t t be x(f). Factor -2 - 4*s**2 + 4*s + 6*s**t - s**2 - 3*s.
(s - 1)*(s + 2)
Let r(i) be the third derivative of 1/110*i**5 + 0*i + 0*i**4 + 1/660*i**6 + 0 - 4/33*i**3 + 11*i**2. Determine f so that r(f) = 0.
-2, 1
Let z be (-1234)/(-11) - 28/154. Suppose 0 = 4*p - 0*p - z. Find h such that 38*h**3 + h**3 - 30*h**4 + 8*h - 3*h**3 + 4*h**5 + 10*h**4 - p*h**2 = 0.
0, 1, 2
Suppose -426*k + 1 = -369*k + 1. Factor 2/19*f**4 - 6/19 - 12/19*f**2 + 16/19*f + k*f**3.
2*(f - 1)**3*(f + 3)/19
Factor 532*g + 480*g**3 - 80*g**4 - 768 + 995*g + 73*g - g**5 - 1280*g**2 + 5*g**5 + 0*g**5.
4*(g - 12)*(g - 2)**4
Suppose 4*a - j = 63, 3*j = -3*a + 21 + 30. Let f = a - 14. Factor 23 - 45*s - 4*s**3 + s**3 + 5 + 21*s**f - 1.
-3*(s - 3)**2*(s - 1)
Find c, given that 20*c**2 - 29 + 11 + 12*c - 50*c**2 + 28*c**2 = 0.
3
Factor -2/5*u**2 - 2/15*u**4 + 0*u - 2/3*u**3 + 0 + 2/15*u**5.
2*u**2*(u - 3)*(u + 1)**2/15
Factor -77/4*u**3 + 27/4*u**4 + 69/4*u**2 - 1 - 15/4*u.
(u - 1)**3*(27*u + 4)/4
Suppose a - 1 = 0, 4*g + 89*a = 93*a - 4. Let n(q) be the second derivative of -1/10*q**6 - 8*q + 0*q**2 + 0*q**3 + g + 0*q**5 + 1/4*q**4. Factor n(j).
-3*j**2*(j - 1)*(j + 1)
Let g = 1399/1084 + -11/271. Factor 0 + g*k - 1/4*k**2.
-k*(k - 5)/4
Let b(d) = 2*d**2 + 5*d + 7. Let a be b(-2). Let c(z) be the first derivative of a*z**3 + 3/5*z**5 - 3*z**4 + 1 + 0*z - 3*z**2. Suppose c(r) = 0. Calculate r.
0, 1, 2
Let y(m) be the second derivative of 128/7*m**7 + 3/2*m**2 - 15/2*m**3 + 5*m - 24*m**5 + 0*m**6 + 0 + 20*m**4. Suppose y(p) = 0. Calculate p.
-1, 1/4
Let s = -61 - -125. Factor -16*u + 0*u**2 + 2*u**2 + s - 32.
2*(u - 4)**2
Let d(a) be the third derivative of -a**8/3360 + a**7/180 - 11*a**6/360 + a**5/12 + a**4/3 - 24*a**2. Let p(j) be the second derivative of d(j). Factor p(s).
-2*(s - 5)*(s - 1)**2
Let p be -36*15/(-225) + 16/10 + -2. Solve 2/11*g**p - 2/11 + 0*g = 0.
-1, 1
Let z(d) be the first derivative of -1/6*d**4 + 4/3*d + d**2 + 0*d**3 - 4. Factor z(q).
-2*(q - 2)*(q + 1)**2/3
Let r(d) = -d**2 + 8*d + 20. Let t(j) = -j**2 - j + 2. Let u(q) = -r(q) - 2*t(q). Let u(g) = 0. What is g?
-2, 4
Let q(n) be the second derivative of n**6/60 + 3*n**5/4 + 75*n**4/8 - 2*n - 13. Suppose q(k) = 0. What is k?
-15, 0
Let b = -141 + 152. Suppose 3*m = -2*g - b, -g + 9*m + 12 = 7*m. Factor -2/5 - 1/5*n + 1/5*n**g.
(n - 2)*(n + 1)/5
Determine w so that -2*w**2 + 40*w - 42*w**2 - 96 + 40*w**2 = 0.
4, 6
Let c(y) = y**2 + 6*y - 9. Let l be c(-9). Let u be l/10*(-45)/(-27). Find f, given that -u*f + f + 26 - 12 - 11 - f**2 = 0.
-3, 1
Let n(b) be the first derivative of -14 - 5/6*b**3 + 5/4*b**4 + 1/6*b**6 - 3/4*b**5 + 0*b**2 + 1/4*b. Factor n(u).
(u - 1)**4*(4*u + 1)/4
Let w(n) = 10*n**5 + 272*n**4 + 112*n**3 - 6*n + 6. Let h(f) = -10*f**5 - 270*f**4 - 112*f**3 + 7*f - 7. Let l(k) = 6*h(k) + 7*w(k). Solve l(c) = 0 for c.
-28, -2/5, 0
Suppose -18*m = -44 + 8. Let u(g) be the third derivative of 0*g + 1/120*g**5 + 1/48*g**4 - 1/12*g**3 + 0 - 1/240*g**6 + 3*g**m. Factor u(x).
-(x - 1)**2*(x + 1)/2
Find w, given that 4*w**5 + 5*w**2 - 31*w**4 - 16*w**3 + 39*w**4 - 25*w**4 = 0.
-1, 0, 1/4, 5
Suppose 0 = -11*c - 4*z + 8, -3*z - 11 = 75*c - 71*c. Factor 0 + 0*w + 3/4*w**2 - 1/4*w**5 - 7/4*w**3 + 5/4*w**c.
-w**2*(w - 3)*(w - 1)**2/4
Let o(m) be the second derivative of m**4/3 - 16*m**3/3 + 32*m**2 - 177*m. Let o(s) = 0. Calculate s.
4
Let x(c) be the third derivative of -c**6/900 + 11*c**5/225 + 5*c**4/36 - 46*c**3/45 - c**2 + 101*c. Suppose x(p) = 0. What is p?
-2, 1, 23
Let r(u) be the first derivative of -u**4/60 + 10*u + 4. Let i(a) be the first derivative of r(a). Find j, given that i(j) = 0.
0
Let s(a) = a + 30. Let r be s(3). Suppose -o + r - 30 = 0. Determine j, given that -1/3*j - 1/3*j**5 - 4/3*j**4 - 4/3*j**2 + 0 - 2*j**o = 0.
-1, 0
Let r = -388 - -1166/3. Let u(p) be the third derivative of 1/6*p**5 + 0 + 1/4*p**4 - r*p**3 - 2*p**2 + 0*p. Find x, given that u(x) = 0.
-1, 2/5
Factor -g**3 - 13/5*g - 2 + 28/5*g**2.
-(g - 5)*(g - 1)*(5*g + 2)/5
Suppose -2*j + 14 = -2*b, -4*b - 18 + 4 = 3*j. Suppose 0 = -f - 2*a + 4, 0*f = j*f + 5*a - 9. Suppose 9*v - 22*v**2 + 25*v**f - v + 4 = 0. What is v?
-2, -2/3
Let v = 353/21 + -30791/1848. Let m = v + 3/88. Factor 0 + m*n**4 - 2/11*n**2 + 2/11*n**3 - 2/11*n.
2*n*(n - 1)*(n + 1)**2/11
Suppose 37 = 6*o + 19. Let c(d) be the second derivative of -1/45*d**6 + 5/54*d**4 + 3*d + 1/90*d**5 - 1/27*d**o - 2/9*d**2 + 0. Solve c(m) = 0.
-1, -2/3, 1
Let v be 79/1501 + 146/114. Factor 2/3*h + v*h**3 + 0 + 5/3*h**2 + 1/3*h**4.
h*(h + 1)**2*(h + 2)/3
Let d be (8 + -22)*4/(-7) - 5. Let a(z) be the second derivative of 1/96*z**4 - 1/80*z**5 + 3*z + 5/48*z**d + 1/8*z**2 + 0. Solve a(w) = 0 for w.
-1, -1/2, 2
Let f(t) be the first derivative of 0*t**5 + 1/6*t**2 - 1/6*t**4 + 0*t + 5 + 1/18*t**6 + 0*t**3. Suppose f(u) = 0. Calculate u.
-1, 0, 1
Suppose -53*d + 72 + 140 = 0. Factor d*g - 3/2*g**3 + 1/2*g**2 + 2.
-(g - 2)*(g + 1)*(3*g + 2)/2
Suppose 4*i + 106 - 126 = 0. Suppose -4*c = -k + 17, 3*k + i*c - 8 = -25. Find n, given that -k + 1/4*n**3 - n + 1/4*n**2 = 0.
-2, -1, 2
Let b(g) = 17*g**2 + 62*g - 45. Let o(p) = -25*p**2 - 92*p + 67. Let i(q) = 7*b(q) + 5*o(q). Find f, given that i(f) = 0.
-5, 2/3
Let v(b) be the first derivative of b**5/15 - b**4/12 - 7*b**3/9 + 13*b**2/6 - 2*b - 158. Factor v(j).
(j - 2)*(j - 1)**2*(j + 3)/3
Let m(n) = 3*n + 20. Let t = 53 - 59. Let x be m(t). Find i such that 0*i**x + 6/5*i - 4/5 - 2/5*i**3 = 0.
-2, 1
Let j(l) be the third derivative of 2*l**7/105 - 7*l**6/30 + l**5 - 13*l**4/6 + 8*l**3/3 - 11*l**2 - l. Find w such that j(w) = 0.
1, 4
Let p be 2*(-20)/(-24)*6. Find n, given that 5*n**4 - 7 - p*n**2 + 7 - 5*n**3 = 0.
-1, 0, 2
Factor 3/4*b**2 + 12 - 6*b.
3*(b - 4)**2/4
Determine k, given that 3/2*k + 3/2*k**2 + 0 = 0.
-1, 0
Let c(z) = 42*z**5 + 124*z**4 - 232*z**3 + 2*z**2 + 70*z - 24. Let v(g) = -g**5 + g**4 - g. Let u(x) = -2*c(x) + 36*v(x). Suppose u(t) = 0. Calculate t.
-3, -2/3, 2/5, 1/2, 1
Let o(c) be the third derivative of c**6/40 + c**5/12 + c**4/12 - 3*c**2 + 10*c. Find y such that o(y) = 0.
-1, -2/3, 0
Factor 5/2*k**3 - 1/4*k**4 - 23/4*k**2 + 7/2*k + 0.
-k*(k - 7)*(k - 2)*(k - 1)/4
Suppose 33*s**2 - 2500/3 + 1/3*s**3 + 800*s = 0. Calculate s.
-50, 1
Find t such that -16/5*t**3 + 76/5*t**2 + 4*t + 0 = 0.
-1/4, 0, 5
Let b(y) be the first derivative of y**5 - 45*y**4/4 + 25*y**3 + 125*y**2/2 - 646. Factor b(u).
5*u*(u - 5)**2*(u + 1)
Let p(z) be the third derivative of -z**8/672 - z**7/105 - z**6/40 - z**5/30 - z**4/48 - z**2 + 17. Solve p(s) = 0.
-1, 0
Let i(v) be the third derivative of -v**5/24 + 25*v**4/48 + 5*v**3/2 - 67*v**2. Factor i(t).
-5*(t - 6)*(t + 1)/2
Let s(l) = 11*l**5 - 61*l**4 + 101*l**3 - 39*l**2 + 6*l. Let z(p) = 10*p**5 - 60*p**4 + 100*p**3 - 40*p**2 + 5*p. Let u(r) = -5*s(r) + 6*z(r). Factor u(a).
5*a**2*(a - 9)*(a - 1)**2
Solve 35*k**4 - 10*k**3 + 33 + 10*k - 28 + 40 - 80*k**2 = 0.
-1, 1, 9/7
Let t be 2/(-12)*7/(-14)*8. Let k(q) be the first derivative of 1/9*q**6 - t*q - 2/15*q**5 - 2 - 1/3*q**4 + 4/9*q**3 + 1/3*q**2. Factor k(i).
2*(i - 1)**3*(i + 1)**2/3
What is a in -2*a - 14*a**3 + 80 + 11*a**3 - 7*a**2 - 80 = 0?
-2, -1/3, 0
Let m(p) = -3*p**2 + 5*p + 12. Let b(k) = -2*k**2 + 31*k - 12. Let l be b(15). Let n(o) = -2*o**2 + 5*o + 13. Let z(c) = l*m(c) - 2*n(c). Factor z(u).
-5*(u - 2)*(u + 1)
Solve -10/3*w**4 - 2 - 1/3*w**5 - 10*w**3 - 25/3*w - 40/3*w**2 = 0.
-6, -1
Let 0*f**2 - 9*f**2 - 5*f**2 - 6*f**2 + 15 - 55*f = 0. Calculate f.
-3, 1/4
Let g = 827 + -821. Let a(t) be the third derivative of -1/6*t**4 + 0 + 1/3*t**3 + 0*t + 1/30*t**5 - g*t**2. Factor a(x).
2*(x - 1)**2
Let p(k) be the first derivative of -31 + 6*k**2 + 0*k - 2*k**4 - 10/3*k**3. Factor p(a).
-2*a*(a + 2)*(4*a - 3)
Factor 0 + 8/7*z**2 - 36/7*z.
4*z*(2*z - 9)/7
Suppose 10*z = 7*z + 6. Factor -4 + 8*h**2 - z - 1 + 14*h + 3.
2*(h + 2)*(4*h - 1)
Let i be ((-8)/(-45))/((-72)/27*18/(-120)). Factor 0*h - i*h**2 + 0 + 20/9*h**4 + 16/9*h**3.
4*h**2*(h + 1)*(5*h - 1)/9
Let z(p) = -p**2 - 8*p + 3. Let s(d) = 12*d**2 + 88*d - 32. Let x(u) = 6*s(u) + 68*z(u). Solve x(t) = 0.
1, 3
Let r(c) be the second derivative of 17*c + 11/2*c**4 + 121*c**3 + 0 + 1/10*c**5 + 1331*c**2. Solve r(q) = 0.
-11
Factor 0*n + 5/4*n**2 - 5.
5*(n - 2)*(n + 2)/4
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