1)/9
Let g = -77 - -81. Let 1/3*n**2 - 1/3*n**3 + 0 + 1/3*n - 1/3*n**g = 0. Calculate n.
-1, 0, 1
Let a(x) be the third derivative of 9*x**6/40 + 7*x**5/5 + 21*x**4/8 + x**3 + 5*x**2 - x. Determine r so that a(r) = 0.
-2, -1, -1/9
Let i be 46/(-161) + 68/42. Factor -i*p**2 - 7/6*p + 1/6*p**5 - 1/3 + 1/3*p**4 - 1/3*p**3.
(p - 2)*(p + 1)**4/6
Let f be 5/((-10)/(-6)) - 3. Let o(m) be the second derivative of -1/6*m**4 + 0*m**5 + 0 + 1/15*m**6 + m + 0*m**3 + f*m**2. Factor o(r).
2*r**2*(r - 1)*(r + 1)
Let l be (-1)/((0 - -1)/(-6)). Suppose 90 + 27 = 5*j + 3*r, -5*j - 4*r = -121. Factor l*g**2 - 13*g - j*g**3 - 2*g**4 + 13*g - 10*g**4.
-3*g**2*(g + 2)*(4*g - 1)
Let t(n) be the third derivative of -n**8/60480 - n**7/5040 - n**6/1080 - n**5/30 - 2*n**2. Let d(p) be the third derivative of t(p). Factor d(q).
-(q + 1)*(q + 2)/3
Suppose 7 = 3*x - 2*a, -4*x - x + a = -14. Let w(q) be the third derivative of 1/330*q**6 + 0*q + 0*q**4 + 0 - q**2 - 1/33*q**x + 1/110*q**5. Factor w(z).
2*(z + 1)**2*(2*z - 1)/11
Let m be (-48)/(-126) + (-18)/(-14) + -1. Let v = 79/15 - 23/5. Let 4/3*q**2 - v - m*q = 0. Calculate q.
-1/2, 1
Let g be (-2)/(-12)*3*2/3. Factor k**3 + 2/3 - g*k**4 - 1/3*k**2 - k.
-(k - 2)*(k - 1)**2*(k + 1)/3
Let b(c) = -12*c**3 - 9*c**2 + 12*c + 9. Let l(k) = -3*k**3 - 2*k**2 + 3*k + 2. Let o(f) = -4*b(f) + 15*l(f). Factor o(q).
3*(q - 1)*(q + 1)*(q + 2)
Let i(s) be the second derivative of 7*s**5/90 - 8*s**4/27 + 11*s**3/27 - 2*s**2/9 - 22*s. Factor i(z).
2*(z - 1)**2*(7*z - 2)/9
Let n be (2/(-30))/((-1)/6). Factor -n*f + 2/5*f**2 + 2/5*f**3 - 2/5.
2*(f - 1)*(f + 1)**2/5
Let y(f) = f + 8. Let j be -7 + 1/1 + 1. Let a be y(j). Factor a + t**2 - 3 - t.
t*(t - 1)
Suppose -a + 48 = -40. Let u = a + -260/3. Factor 4/3*y + 0 - u*y**2 + 1/3*y**3.
y*(y - 2)**2/3
Let l be 14/(-91) - (-72)/(-39) - -7. Let q(u) be the third derivative of 0*u**3 + 3*u**2 + 1/300*u**6 + 0*u**l + 0 + 1/525*u**7 + 0*u**4 + 0*u. Factor q(g).
2*g**3*(g + 1)/5
Let q = 197 - 1377/7. Factor 8/7*p**3 - 6/7*p + 0*p**2 - q.
2*(p - 1)*(2*p + 1)**2/7
Let p be 0 + ((-20)/(-4) - 2 - 3). Let y(a) be the second derivative of p*a**2 + 2*a - 1/10*a**5 + 2/21*a**3 + 5/42*a**4 + 0. Factor y(z).
-2*z*(z - 1)*(7*z + 2)/7
Let b(d) be the second derivative of -d**6/50 + d**5/100 + 2*d**4/15 + 2*d**3/15 - 5*d. Factor b(p).
-p*(p - 2)*(p + 1)*(3*p + 2)/5
Let k be 210/55 + -4 + (-46)/(-11). Let l(u) be the third derivative of -1/360*u**6 - 3*u**2 + 1/180*u**5 - 1/18*u**3 + 0*u + 0 + 1/72*u**k. Factor l(i).
-(i - 1)**2*(i + 1)/3
Let c(h) = -14*h**3 + 12*h**2 + 12*h. Let o(q) = -5*q**3 + 4*q**2 + 4*q. Let r(x) = 3*c(x) - 10*o(x). Find y such that r(y) = 0.
-1/2, 0, 1
Suppose -2*g = 2*w - 6, -5 = -3*g - 6*w + w. Solve -5*j**2 + 41*j**2 - 22*j**4 - 2*j**4 - 18*j**g - 16 - 24*j + 46*j**3 = 0 for j.
-2, -2/3, 1
Factor -2/5*n**4 + 0 + 6/5*n**3 - 4/5*n**2 + 0*n.
-2*n**2*(n - 2)*(n - 1)/5
Let n(x) be the first derivative of x**4/38 + 8*x**3/57 + 5*x**2/19 + 4*x/19 - 21. Find o such that n(o) = 0.
-2, -1
Let n(z) be the third derivative of 1/150*z**5 - 1/100*z**6 + 0 + 3*z**2 - 1/840*z**8 + 0*z**3 + 0*z**4 + 1/175*z**7 + 0*z. Find g, given that n(g) = 0.
0, 1
Let w = 28 + -26. Factor 1/2*f + 3/2*f**3 - 3/2*f**w - 1/2*f**4 + 0.
-f*(f - 1)**3/2
Let j = -173/7 + 25. Determine z, given that -j*z - 2/7 + 2/7*z**2 + 2/7*z**3 = 0.
-1, 1
Let z(t) be the first derivative of 3*t**5/5 + 3*t**4/2 - 3*t**2 - 3*t + 9. Factor z(m).
3*(m - 1)*(m + 1)**3
Suppose 0 = -12*z - 12*z + 5*z. Suppose -1/3*o**3 + 5/6*o**4 - 1/2*o**5 + 0 + 0*o**2 + z*o = 0. Calculate o.
0, 2/3, 1
Let p = -9/152 - -179/456. Let -2/3*k**2 - 1/6*k + 1/3*k**4 + 1/3 - 1/6*k**5 + p*k**3 = 0. Calculate k.
-1, 1, 2
Suppose 5*v = 3*t - 6, t = 5*v - 1 + 3. Find f such that -1/2*f**4 - 1/2*f**5 + 0 + 3/2*f**3 + f + 5/2*f**t = 0.
-1, 0, 2
Let w(d) = -481*d**3 + 32*d**2 + 84*d + 7. Let j(g) = -480*g**3 + 33*g**2 + 84*g + 6. Let b(u) = 5*j(u) - 6*w(u). Factor b(k).
3*(2*k - 1)*(9*k + 2)**2
Let l(s) be the first derivative of -s**6/2 + 3*s**5/5 + 3*s**4/4 - s**3 - 10. Factor l(k).
-3*k**2*(k - 1)**2*(k + 1)
Let m(u) be the first derivative of -u**5/390 + u**3/39 - 5*u**2/2 + 4. Let h(p) be the second derivative of m(p). Factor h(z).
-2*(z - 1)*(z + 1)/13
Let i = -9 + 37/4. Factor 0*x + i*x**3 - 1/4*x**2 + 0.
x**2*(x - 1)/4
Let u(d) = -6*d. Let p be u(-2). Let z be (-238)/51*p/(-14). Let 0*s - 2/5*s**2 + 0 + 2/5*s**z + 0*s**3 = 0. What is s?
-1, 0, 1
Let i(f) be the first derivative of -45*f**4/2 - 38*f**3 - 64*f**2/5 - 8*f/5 + 15. Factor i(z).
-2*(z + 1)*(15*z + 2)**2/5
Let u(i) be the first derivative of i**5/150 - i**4/10 + 3*i**3/5 - 2*i**2 + 1. Let v(l) be the second derivative of u(l). Find f such that v(f) = 0.
3
Let -6/5*x - 1/5*x**2 - 9/5 = 0. What is x?
-3
Factor -3*x**3 + 0*x + x**3 - 2*x - 4*x**2.
-2*x*(x + 1)**2
Let z be 2/19 - 2244/(-3230). Determine j so that 0 + 8/5*j**3 + z*j + 2/5*j**4 + 2*j**2 = 0.
-2, -1, 0
Solve 457*o**3 + 2*o**2 - 2 + 0 - o - 456*o**3 = 0 for o.
-2, -1, 1
Let p(o) be the second derivative of o**7/105 - o**6/50 + o**4/60 - 3*o. Factor p(u).
u**2*(u - 1)**2*(2*u + 1)/5
Factor -3*z + 6*z**2 - 4*z**3 + 5*z**3 + 12*z.
z*(z + 3)**2
Solve 4/5*g**2 + 2/5*g**3 + 0*g + 0 = 0 for g.
-2, 0
Let a(m) be the third derivative of -m**2 + 0*m + 1/96*m**6 + 0*m**4 - 1/280*m**7 - 1/120*m**5 + 0 + 0*m**3. Let a(v) = 0. What is v?
0, 2/3, 1
Suppose -3 = -2*p - 11. Let u be (p - -11)*(2 - 1). What is z in -2*z**2 + u*z**3 - 3*z**4 - z**4 - z**4 = 0?
0, 2/5, 1
Let k = 8 + -8. Suppose k*j = -3*j. Factor -6 + 4*z + 6*z - z - 3*z**2 + j.
-3*(z - 2)*(z - 1)
Let s(m) be the first derivative of -m**4/4 + m**3/3 - 6. What is w in s(w) = 0?
0, 1
Factor 18/7 - 16/7*i**3 - 48/7*i + 44/7*i**2 + 2/7*i**4.
2*(i - 3)**2*(i - 1)**2/7
Let w(l) be the third derivative of -l**8/30240 + l**6/3240 + 3*l**4/8 - 4*l**2. Let g(s) be the second derivative of w(s). Determine v so that g(v) = 0.
-1, 0, 1
Let s(i) be the second derivative of -i**7/21 - i**6/5 - 3*i**5/10 - i**4/6 - 3*i. Factor s(b).
-2*b**2*(b + 1)**3
Let m(z) = -4*z**2 + 2*z - 2. Let p(w) = 17*w**2 - 7*w + 8. Let d(i) = 9*m(i) + 2*p(i). Find r, given that d(r) = 0.
1
Let q be ((-14)/(-21))/((-2)/(-4)) + -1. Find a, given that 1/3 + 0*a**2 - 2/3*a - q*a**4 + 2/3*a**3 = 0.
-1, 1
Factor -3*s - s**5 - 16*s**2 - 12*s**3 - 16*s**2 + 22*s**2 - 6*s**4.
-s*(s + 1)**3*(s + 3)
Let i = 5455/7 + -779. Solve -2/7*j + 0 - i*j**2 = 0.
-1, 0
Let p(r) be the second derivative of -r**4/48 + 8*r. Factor p(n).
-n**2/4
Let a(u) be the third derivative of -1/36*u**4 + 1/60*u**5 + 0 + 0*u - 1/360*u**6 + 0*u**3 - 2*u**2. Factor a(y).
-y*(y - 2)*(y - 1)/3
Factor 0 - 1/5*a**2 - 4/5*a + 1/5*a**4 + 4/5*a**3.
a*(a - 1)*(a + 1)*(a + 4)/5
Let y(v) be the third derivative of 1/20*v**5 + 1/2*v**3 + 0*v + 0 + 2*v**2 + 1/4*v**4. Let y(t) = 0. Calculate t.
-1
Suppose 0 = 4*f - 1 + 5. Let n be 2/(-10) + f/(-5). Factor -1/2*y + n - 1/2*y**2.
-y*(y + 1)/2
Let v(q) be the first derivative of -q**4 - 13. Solve v(z) = 0 for z.
0
Factor 3*c + 12/5*c**2 + 6/5 + 3/5*c**3.
3*(c + 1)**2*(c + 2)/5
Let h(f) be the second derivative of 3*f**4/5 - 8*f**3/3 + 8*f**2/5 + 4*f - 5. Factor h(q).
4*(q - 2)*(9*q - 2)/5
Let h(j) be the third derivative of j**6/780 + 7*j**5/390 + j**4/26 - 41*j**2. Factor h(k).
2*k*(k + 1)*(k + 6)/13
Let u(a) be the second derivative of -a**6/240 - a**5/80 - a**3/6 - a. Let y(f) be the second derivative of u(f). Factor y(x).
-3*x*(x + 1)/2
Suppose 2 = p - 1. Factor -3*h**5 - 16*h**2 + 3*h**4 - 2*h**p + 5*h**3 + 13*h**2.
-3*h**2*(h - 1)**2*(h + 1)
Let p be ((-30)/9)/5*-6. Suppose -p*j + f + 11 = 0, -3 = -5*j + f + 11. Factor -9*t + t - 4 + 4*t**j - 5*t**2 - 5*t**3.
-(t + 1)*(t + 2)**2
Let w(h) be the third derivative of 1/20*h**5 + 0*h + h**3 - h**2 - 9/8*h**4 + 0 - 3/70*h**7 + 23/40*h**6 - 1/8*h**8. Let w(i) = 0. Calculate i.
-1, 2/7, 1/2, 1
Factor 1 + y - 1/4*y**2 - 1/4*y**3.
-(y - 2)*(y + 1)*(y + 2)/4
Let s(j) = j + 9. Let k be s(-6). Factor 3*u**2 - 9*u**4 + 13*u**3 - 2*u - u**k - 4*u.
-3*u*(u - 1)**2*(3*u + 2)
Let j = 32 + -30. Factor -1/3*i**j - 2/3*i + 0.
-i*(i + 2)/3
Let p = -741 - -5191/7. Determine n, given that 26/7*n**2 - p*n + 0 - 40/7*n**3 = 0.
0, 1/4, 2/5
Let z(q) be the first derivative of -2*q**3/7 - 10*q**2/7 - 6*q/7 