.
-3, 0
Suppose 761 - 789 = -14*k. Factor -1/2*u - u**4 + 0*u**3 + 1/2*u**5 + u**k + 0.
u*(u - 1)**3*(u + 1)/2
Let i = -35 + 38. Suppose -24*v**i - 10 - 4 - 4*v**4 - 40*v - 48*v**2 + 2 = 0. Calculate v.
-3, -1
Suppose 3051 = -4*t - 5*t. Let p = 693/2 + t. Suppose 3/2*i + 7/4*i**4 + 29/4*i**2 + 0 + p*i**3 = 0. What is i?
-3, -1, -2/7, 0
Let x(r) be the second derivative of 5/2*r**2 + 0 - 2/3*r**3 - 1/12*r**4 - 14*r. Factor x(l).
-(l - 1)*(l + 5)
Let h(z) be the second derivative of z**5/100 + 3*z**4/40 + 11*z**2/2 + 13*z. Let l(r) be the first derivative of h(r). Factor l(p).
3*p*(p + 3)/5
Let o(z) be the third derivative of -1/120*z**6 - 1/20*z**5 - 1/12*z**4 + 49*z**2 + 0*z**3 + 0*z + 0. Factor o(r).
-r*(r + 1)*(r + 2)
Let k(z) = z + 32. Let w be k(-24). Find h such that -12*h**2 + w*h**2 + 14*h**2 - h**3 - 25*h = 0.
0, 5
Suppose -7*y + 81 = 4. Let -y*k + 4*k**2 - 5*k**2 + 6*k = 0. What is k?
-5, 0
Let q(l) be the first derivative of 2*l**5/45 - 7*l**4/9 + 22*l**3/9 + 112*l**2/9 + 128*l/9 - 190. Factor q(b).
2*(b - 8)**2*(b + 1)**2/9
Find t, given that 3*t**3 - 24*t**2 + 26*t - 4*t**3 - 4*t**3 + 3*t**3 - 30 + 30*t**2 = 0.
-3, 1, 5
Let q = -425/6 - -71. Let p be (-6 - 161/(-21)) + 6/(-4). Factor -1/6 - 1/6*b**4 + 1/3*b**2 + p*b - 1/3*b**3 + q*b**5.
(b - 1)**3*(b + 1)**2/6
Let o(u) = -u - 1. Let w be o(-3). Suppose -4*l + w*v - 2 = 0, -l - 19 = -3*l - 3*v. Factor 6*p + 2*p**2 + 0*p**2 - 6*p + l*p**4 - 4*p**3.
2*p**2*(p - 1)**2
Let m(d) = -9*d**2 + 4*d + 13. Let x(b) be the first derivative of 4*b**3/3 - b**2 - 6*b - 1. Suppose 0*r = -5*r - 70. Let i(z) = r*x(z) - 6*m(z). Factor i(y).
-2*(y - 3)*(y + 1)
Suppose -46*o**4 - 33*o**4 + 0*o**4 + 256*o**5 - 61*o**3 - 44*o**2 - 83*o**3 - 4*o + 15*o**4 = 0. Calculate o.
-1/4, 0, 1
Let d(q) = -9*q**3 - q**2 - q - 9. Let b(h) = 5*h**3 + h**2 + h + 5. Let k = -264 + 267. Let j be (-20)/6*(-6)/4. Let g(c) = j*b(c) + k*d(c). Factor g(t).
-2*(t - 1)**2*(t + 1)
Let k(c) = -3*c**3 + 17*c**2 + 9*c + 6. Let b(p) be the first derivative of -p**4/4 + 2*p**3 + 3*p**2/2 + 2*p - 11. Let g(r) = 17*b(r) - 6*k(r). Factor g(s).
(s - 2)*(s + 1)**2
Let k(p) be the third derivative of 0*p + 1/672*p**8 + 1/16*p**4 + 0*p**7 - 1/60*p**6 + 1/60*p**5 - 10*p**2 + 0 - 1/6*p**3. Factor k(o).
(o - 1)**3*(o + 1)*(o + 2)/2
Let p(o) = o + 1. Let t be p(5). Factor -t*i - 5*i**3 - 24*i - 26*i - 20 + 16*i - 25*i**2.
-5*(i + 1)*(i + 2)**2
Suppose 9*q - 75 = -16*q. Let u(f) be the first derivative of 1/4*f**4 + 5/2*f**2 - 2*f - 9 - 4/3*f**q. Determine l, given that u(l) = 0.
1, 2
Let q = -47/56 + 683/280. Factor -q - 28/5*t**4 - 108/5*t**2 + 52/5*t + 92/5*t**3.
-4*(t - 1)**3*(7*t - 2)/5
Let c(g) be the third derivative of 0 + 3/70*g**7 + 0*g + 29/30*g**5 + 4/3*g**3 - 23*g**2 + 13/40*g**6 + 3/2*g**4. Find d, given that c(d) = 0.
-2, -1, -2/3
Let 96*p**2 - 6 - 98*p**2 - 2 - 8*p = 0. Calculate p.
-2
Let t(m) be the first derivative of m**3 + 10*m - 23 + 17/2*m**2. Solve t(z) = 0 for z.
-5, -2/3
Let l be 1/((-44)/36 + 1)*(-15)/27. Factor -5/2*z**2 + 0*z + l.
-5*(z - 1)*(z + 1)/2
Suppose 2*p + 0 = 4. Suppose 4*r - 9 = -5*h + p*r, 5*h = r + 18. Solve 8/3*i**h + 0 + 2/3*i**2 - 4/9*i + 14/9*i**4 = 0.
-1, 0, 2/7
Let j(s) = 25*s**2 - 1055*s + 4245. Let d(w) = -w**2 + 48*w - 193. Let k(r) = 45*d(r) + 2*j(r). Factor k(x).
5*(x - 3)*(x + 13)
Let g be (-2)/(-7) + (-406)/1764. Let h(o) be the first derivative of 1/9*o**3 + 0*o + 0*o**2 + 3 + 1/12*o**4 - 1/15*o**5 - g*o**6. Let h(n) = 0. Calculate n.
-1, 0, 1
Let w(j) be the second derivative of -j**7/70 + j**5/10 - j**3/2 - 5*j**2/2 - 4*j. Let q(s) be the first derivative of w(s). Factor q(r).
-3*(r - 1)**2*(r + 1)**2
Let b(l) be the second derivative of -15/4*l**4 + 27/20*l**5 - 1/10*l**6 - 8 + 0*l**2 + 7/2*l**3 + l. Determine i, given that b(i) = 0.
0, 1, 7
Factor -72*v**2 - 33 + 83 + 50*v**4 + 332*v**2 - 26*v + 170*v**3 + 5*v**5 + 211*v.
5*(v + 1)**3*(v + 2)*(v + 5)
Let s(r) = 3*r**2 - 17*r + 4. Let c be s(5). Let k be c/30*(5 - 7). Solve k*g - 4/5*g**2 + 4/5 - 2/5*g**3 = 0.
-2, -1, 1
Let i be 15/(-3)*(-16 - 2). Factor -27 - 27*x**4 - i*x**3 - 48*x + 802*x**2 - 940*x**2 - 3*x**5 - 51*x.
-3*(x + 1)**3*(x + 3)**2
Factor -201*g**3 + 11*g**2 + 84*g**3 + g**2 - 60*g**4 + 5*g**3 + 4*g**2.
-4*g**2*(g + 2)*(15*g - 2)
Let y(x) be the third derivative of x**8/168 + 11*x**7/105 - 3*x**6/10 - 34*x**5/15 + 14*x**4/3 + 32*x**3 + 2*x**2 + 88*x. Let y(a) = 0. Calculate a.
-12, -2, -1, 2
Let n(w) be the second derivative of w**6/120 - w**5/20 - 11*w**4/48 - w**3/4 + 366*w. Factor n(j).
j*(j - 6)*(j + 1)**2/4
Let w(s) be the third derivative of -s**7/2100 - s**6/600 - s**5/600 + 2*s**2 - 125. Factor w(c).
-c**2*(c + 1)**2/10
Let n(p) = 3*p**4 + 384*p**3 + 22032*p**2 + 514518*p + 4501857. Let x(j) = 2*j**3 + j**2 - j + 1. Let g(c) = -n(c) - 18*x(c). Let g(w) = 0. Calculate w.
-35
Let n(l) be the second derivative of -l**8/3360 + l**6/360 - 5*l**4/12 + 13*l. Let k(z) be the third derivative of n(z). Factor k(v).
-2*v*(v - 1)*(v + 1)
Let m be (4 - 2) + ((-39)/3 - -15). Let g(r) be the third derivative of 0 + 0*r**m + 1/180*r**6 + 2*r**2 + 0*r**3 + 0*r - 1/90*r**5. Factor g(x).
2*x**2*(x - 1)/3
Let z(d) be the third derivative of -1/48*d**4 + 0 - 13*d**2 - 1/6*d**3 + 0*d + 1/120*d**5. Factor z(m).
(m - 2)*(m + 1)/2
Let v(w) be the first derivative of -4*w**5/5 + 11*w**4 - 104*w**3/3 + 32*w**2 + 545. Solve v(t) = 0.
0, 1, 2, 8
Let q(x) be the third derivative of x**8/1008 + 2*x**7/105 + 7*x**6/45 + 7*x**5/10 + 15*x**4/8 + 3*x**3 - 303*x**2. Factor q(r).
(r + 1)*(r + 2)*(r + 3)**3/3
Let x = 402 + -398. Let d(w) be the second derivative of -1/8*w**4 + 0 - 3/80*w**5 + 3/4*w**2 - x*w + 1/8*w**3. Factor d(m).
-3*(m - 1)*(m + 1)*(m + 2)/4
Let u(s) = -s**3 - 5*s**2 + s + 7. Let g be u(-5). Let y(p) be the first derivative of -13 - 30*p**g + 36*p + 28/3*p**3 - p**4. Find d such that y(d) = 0.
1, 3
Let i = 1/16 + 7/16. Let k be 142/(-355) - 12/(-5). Solve -o**k + 0 + i*o + 1/2*o**3 = 0.
0, 1
Let b(m) = 61*m**4 - 3*m**3 - 20*m**2 - 8*m + 13. Let s(f) = -28*f**4 + 2*f**3 + 10*f**2 + 4*f - 6. Let p(k) = -6*b(k) - 13*s(k). Determine c so that p(c) = 0.
-2, -1, 0
Let s be 2/(-3)*(-18 + 17). Let l(g) be the first derivative of -1 + 2/5*g**5 - 1/2*g**4 + 1/3*g**6 + 0*g**2 + 0*g - s*g**3. Factor l(w).
2*w**2*(w - 1)*(w + 1)**2
Let c = -1708 - -1710. Factor -1/2*n + 1/2*n**3 + 1/4 + 0*n**c - 1/4*n**4.
-(n - 1)**3*(n + 1)/4
Find z, given that -72/19 + 64/19*z**2 + 82/19*z + 8/19*z**4 - 84/19*z**3 + 2/19*z**5 = 0.
-9, -1, 1, 4
Let o(l) be the third derivative of 3*l**2 + 0 - 1/90*l**5 - 5/9*l**3 + 1/6*l**4 + 0*l. Factor o(x).
-2*(x - 5)*(x - 1)/3
Let a(r) be the second derivative of r**7/273 + 29*r**6/195 + 223*r**5/130 + 167*r**4/78 - 224*r**3/39 - 196*r**2/13 - 4*r - 18. Let a(c) = 0. What is c?
-14, -1, 1
Let c = -4894/141 + 104/3. Let i = 84/235 - c. Solve 1/5*q - i*q**2 + 0 + 1/5*q**3 = 0.
0, 1
Let q(k) be the second derivative of k**6/10 - 3*k**5/20 + 357*k. Suppose q(w) = 0. What is w?
0, 1
Let r(m) be the second derivative of -25*m + 1/18*m**4 + 1/30*m**5 - 1/3*m**2 + 0 - 1/9*m**3. Factor r(j).
2*(j - 1)*(j + 1)**2/3
Factor -26/17*k - 18/17*k**3 + 4/17 + 40/17*k**2.
-2*(k - 1)**2*(9*k - 2)/17
Let s(y) = -y**2 - 6*y + 4. Let h be s(-6). Factor -30*d**5 + 4*d**3 + 8*d**2 + 18*d**5 + 4*d**h - 20*d**4.
-4*d**2*(d + 1)**2*(3*d - 2)
Let j(w) be the second derivative of -3*w**4/4 - 3*w**3 - 2*w**2 - 11*w. Let a(x) = -8*x**2 - 18*x - 4. Let t(r) = -5*a(r) + 6*j(r). Let t(b) = 0. What is b?
-1, -2/7
Let u(a) be the first derivative of a**6/2 + 12*a**5/5 - 3*a**4/4 - 4*a**3 + 67. Let u(i) = 0. Calculate i.
-4, -1, 0, 1
Let m be (-5 - 189/(-35)) + (-26)/(-10). Let v = 15 + -13. Factor -3/2*r**m + 3*r + 5/4*r**v + 1.
-(r - 2)*(2*r + 1)*(3*r + 2)/4
Suppose 3*n = -2*s - 3*s + 72, -12 = -2*s + 3*n. Let d(w) = -w**2 + w - 4. Let l(i) = -i. Let f(a) = s*l(a) - 3*d(a). Solve f(j) = 0.
1, 4
Let w(a) be the first derivative of 4*a + 196/3*a**3 + 9 + 28*a**2. Factor w(m).
4*(7*m + 1)**2
Let s = -885 + 2831/3. Let r = s - 57. Factor 0 - 2/3*f - r*f**4 + 2/3*f**3 + 5/3*f**2.
-f*(f - 1)*(f + 1)*(5*f - 2)/3
Let v be (-70)/(-25) + 2/10. Let d(l) be the first derivative of 2*l + 46*l + v*l**2 + l**3 - l**2 - 14*l**2 - 7. Factor d(t).
3*(t - 4)**2
Let z = 216 