1)
Let n(f) be the third derivative of 5/24*f**4 + 0*f + 1/3*f**3 + 0 + 1/15*f**5 + 1/120*f**6 + 12*f**2. Suppose n(a) = 0. Calculate a.
-2, -1
Let d(m) = m**3 - 5*m**2 + 2. Let x be d(5). Suppose -3*f = 3*z, -2*z + 4*z + 2 = -3*f. Let 0*l**x - 2 + 7*l + z*l**2 + 6 - l = 0. Calculate l.
-2, -1
Let n = 39141/88 + -3535/8. Let -2/11*d**2 - 16/11*d - n = 0. Calculate d.
-4
Let w be (-7)/((-7)/(-2)) - (1 + -8). Solve d**2 + 0*d**2 + 11 - w*d - 8 + d**3 = 0.
-3, 1
Suppose -9*g + 112 - 94 = 0. Let t(j) be the first derivative of -3/20*j**5 + 0*j - 2*j**3 - 3/2*j**g - 15/16*j**4 + 4. Factor t(b).
-3*b*(b + 1)*(b + 2)**2/4
Suppose -b - 70 + 73 = 0, 5*b - 15 = -2*t. Factor -8/3*p + 8*p**2 - 26/3*p**3 - 2/3*p**5 + 4*p**4 + t.
-2*p*(p - 2)**2*(p - 1)**2/3
Let h(d) = -d - 6. Let q = 193 + -201. Let f be h(q). Factor 8/5 - f*z + 2/5*z**2.
2*(z - 4)*(z - 1)/5
Let l be (-7)/21*41/(-123). Factor 2/9 + l*p - 2/9*p**2 - 1/9*p**3.
-(p - 1)*(p + 1)*(p + 2)/9
Let g(j) be the second derivative of 0 - 1/30*j**5 - 6*j + 1/6*j**4 - j**2 + 0*j**3 - 1/60*j**6. Let b(k) be the first derivative of g(k). Factor b(f).
-2*f*(f - 1)*(f + 2)
What is i in -243 + 123 + 4*i**4 + 16*i**3 + 120 = 0?
-4, 0
Factor -13 + 18 - 2*f**2 + 26*f - 5*f + 7*f - 71.
-2*(f - 11)*(f - 3)
Suppose 13*b - 12 = 10*b. Solve -3*y**5 + 36*y**2 - 32*y**2 + 26*y**2 - 15*y + 3 - 30*y**3 + 15*y**b = 0.
1
Let z = 0 + 3. Suppose 0 = -4*r + z*r. Factor 4*h + r*h - h + 3*h**2.
3*h*(h + 1)
Let f = 229/9 + -25. Let r(n) be the first derivative of -1/6*n**4 - 1/3*n**2 - f*n**3 + 4 + 0*n. Factor r(k).
-2*k*(k + 1)**2/3
Let 52/9*f**2 + 0 - 16/9*f + 8/9*f**4 - 44/9*f**3 = 0. What is f?
0, 1/2, 1, 4
Let j(i) be the second derivative of -5*i**4/12 - 275*i**3/3 - 15125*i**2/2 + 2*i + 3. Let j(g) = 0. What is g?
-55
Let b(u) be the first derivative of 0*u**2 - 2/3*u**3 - 1/12*u**4 - 8 + 9*u. Let g(p) be the first derivative of b(p). Let g(j) = 0. What is j?
-4, 0
Let l = -12 - -9. Let k be 10/l*(-210)/28. Factor 24 + 11*f**2 - f**2 + k*f + 35*f + 8*f**2 - 27*f**3.
-3*(f - 2)*(3*f + 2)**2
Let f(p) = p**2 + 3*p + 5. Let t be f(-4). Let r = t + 9. Factor 2 - 3*y**4 - r*y**2 - 15 + 12*y + 12*y**3 + 10.
-3*(y - 1)**4
Let t(c) be the third derivative of -c**5/15 - 5*c**4/2 - 24*c**3 + 3*c**2. What is w in t(w) = 0?
-12, -3
Find y, given that -9/2*y**3 + 0 + 5/2*y**2 - y**5 - 1/2*y + 7/2*y**4 = 0.
0, 1/2, 1
Let w(b) be the first derivative of -b**4/7 - 12*b**3/7 - 4*b**2 + 14. Determine q so that w(q) = 0.
-7, -2, 0
Find y, given that 15/2*y**5 + 27/2*y**4 - 51/2*y**3 + 9/2*y**2 + 0*y + 0 = 0.
-3, 0, 1/5, 1
Let p(b) be the second derivative of -b**8/8400 + b**7/600 - b**6/120 + 3*b**5/200 + 11*b**3/6 + b. Let j(o) be the second derivative of p(o). Factor j(t).
-t*(t - 3)**2*(t - 1)/5
Let m be (-9)/6*28/70 + (-38)/(-30). Factor -32*q - m*q**3 + 26/3*q**2 + 24.
-2*(q - 6)**2*(q - 1)/3
Let i = 231 - 228. Let t(y) be the third derivative of -2/15*y**5 - i*y**2 + 0 + 1/105*y**7 - 1/30*y**6 + y**3 + 0*y + 1/6*y**4. Factor t(l).
2*(l - 3)*(l - 1)*(l + 1)**2
Let i(f) be the first derivative of -f**5/40 - 7*f**4/16 - 13*f**3/24 - 85. Factor i(j).
-j**2*(j + 1)*(j + 13)/8
Let t(i) be the third derivative of i**6/540 - i**5/180 - 11*i**3/6 + i**2. Let l(g) be the first derivative of t(g). Factor l(u).
2*u*(u - 1)/3
Let z be 39/104 + (-51)/136. Factor 25/2*q**4 - 5*q**3 + z + 0*q + 1/2*q**2.
q**2*(5*q - 1)**2/2
Suppose -4*a + 420 = -a. Suppose -w - 2*m = -20, 4*w - 3*m - a = m. Determine h, given that w*h**3 - 34*h**2 + 38*h**2 - 25*h**2 + 12 - 12*h - 9*h**4 = 0.
-2/3, 1, 2
Let l(x) be the first derivative of x**8/2520 - x**7/420 + x**6/270 + 7*x**3/3 + 8. Let f(b) be the third derivative of l(b). Factor f(u).
2*u**2*(u - 2)*(u - 1)/3
Let d = -5889/7 + 843. Let q be (-3)/(-14) - (-726)/308. Find s, given that d*s + 2/7*s**2 + q = 0.
-3
Suppose -2*r + 13 = -11. Suppose -k = 3*k - r. Factor 0*i**4 + i**5 + k*i**3 - 2*i - i**4 + 5*i**2 - 6*i**3.
i*(i - 1)**3*(i + 2)
Suppose 14 = 3*v - 19. Suppose -1 = -v*t + 21. Suppose 8/3 - 32/3*c + 14/3*c**t = 0. What is c?
2/7, 2
Suppose -10*t + 24 = 2*t. Factor -8*f - 2*f**2 + f**t - 4*f**2 + 7*f**2.
2*f*(f - 4)
Suppose -6*y = -2*y - 3*x - 3, -4*x + 21 = 3*y. Let a(t) = -39*t**3 - 2*t**2 - 2*t - 1. Let r be a(-1). Solve -38 + 2*c + r - y*c**2 = 0 for c.
0, 2/3
Suppose 0*g + 1/2*g**2 - 1/2*g**3 + 0 = 0. Calculate g.
0, 1
Let k be (-212)/22 - 19/(-57)*30. Solve -k + 6/11*y - 2/11*y**2 = 0 for y.
1, 2
Let 102 - 5*n**3 - 45*n + 50*n**2 - 102 = 0. What is n?
0, 1, 9
Let b be 343/14 - 1/(-2). Let s be 2/9 - b/(-9). Let d - 30*d**s + 3 + 36*d**3 - 7*d - 3*d**4 = 0. Calculate d.
-1, 1
Solve -142/5*f - 2/5*f**2 - 28 = 0 for f.
-70, -1
Let q = -610 + 617. Let v(i) be the second derivative of -1/30*i**4 + 1/210*i**q + 0*i**5 + 7*i - 1/30*i**3 + 1/75*i**6 + 0*i**2 + 0. Let v(y) = 0. What is y?
-1, 0, 1
Suppose 12 - 4 = 2*h, 4*i = -2*h. Let k be -1 - (2/i + -2). Factor 4*z + 4*z**2 + 6*z + 8 + k*z.
4*(z + 1)*(z + 2)
Let q be 4 - 2/8*(16 + -16). Let w(f) be the first derivative of 0*f**q + 0*f + 1/6*f**3 - 1/8*f**2 - 1/10*f**5 + 5 + 1/24*f**6. Factor w(s).
s*(s - 1)**3*(s + 1)/4
Let r(s) = -s**3 - 12*s**2 + 129*s + 28. Let h be r(7). Find x, given that 2/5*x**2 + h*x - 8/5 = 0.
-2, 2
Let q(z) be the first derivative of -z**5/330 + z**4/11 - 12*z**3/11 + 2*z**2 + 20. Let k(h) be the second derivative of q(h). Factor k(r).
-2*(r - 6)**2/11
Determine g, given that 6*g**2 - 51*g**2 - 45*g**2 + g**5 - 27 + 81*g - 11*g**4 + 46*g**3 = 0.
1, 3
Let p(g) be the first derivative of 3*g**5/10 - 21*g**4/8 + 8*g**3 - 9*g**2 - 45. Factor p(v).
3*v*(v - 3)*(v - 2)**2/2
Let w = 6 - 2. Let x be 2 + (-8 - -4) + 4. Factor x*r**3 - 2*r - 8 + w - 5*r + r.
2*(r - 2)*(r + 1)**2
Let v(a) be the second derivative of a**7/210 - 3*a**5/100 - a**4/30 + 15*a. Factor v(k).
k**2*(k - 2)*(k + 1)**2/5
Factor 332*d + 166 + 22*d**2 - 34 - 17*d**2.
(d + 66)*(5*d + 2)
Factor -392/5 - 56/5*n - 2/5*n**2.
-2*(n + 14)**2/5
Factor -6*c - 5*c**3 + c**3 - 3 + c**3 + 3*c**2 + 9*c.
-3*(c - 1)**2*(c + 1)
Let t(z) be the third derivative of -25*z**4/24 + 10*z**3/3 - 9*z**2. Let l(r) = r**2 + r. Let b(x) = -5*l(x) - t(x). Factor b(m).
-5*(m - 2)**2
Let l be (-84)/(-63) - ((-140)/(-24))/7. Solve -2*t**4 + 0 - 5/2*t**3 - l*t**5 - t**2 + 0*t = 0 for t.
-2, -1, 0
Let b(u) = u**2 - 7*u - 170. Let q be b(-10). Solve -4/5*d**2 + 0*d + q + 4/5*d**3 = 0 for d.
0, 1
Let l = -2 - -12. Factor 316*z**2 + l*z**3 - 308*z**2 - 38*z**3.
-4*z**2*(7*z - 2)
Let t(i) be the first derivative of -20*i**3/3 + 15*i**2/2 + 5*i + 65. Let t(f) = 0. Calculate f.
-1/4, 1
Let s(w) be the first derivative of w**6/24 - w**5/10 - w**4/2 + 3*w**3/2 - 9*w**2/8 - 86. Determine c, given that s(c) = 0.
-3, 0, 1, 3
Let t(u) be the second derivative of u**6/900 - u**5/30 + 3*u**4/20 - 3*u**3/2 - 6*u. Let v(y) be the second derivative of t(y). Suppose v(j) = 0. Calculate j.
1, 9
Let z(m) = 4*m**2 + 53*m + 39. Let i(l) = -4*l**2 - 52*l - 40. Let d(j) = 5*i(j) + 4*z(j). Solve d(o) = 0 for o.
-11, -1
Let k(s) be the first derivative of -s**3/12 + s**2/8 + 3*s/2 - 798. What is u in k(u) = 0?
-2, 3
Let s(q) = -q**3 - 8*q**2 - 6*q - 1. Let n be s(-7). Let t be 0 + n/(-10) + -7 + 7. Factor -2/5*z**3 - 4/5*z**2 + 2/5*z + t.
-2*(z - 1)*(z + 1)*(z + 2)/5
Let b = -2/373 + 493/22380. Let s(g) be the second derivative of -b*g**4 + 0*g**2 - 1/75*g**6 - g + 0*g**3 + 0 + 3/100*g**5. Factor s(a).
-a**2*(a - 1)*(2*a - 1)/5
Factor 19*v**3 - 5*v**3 - 9*v**3 + 12*v + 135 - 15*v**2 - 57*v.
5*(v - 3)**2*(v + 3)
Let k(q) be the first derivative of -22 + 1/17*q**2 - 2/17*q**3 + 0*q. Find c such that k(c) = 0.
0, 1/3
Let w(m) be the third derivative of -m**5/120 + m**4/8 - 3*m**3/4 - 60*m**2. What is s in w(s) = 0?
3
Let w(b) = 90*b**2 + 88*b + 22. Let q(i) = -27*i**2 - 7 - 9*i**2 - 29*i + 6*i**2. Let c be (-2)/(-2 - -4)*-6. Let p(y) = c*w(y) + 20*q(y). Factor p(r).
-4*(3*r + 2)*(5*r + 1)
Determine u, given that -1/4*u - 1/4*u**2 + 3 = 0.
-4, 3
Factor -2/9*l**4 + 86/9*l**2 + 0*l + 0 + 28/3*l**3.
-2*l**2*(l - 43)*(l + 1)/9
Suppose 2*w - 9 = -4*g + 7*w, -2*g = -5*w - 7. Let t be g/(-4) - -4*(-2)/(-16). Solve 1/4*m**2 - 1/2*m + t = 0 for m.
1
Determine i, given that -36/5*i + 8/5*i**2 + 4/5*i**3 - 72/5 = 0.
-3, -2, 3
Let f be (2/1