) be the third derivative of d**7/30 + d**6/180 - 7*d**5/20 - 2*d**4/3 - 2*d**3/9 - 128*d**2 + 2*d. Solve i(o) = 0 for o.
-1, -2/21, 2
Suppose -21*u - 2601 = -2643. Factor 0 - 2/17*c**u + 2/17*c**3 + 0*c.
2*c**2*(c - 1)/17
Suppose -76 = -17*f - 42. Let z(w) be the first derivative of 4 + 1/21*w**3 + 0*w + 1/7*w**f. Solve z(t) = 0.
-2, 0
Let v(m) = -m**2 - m - 1. Let j(r) = -3*r**3 - 7*r**2 + 2*r - 4. Let b(u) = j(u) - 4*v(u). Factor b(k).
-3*k*(k - 1)*(k + 2)
Let h = 24731/30 - 4116/5. Determine y so that 22/3*y - 2 - h*y**2 = 0.
2/7, 6
Let s(y) be the third derivative of -y**8/840 + y**7/105 - y**6/60 - 19*y**3/6 + 9*y**2. Let c(v) be the first derivative of s(v). Solve c(q) = 0.
0, 1, 3
Let q(i) be the third derivative of -2*i**3 + 9*i**2 - 3/8*i**4 + 0*i + 1/20*i**5 + 0. Factor q(p).
3*(p - 4)*(p + 1)
Let g(j) be the second derivative of 0 + 8/15*j**5 + 0*j**3 - 4/27*j**4 - 14/45*j**6 + 0*j**2 - 14/27*j**7 - 5*j. Factor g(d).
-4*d**2*(d + 1)*(7*d - 2)**2/9
Let u(g) be the second derivative of -g**6/6 + g**5 + 15*g**4/2 + 50*g**3/3 + 35*g**2/2 - 15*g - 3. Factor u(h).
-5*(h - 7)*(h + 1)**3
Let g(r) = -r + 1. Let q(j) = -2*j**2 - 6*j + 6. Let t(n) = 12*g(n) - 2*q(n). Let z be t(1). Suppose z*p**2 + 3 - 2*p + 1 + 0*p - 6*p = 0. Calculate p.
1
Let c(p) be the third derivative of p**8/1512 - 32*p**7/945 + p**6/9 + p**5/135 - 61*p**4/108 + 10*p**3/9 + 1021*p**2. Find d such that c(d) = 0.
-1, 1, 30
Let y = -345 + 347. Let t(u) be the first derivative of 1/2*u**y + 2/3*u**3 - 3*u + 5. Factor t(n).
(n - 1)*(2*n + 3)
Factor 72/5 - 8/5*g**2 + 36/5*g - 4/5*g**3.
-4*(g - 3)*(g + 2)*(g + 3)/5
Let c(f) be the third derivative of f**6/660 + f**5/55 - 32*f**3/33 - 2*f**2. Factor c(v).
2*(v - 2)*(v + 4)**2/11
Let x(p) = 19*p + 3. Let t be x(-4). Let j = 153/2 + t. Factor j*o**2 + 23/2*o + 3.
(o + 3)*(7*o + 2)/2
Let d(k) be the third derivative of 0 - 1/140*k**7 - 1/448*k**8 + 0*k**3 + 1/32*k**4 + 1/40*k**5 + 7*k**2 + 0*k**6 + 0*k. What is s in d(s) = 0?
-1, 0, 1
Let p(y) be the third derivative of 0*y + 1/420*y**7 + 1/120*y**6 + 0*y**4 + 1/120*y**5 + 0 - 21*y**2 + 0*y**3. Factor p(f).
f**2*(f + 1)**2/2
Suppose -8*h + 4*h + 8 = 0. Suppose 7 - 1 = h*m. Determine j, given that 4*j**4 - 3*j - 2*j**4 + 3*j**m + 6*j**2 + 5*j + 3*j**3 = 0.
-1, 0
Let q(z) be the third derivative of 1/9*z**4 + 4/315*z**7 - 1/60*z**6 - 21*z**2 - 1/504*z**8 + 0*z**3 + 0*z - 2/45*z**5 + 0. Let q(w) = 0. Calculate w.
-1, 0, 1, 2
Factor 21*a**3 - 8*a**3 - 5*a + 71*a - 20 + 19*a**3 - 2*a**5 - 76*a**2.
-2*(a - 2)*(a - 1)**3*(a + 5)
Suppose -2*x = 4*z - 20, 5*x = x - 3*z + 35. Let w = x - 6. Find t such that -w*t**2 + 148*t - 144*t + 0 - 2 = 0.
1
Let w(q) be the third derivative of 1/255*q**5 + 0*q + 0*q**3 + 12*q**2 + 0 + 1/1020*q**6 + 0*q**4. What is f in w(f) = 0?
-2, 0
Factor -a**4 + 49/4*a - 21/4*a**2 + 0 - 6*a**3.
-a*(a - 1)*(2*a + 7)**2/4
Solve 17*g - 6*g + 7738*g**2 + 7*g**3 - 7758*g**2 + 2 = 0 for g.
-1/7, 1, 2
Suppose -3*b - 11 = -4*l, -18 = -3*l + 9*b - 10*b. Let j(h) be the third derivative of 1/6*h**4 + 0*h - 1/60*h**l + 0 - 2/3*h**3 + 4*h**2. Factor j(u).
-(u - 2)**2
Let v(l) = -l**3 - 9*l**2 + 10*l - 2. Let o be v(-10). Let r be 3/o - 18/(-4). Factor 3*y - 6*y - 2*y**3 - r*y**5 + 8*y**3.
-3*y*(y - 1)**2*(y + 1)**2
Suppose -79*p**2 + 65*p**3 + 5*p**5 + 3421 + 75*p**4 - 1709 - 70*p + 4*p**2 - 1712 = 0. What is p?
-14, -1, 0, 1
Let o = -155 + 29. Let k = o + 128. Determine d, given that -2/3*d**k + 2/9*d**5 - 4/9*d + 2/9*d**3 + 2/3*d**4 + 0 = 0.
-2, -1, 0, 1
Let i(y) = -6*y**4 + 14*y**3 + 74*y**2 - 40*y. Let h(g) = -6*g**2 - g**4 - g**3 + 21*g**2 - 8*g + 8*g**3 - 4*g**3. Let k(t) = -14*h(t) + 3*i(t). Factor k(s).
-4*s*(s - 1)**2*(s + 2)
Let f(s) = 6*s**3 - 6*s**2 + 12*s + 12. Let b(u) = u**3. Let k(n) = -5*b(n) + f(n). Let l(g) be the first derivative of k(g). Suppose l(h) = 0. Calculate h.
2
Let r(w) be the third derivative of -w**8/151200 - w**7/37800 + w**5/15 - 7*w**2. Let h(x) be the third derivative of r(x). Factor h(q).
-2*q*(q + 1)/15
Factor 500*f**2 - 20*f**4 + 2190 - 87*f**3 + 560*f + 4*f**5 - 8*f**3 - 5326.
(f - 4)**3*(2*f + 7)**2
Let k be 126/105*3/9. Find z such that -16/5*z + k*z**4 + 4/5 + 21/5*z**2 - 11/5*z**3 = 0.
1/2, 1, 2
Let i(w) = 4*w**2 - 10*w - 15. Let j(h) = -h**2 + h - 1. Let g(y) = 2*i(y) + 6*j(y). Factor g(l).
2*(l - 9)*(l + 2)
Let t = -132 - -260. Determine m, given that t*m + 236 - m**3 + m**3 + 2*m**4 - 48*m**2 - 332 = 0.
-6, 2
Let r be (-2)/(3 + 0 + -2) - -17. Let i = 29 - r. Solve -i*g**2 - 4/3 - 34/3*g**3 - 22/3*g - 10/3*g**4 = 0.
-1, -2/5
Let c(a) = -6*a - 3. Let t(p) = 2 + 0*p**2 + 7*p + p**2 + 2 + 0. Let m be ((-4)/(-2) - 0)*1. Let x(b) = m*c(b) + 3*t(b). Factor x(n).
3*(n + 1)*(n + 2)
Suppose 0 = -5*i + 6*i - 3. Let b(x) = 4*x - 10. Let a be b(i). Factor -2/3 - 7/3*w - a*w**2.
-(2*w + 1)*(3*w + 2)/3
Let i be ((-80)/(-110))/(78/143). Determine v so that 2/3*v + 0 - i*v**3 - 2/3*v**2 = 0.
-1, 0, 1/2
Suppose 13*q**3 + 56/3*q**2 + 0 + 49/6*q + 1/6*q**5 + 8/3*q**4 = 0. What is q?
-7, -1, 0
Let y(a) be the third derivative of -1/12*a**5 - 5/24*a**4 + 0 + 1/42*a**7 + 0*a**3 + 1/24*a**6 + 0*a + a**2. Suppose y(m) = 0. What is m?
-1, 0, 1
Suppose 3*g = -l + 2012 - 2011, 5 = -5*g - 3*l. Factor -2/7*y**g - 4/7*y + 0.
-2*y*(y + 2)/7
Suppose 0*q - 4/7*q**4 - 5/7*q**3 - 1/7*q**2 + 0 = 0. What is q?
-1, -1/4, 0
Let w(x) be the third derivative of -x**8/840 - 2*x**7/525 - x**6/300 - 159*x**2. Factor w(j).
-2*j**3*(j + 1)**2/5
Suppose -z + 256 = 5*r + 14, 274 = z - 3*r. Factor 14*y**2 + z - y**5 + y**3 - 2*y**3 + 20*y - 254 - 4*y**4.
-(y - 2)*(y + 1)**2*(y + 2)**2
Let y(q) be the second derivative of q**5/90 + q**4/54 - 40*q**3/27 - 112*q**2/9 + 54*q + 3. Factor y(s).
2*(s - 7)*(s + 4)**2/9
Suppose 3*q - 4*a = 2*q + 9, -2*q = -3*a - 8. Suppose 3 = d - q. Solve 7*s**4 + s**2 + 2*s**5 - 2*s**3 - s**2 + 2*s**2 - 9*s**d = 0 for s.
-1, 0, 1
Let v be (-58)/(-20)*18/63 - 4/10. Let -15/7*n + 18/7 - v*n**2 = 0. What is n?
-6, 1
Let m(f) be the third derivative of -7/300*f**5 + 0*f + 0*f**3 - 1/60*f**4 + 0 + 8*f**2 - 1/120*f**6. Factor m(w).
-w*(w + 1)*(5*w + 2)/5
Suppose 0 = 21*d - 23*d + 4. Factor -2*r + 2/5 + 14/5*r**d - 6/5*r**3.
-2*(r - 1)**2*(3*r - 1)/5
Let j(z) be the second derivative of 3*z**5/20 - 5*z**4/4 - 13*z**3/2 - 21*z**2/2 + 231*z. Factor j(p).
3*(p - 7)*(p + 1)**2
Determine x so that -10253*x - 35*x**3 - 2*x**5 + 10103*x + 7*x**5 - 28*x**4 + 205*x**2 + 3*x**4 = 0.
-3, 0, 1, 2, 5
Let a be -1 - (-6)/10*2. Let j = -895 + 899. Factor 3/5*z**5 + 0 - 1/5*z**2 + z**j + 0*z + a*z**3.
z**2*(z + 1)**2*(3*z - 1)/5
Let i = 2956 + -2954. Factor -1 - 1/4*u**i + u.
-(u - 2)**2/4
Let r(k) be the second derivative of k**4/24 + 17*k**3/6 - 18*k**2 - 519*k. Let r(n) = 0. Calculate n.
-36, 2
Let a(f) be the first derivative of -f**5/10 - f**4/2 - f**3 - f**2 - f/2 - 63. Factor a(d).
-(d + 1)**4/2
Let j(v) be the first derivative of -v**6/2160 + v**5/720 + v**4/72 + v**3/3 - 2. Let a(z) be the third derivative of j(z). Determine h so that a(h) = 0.
-1, 2
Let w(l) be the first derivative of 44*l**3/15 + 128*l**2/5 - 48*l/5 + 411. Factor w(z).
4*(z + 6)*(11*z - 2)/5
Let l be (40/450)/(1/5). Let y(g) be the third derivative of 0*g + 1/360*g**6 + 1/6*g**4 + 5*g**2 - l*g**3 + 0 - 1/30*g**5. Solve y(z) = 0 for z.
2
Let a(v) be the first derivative of 11 + 0*v - 1/4*v**4 + 1/2*v**2 - 1/5*v**5 + 1/3*v**3. What is t in a(t) = 0?
-1, 0, 1
Determine u so that -3*u**4 + 90*u + 54 - 315*u**2 - 17*u**4 - 54 - 175*u**3 = 0.
-6, -3, 0, 1/4
Let v be -15*(-13 - 3014/(-264)). Find y, given that 35/4*y**5 - 305/4*y**4 - 35/2*y + 0 + 435/4*y**3 - v*y**2 = 0.
-2/7, 0, 1, 7
Let o(w) = -w**2 + 34*w + 41. Let j(y) = -2*y**2 + 33*y + 42. Let s(u) = 6*j(u) - 7*o(u). Let s(a) = 0. Calculate a.
-7, -1
Suppose 27*z = 32*z + 3*d - 7, 0 = 2*z + 2*d - 2. Suppose -3/2*m**z - 9*m - 12 = 0. What is m?
-4, -2
Factor -18*o + 6/5*o**2 + 264/5.
6*(o - 11)*(o - 4)/5
Let d = -38 + 41. Factor -658*m**3 + 8*m**2 + 623*m**d - 40 + 140*m + 2*m**2.
-5*(m - 2)*(m + 2)*(7*m - 2)
Let i(a) be the second derivative of a**6/135 - a**4/18 + 2*a**3/27 - 18*a + 3. Factor i(x).
2*x*(x - 1)**2*(x + 2)/9
Let r be ((-2)/5)/((-1)/5). Determine l so that -50*l - 42*l - 8*l**r + 88*l + 4 = 0.
-1, 1/2
Let d(i) = -31*i**3 + 98*i**