3*(a + 2)
Let k be (0 - 1)/(25/(-15)) + 0. Suppose 0 = l, l - 8 = -4*b - 0*b. Factor -k*n - 6/5 + 3/5*n**b.
3*(n - 2)*(n + 1)/5
Let h = 2317/6 - 386. Let q(j) be the first derivative of 18*j + 9*j**2 - 1 + h*j**4 + 2*j**3. Factor q(v).
2*(v + 3)**3/3
Let j(d) be the first derivative of -d**5 + 35*d**4/2 + 335*d**3/3 + 220*d**2 + 180*d + 146. Determine i so that j(i) = 0.
-2, -1, 18
Let f(k) be the second derivative of k**7/630 - k**6/45 + 2*k**5/15 + 5*k**4/6 + k. Let i(t) be the third derivative of f(t). Factor i(y).
4*(y - 2)**2
Let p(f) = -2*f - 7. Let q be p(-5). Suppose -4*w + 4*z = 4, -3*w - 2*z + 20 = 8. What is i in 6*i**w + 0*i + 5*i**3 - 2*i - 2 - 3*i**q - 4*i**2 = 0?
-1, 1
Let a(i) be the second derivative of 2/3*i**2 + 0 - 22*i - 1/18*i**4 + 1/9*i**3. Factor a(l).
-2*(l - 2)*(l + 1)/3
Let t be (8/(-10))/(12/(-30)). Suppose 6*r - 3*r + 3*s - 15 = 0, 13 = t*r - s. Determine z, given that -4*z**5 + r*z**5 + z**3 - z**2 + z**4 - 3*z**5 = 0.
-1, 0, 1
Let w(q) be the second derivative of q**6/15 + 4*q**5/5 + 3*q**4 - 27*q**2 + 8*q + 4. What is c in w(c) = 0?
-3, 1
Let c(f) be the first derivative of f**5/15 + 2*f**4/9 - 2*f**3/9 - 4*f**2/3 + 10*f + 14. Let i(s) be the first derivative of c(s). Factor i(o).
4*(o - 1)*(o + 1)*(o + 2)/3
Let u(r) = -r**3 - 9*r**2 - 10*r - 11. Let k be u(-8). Factor -4*x**4 - 29*x**3 + 4*x**2 + 4*x**k + 25*x**3 - 4*x + 4*x.
4*x**2*(x - 1)**2*(x + 1)
Let d = -21/968 - -15551/2904. Let -8/3*a**2 + 4*a - d*a**3 + 8/3*a**4 + 0 + 4/3*a**5 = 0. What is a?
-3, -1, 0, 1
Let h(n) be the first derivative of -6*n - 11/2*n**2 - 1/4*n**4 + 5 - 2*n**3. Factor h(s).
-(s + 1)*(s + 2)*(s + 3)
Let z be ((-477)/(-1645))/1 - 8/28. Let d = 142/235 - z. What is c in -6/5 + d*c**2 - 3/5*c = 0?
-1, 2
Let a be (4 + (-180)/42)/(4/(-56)). Let x(i) be the second derivative of 0 + 11/10*i**5 - 8*i**2 + 2/5*i**6 + 1/21*i**7 - 4*i**3 + 8*i + 1/3*i**a. Factor x(p).
2*(p - 1)*(p + 1)*(p + 2)**3
Let a(u) be the first derivative of u**5/30 + u**4/24 - 5*u**3/6 + 23*u**2/12 - 5*u/3 + 347. Suppose a(y) = 0. Calculate y.
-5, 1, 2
Let z(k) be the first derivative of k**8/560 + k**7/40 + k**6/15 - 2*k**5/5 - 11*k**3 - 2. Let w(d) be the third derivative of z(d). Factor w(s).
3*s*(s - 1)*(s + 4)**2
Let x(c) be the third derivative of c**6/120 + c**5/12 - c**4 + 705*c**2. Solve x(p) = 0 for p.
-8, 0, 3
Let z(v) be the first derivative of -v**6/3 + 2*v**5/5 - 68. Factor z(l).
-2*l**4*(l - 1)
Factor 19*q + 0 + 1/2*q**3 + 21/2*q**2.
q*(q + 2)*(q + 19)/2
Let w(q) = -18*q**4 + 24*q**3 + 20*q**2 - 24*q + 22. Let d(m) = -12*m**4 + 16*m**3 + 13*m**2 - 16*m + 14. Let a(i) = 8*d(i) - 5*w(i). Find y such that a(y) = 0.
-1, 1/3, 1
Determine n so that -8427/5 - 3/5*n**3 + 63*n**2 - 8109/5*n = 0.
-1, 53
Let w(o) = o. Let v(y) = 2*y - 11. Let l(z) = v(z) - w(z). Let h be l(13). Solve -4/13 + 10/13*x**4 + 8/13*x**5 - 22/13*x**3 - 2*x - 46/13*x**h = 0 for x.
-1, -1/4, 2
Let i(y) be the third derivative of -y**8/896 + 13*y**7/560 - 11*y**6/64 + 71*y**5/160 + 5*y**4/8 - 25*y**3/4 + 82*y**2. Let i(c) = 0. What is c?
-1, 2, 5
Suppose 30 = 3*x + 2*x. Suppose 0 = -f - x + 9. Factor -2*i**3 - 2*i**2 + 2*i**2 + 0*i**f.
-2*i**3
Let c(k) = 128*k**4 + 107*k**3 - 28*k**2 - 12*k. Let v(l) = 64*l**4 + 53*l**3 - 14*l**2 - 6*l. Let i(o) = 3*c(o) - 5*v(o). Find f such that i(f) = 0.
-1, -1/4, 0, 3/8
Let o(y) be the first derivative of 24 - y**4 + 8*y**2 - 8*y**3 + 4/5*y**5 + 32*y. Factor o(s).
4*(s - 2)**2*(s + 1)*(s + 2)
Let b(a) be the first derivative of -a**6/21 - 44*a**5/35 - 95*a**4/7 - 1600*a**3/21 - 1625*a**2/7 - 2500*a/7 + 218. Let b(t) = 0. What is t?
-5, -2
Let p = -10 + 14. Suppose -p*r - 4 = 0, r - 3 = -5*k + 6. Factor l**4 + 51 - l**k - l**2 - 50.
(l - 1)**2*(l + 1)**2
Let l(x) = x**2 + 7*x + 9. Let b be l(-6). Determine o, given that -8*o**2 + 22*o**4 + 14*o**4 + 4*o**5 - 12*o**b - 36*o**4 = 0.
-1, 0, 2
Factor 4/5*r**2 - 36/5*r + 72/5.
4*(r - 6)*(r - 3)/5
Let t be 2/5 - (-96)/10. Factor -13*z + t - z**3 + 6*z**3 + 2*z - 4*z.
5*(z - 1)**2*(z + 2)
Let y(c) be the third derivative of 13*c**2 - 1/3*c**3 - 1/210*c**5 + 2/21*c**4 + 0 + 0*c. Suppose y(d) = 0. Calculate d.
1, 7
Let p = 2058 - 2055. Factor -p*i**2 + 12/7 + 9/7*i.
-3*(i - 1)*(7*i + 4)/7
Suppose 0 = 4*g - 3*c + 4*c - 10, -5*g + 20 = 5*c. Suppose 18 = 3*j + g*j + d, -3*j - 3 = -4*d. Factor -2/15*w**j + 2/5*w + 0*w**2 + 4/15.
-2*(w - 2)*(w + 1)**2/15
Suppose u + 2 = 3*k + 18, -5*k - 36 = -4*u. Factor 11 - 14 - 4*y**3 + 40*y - u*y**2 - 29.
-4*(y - 2)*(y - 1)*(y + 4)
Let c(z) = 48*z - 16. Let x be c(6). Factor -12*k**3 - 10 + 5*k**4 + 5*k**2 + x*k - 257*k - 3*k**3.
5*(k - 2)*(k - 1)**2*(k + 1)
Suppose n - 4*d - 4 = 18, -3*d - 5 = 5*n. Let x(w) be the first derivative of 4/3*w**3 + 0*w + 4*w**n + 11. Factor x(r).
4*r*(r + 2)
Let o(p) = -5*p**3 + 5*p**2 + 4*p - 4. Let t(x) = 11*x**3 - 11*x**2 - 8*x + 8. Let u(y) = 9*o(y) + 4*t(y). Factor u(k).
-(k - 2)*(k - 1)*(k + 2)
Suppose 6 = -2*u, x = 2*x + 2*u - 53. Suppose -17*w - 8 = -x. Solve 0*a + 3/5*a**w - 6/5*a**2 - 3/5*a**5 + 6/5*a**4 + 0 = 0.
-1, 0, 1, 2
Let s(i) be the second derivative of -5/6*i**3 + 0 + 35/12*i**4 + 5/21*i**7 - 1/4*i**5 - 7*i - 5/6*i**6 - 5*i**2. Determine u so that s(u) = 0.
-1, -1/2, 1, 2
Let k(t) be the second derivative of 0 - 1/15*t**4 + 18/5*t**2 + 22*t + 0*t**3. Factor k(r).
-4*(r - 3)*(r + 3)/5
Let d(r) be the first derivative of -2*r**3/15 + 14*r**2/5 + 6*r - 42. Suppose d(j) = 0. What is j?
-1, 15
Let n(f) be the second derivative of -2048383*f**5/10 - 16129*f**4 - 508*f**3 - 8*f**2 - 4*f - 28. Determine m, given that n(m) = 0.
-2/127
Let h(j) be the first derivative of -j**3/6 + 5*j**2/4 + 33*j + 816. What is r in h(r) = 0?
-6, 11
Let j(i) be the second derivative of -i**8/1260 + i**6/270 - 13*i**3/6 + 16*i. Let w(g) be the second derivative of j(g). Factor w(k).
-4*k**2*(k - 1)*(k + 1)/3
Let g = -15545/7 - -2223. Factor g*y**2 - 4/7*y + 0.
4*y*(4*y - 1)/7
Suppose 0 = y - 3*h, 2*h - h = 3*y - 16. Suppose 0 = y*u - u + 5*t - 15, -u = 4*t - 12. Suppose 4/3*w**3 + 0*w + 0*w**2 + u = 0. Calculate w.
0
Let w(a) be the first derivative of a**5 + 5*a**4/4 - 55*a**3/3 - 45*a**2/2 + 90*a - 185. What is m in w(m) = 0?
-3, -2, 1, 3
Let r = 56 + -52. Suppose -2*h - 2*n - r = 0, -5*h + 0*h + n = -2. Suppose 2/5*d - 2*d**2 + h - 8/5*d**4 + 16/5*d**3 = 0. Calculate d.
0, 1/2, 1
Let s = -11 + 23. Suppose 3*q - q - s = 0. Let 3*z + 6*z**2 - 3*z**3 + 0*z - q*z**2 = 0. What is z?
-1, 0, 1
Let s(b) = -10*b - 66. Let o be s(-7). Let x(l) be the first derivative of 4*l**4 + 8*l**2 + 1 - 8*l**3 - o*l - 4/5*l**5. Find v such that x(v) = 0.
1
Determine q so that -2/3 - 5/3*q**3 - 13/3*q - 16/3*q**2 = 0.
-2, -1, -1/5
Let i(j) = j**3 - 11*j**2 + 11*j + 13. Let u be i(10). Let q = u - 12. Factor -20*t**3 - 57*t**2 - 32 - 31*t**2 + q*t - 45*t - 78*t.
-4*(t + 2)**2*(5*t + 2)
Let i = 793/3255 - -5/217. Let t(h) be the first derivative of i*h**3 - 4/5*h + 0*h**5 + 3/5*h**2 - 5 - 2/5*h**4 + 1/15*h**6. Factor t(c).
2*(c - 1)**3*(c + 1)*(c + 2)/5
Let y(m) = -8. Let c(q) = 5*q**2 + 2110*q + 222629. Let s(g) = c(g) + 3*y(g). Factor s(o).
5*(o + 211)**2
Find h, given that 2/9*h**2 + 202/9 + 68/3*h = 0.
-101, -1
Let t(j) be the first derivative of 0*j**4 + 0*j**2 - 1/3*j**3 + 0*j + 7 - 1/60*j**5 - 1/72*j**6. Let i(l) be the third derivative of t(l). Factor i(u).
-u*(5*u + 2)
Let z(v) = -6*v + 23. Let r be z(2). Suppose r*x - 2*x = -2*x. Factor x*q - 2/13*q**4 - 18/13*q**2 + 12/13*q**3 + 0.
-2*q**2*(q - 3)**2/13
Let j be ((-8)/(-28))/((-117)/(-126)). Let 2/13*r**5 - 4/13*r**4 + 6/13*r + 0 - 8/13*r**3 + j*r**2 = 0. What is r?
-1, 0, 1, 3
Suppose 5 = 5*r - 10. Let u(q) be the third derivative of -1/12*q**4 - 1/60*q**6 - 1/15*q**5 + 0*q + 0 - r*q**2 + 0*q**3. Factor u(g).
-2*g*(g + 1)**2
Factor 88*g - 7*g**2 + 466 + 3*g**2 - 374.
-4*(g - 23)*(g + 1)
Suppose -b + 3*d = 2*d, -5*d = -5. Let c be (b/(-1))/(2/(-6)). Determine j so that -c*j**2 + 2*j**2 + 3*j**2 + 2 - 6*j**2 + 7*j = 0.
-1/4, 2
Let g(u) be the third derivative of -u**7/525 - u**6/300 + 3*u**5/50 - 11*u**4/60 + 4*u**3/15 - 30*u**2 - 2. Factor g(a).
-2*(a - 1)**3*(a + 4)/5
Suppose 3*n = -4*x + 1, 2*x + 8 = -n + 7. Suppose 0 - 1/3*g**n + 1/3*g - 1/3*g**2 + 1/3*g**4 = 0. Calculate g.
-1, 0, 1
Let r(o) be the second deriva