tive of -11*c + 25*c**2 + 0 + 1/6*c**k + 10/3*c**3. Factor o(f).
2*(f + 5)**2
Let r(d) = 463*d - d**2 + 0*d**2 - 483*d + 79. Let h(t) = -t**2 - t - 1. Let s(a) = 2*h(a) - r(a). Factor s(o).
-(o - 9)**2
Factor 4*t**2 - 9*t**2 + 0*t**2 + 5*t**4.
5*t**2*(t - 1)*(t + 1)
Let t(b) be the third derivative of 1/450*b**5 + 1/2520*b**8 + 0*b**3 + 0*b + b**2 - 1/900*b**6 - 1/1575*b**7 + 0*b**4 + 0. Determine d so that t(d) = 0.
-1, 0, 1
Factor 4*c - 2/7*c**2 + 0.
-2*c*(c - 14)/7
Find t such that 4*t**3 - 4/7*t**5 + 24/7*t + 4/7*t**4 + 0 - 52/7*t**2 = 0.
-3, 0, 1, 2
Factor -100/9 + 16/9*f**2 - 2/9*f**3 - 10/9*f.
-2*(f - 5)**2*(f + 2)/9
Let y = -93 - -97. Factor y + 3*c - c**3 - 10 - c**3 + 6*c**2 - c**3.
-3*(c - 2)*(c - 1)*(c + 1)
Let x be 16/(-144) + 128/126 + (-4)/12. Suppose 0 - 4/7*b**2 + x*b - 4/7*b**3 + 4/7*b**4 = 0. What is b?
-1, 0, 1
Factor 3508*t**4 - 1095 - 3503*t**4 + 135*t**3 - 3075*t + 3345 + 381*t**2 + 304*t**2.
5*(t - 2)*(t - 1)*(t + 15)**2
Suppose -6*r = -39 - 3. Suppose -15 = -r*a + 13. Factor -10*p**2 + 3*p**3 + 9/2*p**a + 0 + 4*p.
p*(p + 2)*(3*p - 2)**2/2
Let r be (-2)/(-3)*-9*6/(-24). Let q(l) be the first derivative of -4*l**2 + 0*l + 28*l**5 + 5 - 40/3*l**3 - 49/3*l**6 + r*l**4. Factor q(g).
-2*g*(g - 1)**2*(7*g + 2)**2
Let h = 107/4 + -26. Let m = 2/1169 + 1161/4676. Let m*z**3 - 1/4 - h*z**2 + 3/4*z = 0. What is z?
1
Let w(a) be the second derivative of -3/2*a**2 - 11*a + 1/4*a**4 + 1/2*a**3 + 0 - 3/20*a**5. Factor w(c).
-3*(c - 1)**2*(c + 1)
Let p be (200/150)/((-2)/6) + 7. Let n(w) be the first derivative of -1/4*w**p + 0*w - 4 + 0*w**2 - 3/20*w**5 + 3/8*w**4. Solve n(t) = 0 for t.
0, 1
Let v(s) be the third derivative of s**7/1050 - 9*s**6/200 - s**5/100 + 79*s**4/120 + 9*s**3/5 + 559*s**2. Factor v(n).
(n - 27)*(n - 2)*(n + 1)**2/5
Suppose 27*r = 183 - 75. Let x(z) be the second derivative of -1/50*z**5 + 1/6*z**r + 0 + 3/5*z**2 - 7/15*z**3 + 7*z. Determine a, given that x(a) = 0.
1, 3
Let p(n) be the third derivative of -n**5/30 - 97*n**4/12 - 32*n**3 + 176*n**2. Solve p(x) = 0 for x.
-96, -1
Let k(f) = -f**3 - 2*f**2 - 5. Let l be k(-3). Factor 4*a**2 - 6*a**5 + 15*a**5 + 9*a**5 + 36*a**l + 24*a**3 - 2*a**5.
4*a**2*(a + 1)**2*(4*a + 1)
Let a = 8174 - 24518/3. Factor -2 - 10/3*s - a*s**2.
-2*(s + 1)*(2*s + 3)/3
Let h(p) be the first derivative of -p**5/15 + 7*p**4/12 - 2*p**3/3 - 14*p**2/3 + 40*p/3 + 240. Factor h(t).
-(t - 5)*(t - 2)**2*(t + 2)/3
Let k = 4282 - 64283/15. Let q = 13/3 + k. Solve -8/5*p - q - 4/5*p**2 = 0.
-1
Let s(v) = 2*v**2 + 3*v + 5. Let m(r) = -r**2 - r + 1. Suppose 6*g + 56 = -8*g. Let u(y) = g*m(y) + s(y). Solve u(x) = 0 for x.
-1, -1/6
Find k, given that -11/6*k**3 - 13/6*k**2 - 1/3*k + 0 = 0.
-1, -2/11, 0
Factor -1572*v**2 - 72*v**3 + 72 - 240*v + 1806*v**2 - 3*v**4 + 9.
-3*(v - 1)**3*(v + 27)
Factor 529*v - 255*v - v**2 - 260*v - 49.
-(v - 7)**2
Find a, given that 5*a**5 - 40*a**3 - 15*a**4 + 0*a**2 + 0*a**4 + 50*a**3 + 0*a**2 = 0.
0, 1, 2
Factor 2/5*w**2 + 482/5*w - 484/5.
2*(w - 1)*(w + 242)/5
Let o(y) be the second derivative of -y**4/20 + 3*y**3/5 + 12*y**2 + 11*y + 18. Let o(k) = 0. What is k?
-4, 10
Let q(c) be the second derivative of -c**5/80 - c**4/16 - c**3/8 + 9*c**2 - 12*c. Let l(p) be the first derivative of q(p). Factor l(o).
-3*(o + 1)**2/4
What is w in -74/5*w + 0 + 1/5*w**2 = 0?
0, 74
Suppose -4*p - 4 = 2*a, a + 4*p = 8*p + 16. Solve 17*t**2 + 6*t - 14*t**2 - a + 1 - 6*t**3 = 0 for t.
-1, 1/2, 1
Let j = -91/200 + 12/25. Let m(v) be the third derivative of -1/6*v**3 + 0 - v**2 + 1/12*v**5 + 1/8*v**4 - j*v**6 - 2/105*v**7 + 0*v. Factor m(q).
-(q - 1)*(q + 1)**2*(4*q - 1)
Factor -7/3*j**2 + 5*j - 3 + 1/3*j**3.
(j - 3)**2*(j - 1)/3
Let o(m) be the first derivative of m**3 + 6*m**2 - 63*m + 505. Factor o(h).
3*(h - 3)*(h + 7)
Let h = -2993/206 + 3/103. Let b = 15 + h. Find u, given that -1/2*u - b*u**2 + 0 = 0.
-1, 0
Let f = 16515 + -16515. Factor -1/2*s**2 + s + f.
-s*(s - 2)/2
Let d(f) be the second derivative of -f**4/72 - f**3/6 - 2*f**2/3 - f + 140. Factor d(x).
-(x + 2)*(x + 4)/6
Let p be 517*1/3 + 2. Let t = p + -174. Factor t*o**2 + 0*o**3 + 0 + 0*o - 1/3*o**4.
-o**2*(o - 1)*(o + 1)/3
Let p(v) = v**3 - 19*v**2 + 19*v - 7. Let r be p(18). Factor -43*x**3 - x**4 + 18*x**5 - r*x**4 + 45*x**3.
2*x**3*(3*x - 1)**2
Find f such that 2*f**3 + 0 - 1/2*f**4 - 2*f + 1/2*f**2 = 0.
-1, 0, 1, 4
Let f(b) be the second derivative of 0 - 25*b + 0*b**4 + 0*b**3 - 1/20*b**5 + 0*b**2. Factor f(h).
-h**3
Solve 16*b**4 - 9*b**5 + 508*b**2 + 342*b + 7*b**4 + 8*b**5 + 86 - b**5 + 332*b**3 + 55*b**4 = 0 for b.
-1, 43
Solve 20*d - 46/3*d**2 - 25/3 - 1/3*d**4 + 4*d**3 = 0.
1, 5
Let u(j) be the third derivative of 1/60*j**4 + 0*j**3 - 1/300*j**5 + 0 + 0*j - 3*j**2. Determine l so that u(l) = 0.
0, 2
What is b in -5/4*b**2 - 79/4*b + b**3 + 5 = 0?
-4, 1/4, 5
Let g(y) be the first derivative of -y**6/1260 - y**5/70 - 2*y**4/21 + 10*y**3 + 51. Let z(w) be the third derivative of g(w). What is d in z(d) = 0?
-4, -2
Let n = 6333 + -25331/4. Factor -5/4 + 3/2*r - n*r**2.
-(r - 5)*(r - 1)/4
Let b = 537 + -345. Let x = 196 - b. Determine o, given that 4/7 - 18/7*o**5 - 10/7*o - 16/7*o**2 + 12/7*o**4 + x*o**3 = 0.
-1, -2/3, 1/3, 1
Let a = -244 + 246. Let m(x) be the first derivative of -46/33*x**3 - 5 - 8/11*x - 20/11*x**a - 7/22*x**4. Solve m(c) = 0 for c.
-2, -1, -2/7
Suppose 8 = -2*d - 4*o, 5*d + o - 4 = 3. Let x(y) be the first derivative of -1/12*y**3 + 1/16*y**4 + 1/4*y + 4 - 1/8*y**d. Factor x(z).
(z - 1)**2*(z + 1)/4
Let c be (60/(-50))/((-66)/20). Let 10/11*k - c + 4/11*k**2 - 10/11*k**3 = 0. What is k?
-1, 2/5, 1
Let h(k) be the third derivative of 0*k + 1/630*k**7 + 0*k**3 + 1/60*k**5 + 1/72*k**6 - 1/8*k**4 + 7*k**2 + 0. Factor h(l).
l*(l - 1)*(l + 3)**2/3
Let u = 39/22 + -53/33. Let l(c) be the third derivative of u*c**7 - 43/40*c**6 + 19/15*c**5 + 2*c**2 - 1/2*c**4 + 0*c**3 + 0*c + 0. Factor l(i).
i*(i - 3)*(5*i - 2)*(7*i - 2)
Factor -1/5*f**4 - 8/5*f + 7/5 + 8/5*f**3 - 6/5*f**2.
-(f - 7)*(f - 1)**2*(f + 1)/5
Let q = -5/4 - -11/8. Let k(c) be the second derivative of 1/80*c**5 - 1/8*c**2 + 0 + q*c**3 + 2*c - 1/16*c**4. Determine a, given that k(a) = 0.
1
Suppose 4*d - 4*d = -3*d. Factor d + 0*l**3 - 1/4*l**2 + 0*l + 1/4*l**4.
l**2*(l - 1)*(l + 1)/4
Let c(s) be the third derivative of s**8/1008 + 11*s**7/315 - s**6/180 - 11*s**5/45 + s**4/72 + 11*s**3/9 + 13*s**2 + 5*s. Determine w, given that c(w) = 0.
-22, -1, 1
Let q = 13 + -19. Let o be (-2)/2 - q/2. Find c, given that -3*c**o + 3*c**2 - 3*c**3 + 0*c**2 - 6*c**2 - 3*c = 0.
-1, 0
Let o(q) be the second derivative of -q**6/45 + q**5/60 + q**4/18 - q**3/18 - q + 54. What is n in o(n) = 0?
-1, 0, 1/2, 1
Let y(a) be the first derivative of -2/35*a**5 + 0*a + 1/7*a**6 - 6 - 1/7*a**4 + 0*a**3 + 0*a**2. Factor y(l).
2*l**3*(l - 1)*(3*l + 2)/7
Let s(d) = -3*d**4 - 3*d**3 - d**2 - 1. Let v = 36 + -35. Let z(q) = q**4 + q**3 + q**2 + 1. Let j(y) = v*s(y) + z(y). Let j(w) = 0. Calculate w.
-1, 0
Let i(h) be the first derivative of -4*h**6/33 + 2*h**5/55 + 45*h**4/44 + 5*h**3/3 + 23*h**2/22 + 3*h/11 + 18. Suppose i(l) = 0. What is l?
-1, -1/2, -1/4, 3
Let k(u) be the second derivative of -u**4/114 + 278*u**3/57 - 19321*u**2/19 - u + 30. Factor k(b).
-2*(b - 139)**2/19
Factor 52*o**3 + 3*o + 78*o**3 + 80*o**3 + 80*o**2 - 171*o**3 + o.
o*(o + 2)*(39*o + 2)
Suppose -3*p - 13 = -q - 6, 0 = -3*q - 5*p + 7. Factor -45*u - 30*u**q - 80*u**2 + 0 - 5*u**5 - 14 + 4 - 70*u**3.
-5*(u + 1)**4*(u + 2)
Let a(k) = 20*k**2 + 900*k + 924. Let h(w) = 4*w**2 + 180*w + 184. Let m(g) = -2*a(g) + 11*h(g). Solve m(c) = 0 for c.
-44, -1
Suppose 9 = 2*w + 3. Suppose w*c + 10 = 34. Suppose c + 0*k - 4*k + 2*k**2 - 4*k = 0. Calculate k.
2
Factor 1/4*t**4 + 21/4*t**3 + 0*t - 1/4*t**5 + 0 - 45/4*t**2.
-t**2*(t - 3)**2*(t + 5)/4
Let j(l) = l**2 - 4*l + 5. Let k(i) = 4. Let v(c) = 5. Let t(y) = 6*k(y) - 5*v(y). Let w(d) = 3*j(d) + 15*t(d). Solve w(x) = 0 for x.
0, 4
Factor 57*m**3 - 745*m - 2*m**4 - 2*m**4 + 808*m + m**4 + 123*m**2.
-3*m*(m - 21)*(m + 1)**2
Let s(h) be the second derivative of -3*h**5/20 + 537*h**4/4 - 96123*h**3/2 + 17206017*h**2/2 + 109*h - 3. Suppose s(z) = 0. What is z?
179
Let s(n) be the third derivative of -n**6/1260 + n**5/420 + 5*n**3/2 - 18*n**2. Let g(o) be the f