**2/2
Let q(h) = 28*h**4 + 40*h**3 + 12*h**2. Let n(d) = -9*d**4 - 13*d**3 - 4*d**2. Let x(g) = -16*n(g) - 5*q(g). What is t in x(t) = 0?
-1, 0
Suppose 3*c**5 + 5*c**2 - 5*c**4 - 3*c**5 + 5*c**3 - 3*c**5 - 2*c**5 = 0. What is c?
-1, 0, 1
Let h(p) = p**3 - 6*p**2 - 5*p - 10. Let u be h(7). Suppose -3*i = 4*w, -1 = u*i + 15. Determine v so that 3*v + w + 3 - 2*v**2 - v**2 = 0.
-1, 2
Factor -13*z**3 + 2*z**2 - 3*z**4 + 15*z**3 - 2*z + 3*z**4 - 2*z**4.
-2*z*(z - 1)**2*(z + 1)
Let n(l) = -2*l**2 - 31*l - 13. Let d be n(-15). Factor -2/7*q + 0 - 2/7*q**3 + 4/7*q**d.
-2*q*(q - 1)**2/7
Let a(l) = -l**3 + l + 2. Let z be a(-1). Factor 0 - 2/7*u**z + 0*u.
-2*u**2/7
Suppose 4*i - 73 = 15. Suppose x = -5*p + 47 + i, 5*p + 4*x - 66 = 0. Factor -p*w**3 - 10*w**4 - 1 + 1 - 4*w**2.
-2*w**2*(w + 1)*(5*w + 2)
Let q(k) = k**2 - 6*k - 2. Let n be q(8). Let x be (-50)/n + 3 + 2. Find a, given that 0*a + x*a**3 - 4/7*a**2 + 2*a**4 + 0 = 0.
-1, 0, 2/7
Let v(i) = -13*i**5 + 31*i**3 + 12*i**2 - 25*i - 5. Let p(z) = -4*z**5 + 10*z**3 + 4*z**2 - 8*z - 2. Let k(c) = 7*p(c) - 2*v(c). Find u such that k(u) = 0.
-1, 1, 2
Let t(g) be the first derivative of g**3/3 + 2*g**2 + 3*g + 10. Factor t(z).
(z + 1)*(z + 3)
Suppose 0 = -2*p - 3*p + 40. Solve -62*a**2 - 13*a**5 + p - 15*a**3 + 44*a**3 - 41*a**5 + 54*a**4 + 25*a**3 = 0 for a.
-1, -1/3, 2/3, 1
Let n be 0 - (-1)/((-5)/(-2)). Let a(z) = -27*z - 160. Let v be a(-6). Suppose -2/5*k + n - 4/5*k**v = 0. Calculate k.
-1, 1/2
Suppose 3*a = o + 4*o + 11, -6 = -a + 4*o. Factor -20*s**3 + 2*s**2 - s**2 - 16*s**4 - 5*s**a.
-4*s**2*(s + 1)*(4*s + 1)
Let -8/9*b + 0 - 4/3*b**2 - 4/9*b**3 = 0. Calculate b.
-2, -1, 0
Let d(n) = -12*n**2 + 3*n + 27. Let t(h) be the third derivative of -h**5/60 - h**4/24 + 4*h**2. Let f(a) = -d(a) + 15*t(a). Factor f(b).
-3*(b + 3)**2
Find l, given that -2/9*l**4 + 4/9*l**3 + 0 - 2/9*l**5 + 0*l**2 + 0*l = 0.
-2, 0, 1
Let h be (144/612)/((-6)/(-17)). Factor 0 - 2/3*l**3 - 4/3*l**2 - h*l.
-2*l*(l + 1)**2/3
Factor 8/3*z + 0 - 2/3*z**4 + 0*z**2 - 2*z**3.
-2*z*(z - 1)*(z + 2)**2/3
Let n(r) be the second derivative of -r**5/4 + 25*r**4/12 - 10*r**3/3 + 14*r. Suppose n(a) = 0. What is a?
0, 1, 4
Determine y so that -14*y**2 + 5*y**5 - 19*y**3 + 33*y + 3 + 10*y - 11 + 8*y**4 - 15*y = 0.
-2, 2/5, 1
Let f(z) = 5*z**3 + 12*z**2 - 24*z + 13. Let j(q) = 7*q**3 + 13*q**2 - 24*q + 12. Let g(a) = -4*f(a) + 3*j(a). Factor g(w).
(w - 4)**2*(w - 1)
Let f(w) be the first derivative of -w**4/12 - 2*w**3/9 - w**2/6 + 12. Factor f(b).
-b*(b + 1)**2/3
Let d be (-393)/(-1572) - 1/4*-1. Let 0 + d*y**3 + 0*y**2 + 0*y + 1/2*y**5 + y**4 = 0. What is y?
-1, 0
Let y(n) be the second derivative of n**6/120 - n**5/80 - n**4/48 + n**3/24 + 11*n. Solve y(u) = 0 for u.
-1, 0, 1
Let z(t) be the first derivative of 4 - 1/12*t**4 - 1/6*t**2 + 2/9*t**3 + 0*t. Factor z(o).
-o*(o - 1)**2/3
Let l = -6 - -9. Let c(m) be the second derivative of -3*m - 1/5*m**2 + 1/30*m**4 + 0 + 1/15*m**l - 1/50*m**5. Find k, given that c(k) = 0.
-1, 1
Let z be 10/25 - (-23)/5. Let a = -2 + z. What is x in 4*x**2 + 14*x**a + 3*x**2 + 3*x**2 - 4*x = 0?
-1, 0, 2/7
Let v = -6 + 14. Suppose 4 = 4*p - v. Suppose 3 + 4*d**2 - 10*d**2 + p*d**4 + 0 = 0. Calculate d.
-1, 1
Suppose 16 = 91*l - 87*l. Let q(s) be the second derivative of 1/90*s**5 + 0*s**l - 2/9*s**2 + 0 - 1/9*s**3 - 3*s. Suppose q(n) = 0. What is n?
-1, 2
Let d(f) be the third derivative of f**9/7560 - f**8/3360 - f**7/252 - f**6/120 - 7*f**4/24 - 7*f**2. Let q(l) be the second derivative of d(l). Solve q(j) = 0.
-1, 0, 3
Let t(i) be the first derivative of 7*i**3/6 - 3*i**2 - 2*i + 10. Determine q so that t(q) = 0.
-2/7, 2
Let v(m) = -48*m**3 + 140*m**2 + 72*m - 152. Let z(d) = -19*d**3 + 56*d**2 + 29*d - 61. Let l(u) = -5*v(u) + 12*z(u). Factor l(x).
4*(x - 1)*(x + 1)*(3*x - 7)
Let s(f) be the first derivative of -f**7/2940 + f**5/420 - f**3 + 3. Let q(d) be the third derivative of s(d). Factor q(z).
-2*z*(z - 1)*(z + 1)/7
Let x = -42 - -169/4. Let k = 247 + -244. Let -1/4*l - 1/2*l**2 - 1/4*l**5 + 1/4 + x*l**4 + 1/2*l**k = 0. What is l?
-1, 1
Let a(v) = v**2 + 1. Let q(d) = -3*d**3 + 4*d**2 - 3*d - 2. Let h(m) = 2*a(m) + q(m). Determine k, given that h(k) = 0.
0, 1
Let k(f) = -5*f**3 + 7*f**2. Suppose -4*n = 2*p + 12, -2*p - 10 = -p + 3*n. Let h(z) = z**3 - z**2 - z. Let b(i) = p*k(i) + 4*h(i). Factor b(w).
-2*w*(w - 1)*(3*w - 2)
Let x(n) be the first derivative of -3 + 1/3*n**3 + 0*n + 1/2*n**2. Let x(b) = 0. What is b?
-1, 0
Let i = 76/7 - 7. What is h in -3/7*h**2 - i + 18/7*h = 0?
3
Let m be (1/3)/(3/6). Let u(g) = 9*g + 21. Let r be u(-2). Suppose 0 - c**r - m*c**2 + 0*c = 0. What is c?
-2/3, 0
Let z(j) be the first derivative of -6*j**5/35 - 4*j**4/7 - 4*j**3/7 + 2*j/7 - 1. Factor z(c).
-2*(c + 1)**3*(3*c - 1)/7
Factor 0 - 3/5*s**2 + 1/5*s.
-s*(3*s - 1)/5
Let o(f) be the third derivative of -f**7/420 - f**6/240 + f**5/40 + 5*f**4/48 + f**3/6 - 14*f**2. Factor o(b).
-(b - 2)*(b + 1)**3/2
Let j(h) = -2*h**4 + 10*h**3 - 4*h**2 - 8*h + 6. Let y(q) = -q**5 + q**4 - q**3 + q - 1. Let v(i) = -j(i) - 2*y(i). Solve v(n) = 0 for n.
-2, -1, 1
Suppo