Let m be z(5). Suppose 0 = v - m. Find i, given that -i**5 - 7*i**5 + v*i**4 + 34*i**3 + 8 - 38*i**2 + 2*i**5 - 4*i**5 = 0.
-2, -2/5, 1
Let i = -5 - -10. Suppose i*m - 8 = m. Factor -9*s**2 + 11*s**2 - m*s**3 + 0*s + 2*s - 2*s**4.
-2*s*(s - 1)*(s + 1)**2
Let c(j) be the third derivative of j**9/30240 + j**8/5040 - j**7/840 + j**5/12 - 14*j**2. Let d(s) be the third derivative of c(s). Factor d(n).
2*n*(n - 1)*(n + 3)
Let u(l) = -l**3 + 2*l**2 - 3*l + 1. Let t be u(3). Let m = t + 21. Factor 2*a**3 + a - 2*a + 2*a**5 - 4*a**m + a.
2*a**3*(a - 1)**2
Let n = 11479/44 - 2284/11. Let t = -53 + n. Suppose t*b**3 + 0 + 1/2*b - 3/4*b**2 = 0. Calculate b.
0, 1, 2
Suppose -21 = -3*f - 0*f. Let v = f + -7. Determine y so that -6*y**2 + 0*y**2 + v*y + 9*y + 6 = 0.
-1/2, 2
Factor -3*z**4 - 8*z - 46*z**2 + 2*z**4 + 12*z**3 + 18*z + 25*z**2.
-z*(z - 10)*(z - 1)**2
Let c(h) = 3*h - 14. Let b be c(8). Let t**3 - b*t + 7*t**3 - 4*t**3 + 6*t = 0. Calculate t.
-1, 0, 1
Suppose 2*v + 4 = 4*w - 12, 3*w - 5*v = 5. Suppose -4*b = -w*b + 3. Factor 3*m**b + 2*m + m - 2*m - 2*m**2 - 2*m**3.
m*(m - 1)**2
Let y = 46/51 - 179/255. Factor -6/5*q + 8/5 + y*q**2.
(q - 4)*(q - 2)/5
Factor -40*v**2 - 4*v**3 + 78*v**2 - 38*v**2 - 4*v**4.
-4*v**3*(v + 1)
Factor -2/3*k**2 - 2/3*k**4 + 0*k + 0 + 4/3*k**3.
-2*k**2*(k - 1)**2/3
Let s be ((-12)/(-30))/((-2)/(-5)). Let o = 1 + s. Determine d, given that 1 - 8*d + d**2 + 3*d**2 + 7 - 2*d**o = 0.
2
Factor -8/7*r**2 - 10/7*r - 2/7*r**3 - 4/7.
-2*(r + 1)**2*(r + 2)/7
Let o = -3095 + 3095. Let q = -4/45 + 118/315. Factor 24/7*v**5 - q*v**3 + 0*v**2 - 2/7*v**4 + 0*v + o.
2*v**3*(3*v - 1)*(4*v + 1)/7
Let y = 2 - -7. Let k(x) = -x**3 + 8*x**2 + 9*x + 3. Let s be k(y). Factor 29 + s*j**2 - 29 - 6*j.
3*j*(j - 2)
Let l(g) = 2*g - 10. Let z be l(7). Let t(k) be the first derivative of -7 - 3/4*k**z + 3*k - 9/2*k**2 + 3*k**3. What is q in t(q) = 0?
1
Let k = 3/226 + 388/565. Let d = -1/5 + k. Find l such that -l**2 - d*l**3 + 0 - 1/2*l = 0.
-1, 0
Let o(w) = -w**2 + 6*w + 31. Let m be o(9). Let r(u) be the first derivative of 0*u**2 - 27/5*u**5 + 9/2*u**m + 0*u + 4 - u**3. Factor r(a).
-3*a**2*(3*a - 1)**2
Let w(o) = -4*o - 34. Let r be w(-9). Find c such that -2*c - 4*c**r + 0*c**2 - 6 + 10 + 2*c**3 = 0.
-1, 1, 2
Let o(i) be the second derivative of 0*i**2 - 16/3*i**4 - 9*i + 0 - 2/15*i**6 - 8/5*i**5 + 0*i**3. Suppose o(a) = 0. Calculate a.
-4, 0
Let k = 7 - 17. Let f(s) = -4*s**4 - 17*s**3 - 25*s**2 - 15*s - 3. Let j(t) = -12*t**4 - 50*t**3 - 74*t**2 - 46*t - 10. Let i(q) = k*f(q) + 3*j(q). Factor i(m).
4*m*(m + 1)**2*(m + 3)
Let o(h) = -7*h**2 + 5*h + 27. Let n be (-4)/10*(-19 - -4). Let i(b) = -2*b**2 + b + 7. Let v(s) = n*o(s) - 22*i(s). Factor v(c).
2*(c + 2)**2
Let 62/9*l - 2/9*l**3 - 16/9*l**2 - 44/9 = 0. What is l?
-11, 1, 2
Let p(t) = -6*t**3 - 4*t**2 + 4. Let m(h) = 13*h**3 + 9*h**2 - 9. Let w(z) = 4*m(z) + 9*p(z). Suppose w(s) = 0. What is s?
0
Let b(q) = -3*q**2 - 3*q + 2. Let n = -23 + 40. Let t(s) = -19*s**2 - 2*s + 2 - n*s + 11. Let k(h) = -39*b(h) + 6*t(h). Determine d so that k(d) = 0.
-1, 0
Factor 4*x**3 - 5*x**3 - 7*x - 2*x**3 - 4*x - 12*x**2 - 6 - 4*x.
-3*(x + 1)**2*(x + 2)
Suppose 5*f - 13 = -2*l, -91*f + 4*l - 5 = -94*f. Determine x, given that -17/8*x + 1/2 - 13/8*x**3 + f*x**2 + 1/4*x**4 = 0.
1/2, 1, 4
Let r(f) = f**4 + f**2 + f + 2. Let b(u) = 21*u**4 + 104*u**3 - 338*u**2 + 156*u - 8. Let j(p) = -b(p) + 5*r(p). Factor j(q).
-(q - 2)*(q + 9)*(4*q - 1)**2
Let 2/7*m - 32/7*m**2 - 68/7*m**3 + 4/7 - 52/7*m**4 - 2*m**5 = 0. Calculate m.
-1, 2/7
Let m(d) be the second derivative of -d**7/70 - d**6/50 + 3*d**5/50 + d**4/10 - d**3/10 - 3*d**2/10 + 19*d + 1. Factor m(z).
-3*(z - 1)**2*(z + 1)**3/5
Let h(x) be the first derivative of -2*x**2 - 1/6*x**6 + 0*x + 4/3*x**3 - 12 + 3/4*x**4 - 2/5*x**5. Determine u so that h(u) = 0.
-2, 0, 1
Factor 0 + 1/2*j**3 - 1/2*j**4 + 0*j + j**2.
-j**2*(j - 2)*(j + 1)/2
Let i(y) = y + 2. Let j(r) = -6*r**3 + 56*r**2 + 41*r - 22. Let z(v) = 2*i(v) + 2*j(v). Suppose z(h) = 0. What is h?
-1, 1/3, 10
Let s(l) be the first derivative of 3*l**5/5 + 9*l**4 + 10*l**3 - 18*l**2 - 33*l + 197. Factor s(k).
3*(k - 1)*(k + 1)**2*(k + 11)
Let o(p) be the third derivative of 0 + 18*p**2 - 1/1680*p**8 + 0*p + 0*p**3 + 1/1050*p**7 + 1/600*p**6 - 1/300*p**5 + 0*p**4. Suppose o(g) = 0. What is g?
-1, 0, 1
Suppose u = -0*u + 2. Factor 3 + 14*d + 0*d**u + 10*d**2 + 6 + 2*d**3 - 3.
2*(d + 1)**2*(d + 3)
Factor 64*s - 96*s**2 + 32*s + 9*s**3 - 6*s**3 - 4*s + s**3.
4*s*(s - 23)*(s - 1)
Let y(d) = 7*d + 42. Let k be y(-6). Suppose k = 10*z - 9*z - 4*n, 0 = 3*n. Solve 5/2 + z*a**2 + 5*a - 5*a**3 - 5/2*a**4 = 0.
-1, 1
Factor 0*l + 0 - 7/4*l**2 - 1/8*l**3.
-l**2*(l + 14)/8
Let q(d) be the third derivative of -d**7/525 + 7*d**6/300 - d**5/30 - 7*d**4/60 + 2*d**3/5 + 14*d**2. Find k, given that q(k) = 0.
-1, 1, 6
Suppose -43*y + 53*y = 0. Let t(q) be the first derivative of 0*q + y*q**2 + 1 + 2/21*q**3. Factor t(i).
2*i**2/7
Let w be (6/14)/((-19)/(-133)). Let f(u) be the first derivative of -5/4*u**2 + 1/4*u**w + 9 + 3/4*u. Solve f(p) = 0.
1/3, 3
Suppose 475 - 479 = -4*v. Let w be ((v - 3) + 9)*12/21. Find j, given that 0 + 2/3*j**5 + 8*j**3 + 2*j - w*j**4 - 20/3*j**2 = 0.
0, 1, 3
Let g = 37/442 + 11749/2210. Factor g + 3/5*z**2 + 6*z.
3*(z + 1)*(z + 9)/5
Suppose 5*u - 19 - 6 = 0. Suppose -7 = -u*d + 53. Let -10 + d*s - 2*s**2 - s**2 - 6 + 4 = 0. What is s?
2
Let i = 119 - 111. Let k be 2 + (-6)/i - (-3)/4. Let 0*c**k + 0 + 1/8*c**5 - 1/8*c**3 + 0*c + 0*c**4 = 0. Calculate c.
-1, 0, 1
Let c(j) = 3*j**3 + 3*j + 6. Let i(u) be the third derivative of u**6/30 + u**5/60 + u**4/6 + 7*u**3/6 + 8*u**2. Let m(x) = -7*c(x) + 6*i(x). Factor m(a).
3*a*(a + 1)**2
Let n(a) be the second derivative of a**5/5 - 5*a**4/3 - 11*a - 1. Factor n(r).
4*r**2*(r - 5)
Suppose -29*x + 53 + 5 = 0. Factor -8/5*z + 0 - 6*z**3 - 2/5*z**5 + 26/5*z**x + 14/5*z**4.
-2*z*(z - 4)*(z - 1)**3/5
Let b(m) be the first derivative of -1/2*m**3 + 0*m - 1/4*m**4 + 4 - 1/20*m**5 - 3/2*m**2. Let y(k) be the second derivative of b(k). Factor y(q).
-3*(q + 1)**2
Suppose 2/7*i**4 + 2/7 - 2/7*i - 4/7*i**2 - 2/7*i**5 + 4/7*i**3 = 0. Calculate i.
-1, 1
Suppose -2*w + 125 = 23*w. Let t(o) be the first derivative of 7/16*o**2 + 3/8*o**3 - 4 + 5/32*o**4 + 1/40*o**w + 1/4*o. Suppose t(x) = 0. What is x?
-2, -1
Let j(r) be the third derivative of -r**5/390 - 36*r**2 + r. Let j(i) = 0. What is i?
0
Suppose 2*n - 27 - 13 = 0. Suppose 0 = -13*u + 3*u + n. Factor 0 - 3/2*r**u + 3/4*r + 3/4*r**3.
3*r*(r - 1)**2/4
Let a(o) = o**3 + o**2 - o - 5. Let c(h) = 2*h**4 + 19*h**3 + 13*h**2 - 39*h + 25. Let p(k) = 5*a(k) + c(k). Solve p(s) = 0 for s.
-11, -2, 0, 1
Let n(g) be the third derivative of -g**6/216 + g**5/120 + g**4/36 + 2*g**3/3 + 9*g**2. Let w(f) be the first derivative of n(f). Factor w(y).
-(y - 1)*(5*y + 2)/3
Let s(f) be the second derivative of 1/50*f**5 - 17*f + 1/15*f**4 + 0*f**2 + 1 + 0*f**3. Factor s(o).
2*o**2*(o + 2)/5
Suppose -2 = s - 4. Factor -75*o**2 - 6 - 20*o + 72*o**s + 8*o - 3.
-3*(o + 1)*(o + 3)
Let l(c) be the third derivative of -2*c**7/945 + c**6/270 + c**5/135 - c**4/54 - 2*c**2 - 309. Factor l(s).
-4*s*(s - 1)**2*(s + 1)/9
Let d(k) = 36*k**3 - 176*k**2 - 36*k + 132. Let z(h) = -5*h**3 + 25*h**2 + 5*h - 19. Let n(t) = -6*d(t) - 44*z(t). Factor n(o).
4*(o - 11)*(o - 1)*(o + 1)
Let d(x) be the first derivative of 5*x**3/3 - 5*x**2/2 + 1001. Factor d(w).
5*w*(w - 1)
Factor 2/23*y**2 + 4050/23 + 180/23*y.
2*(y + 45)**2/23
Let i = 631 - 627. Let a(o) be the second derivative of -21/20*o**5 - 11/2*o**3 + i*o**4 + 0 + 6*o + 3*o**2. Factor a(l).
-3*(l - 1)**2*(7*l - 2)
Let b(w) be the third derivative of w**8/25200 + w**7/525 + w**6/25 + 8*w**5/15 - 21*w**2. Let r(c) be the third derivative of b(c). Factor r(m).
4*(m + 6)**2/5
Factor 968*h + 1/9*h**4 + 1364/3*h**2 + 0 - 130/9*h**3.
h*(h - 66)**2*(h + 2)/9
Let y(n) = -n**3 + 5*n**2 - n + 7. Let l be y(5). Let b = 23 + 19. Suppose -b*x**2 + 42*x**l - 3*x**4 + 3*x**3 = 0. Calculate x.
0, 1
Let k = -30 - -30. Let d = 530/11 + -48. Suppose -d*u**3 - 2/11*u**4 + 0*u + k*u**2 + 0 = 0. What is u?
-1, 0
Let q(j) be the third derivative of 3/14*j**4 + 0 - 4/7*j**3 + 1/280*j**6 + 0*j - 3/70*j**5 + 26*j**2. Find v, given that q