k + 8/9 = 0.
-2, -1
Suppose -3*d = 3*t - 5*d - 54, 5*t - 4*d = 90. Let j be 48/t + -1 + 1. Factor 0 - 2*u**3 + 4/9*u**2 - 10/9*u**5 + j*u**4 + 0*u.
-2*u**2*(u - 1)**2*(5*u - 2)/9
Let m = 67/180 + -3/20. Let g = -289/18 - -33/2. Factor g*i + m*i**2 + 2/9.
2*(i + 1)**2/9
Let r(d) be the third derivative of 0*d + d**2 + 1/6*d**3 - 1/420*d**7 + 0*d**6 + 0 + 0*d**4 + 1/60*d**5. Let q(j) be the first derivative of r(j). Factor q(b).
-2*b*(b - 1)*(b + 1)
Let b(s) = -3*s**4 - 12*s**3 + 3*s + 3. Let w(g) = g**3 - g - 1. Let m(r) = b(r) + 3*w(r). Factor m(p).
-3*p**3*(p + 3)
Suppose 0 = 4*b - 6*b - 12. Let h be (-14)/b - 14/(-21). Factor -1/4*z**4 + 1/4*z**2 + 0 + 0*z + 0*z**h.
-z**2*(z - 1)*(z + 1)/4
Let 8/3*n + 2/3*n**2 + 0 = 0. Calculate n.
-4, 0
Factor 2/3*f**2 + 2*f + 4/3.
2*(f + 1)*(f + 2)/3
Suppose -9*o + 48 = 12. Let c = 5/16 - -3/16. Factor -1/2*l**3 + 0 - 1/2*l**o + c*l + 1/2*l**2.
-l*(l - 1)*(l + 1)**2/2
Let m(o) be the third derivative of 0*o**3 + 0*o**4 - 1/420*o**6 + 0 + 0*o - 1/735*o**7 + 1/105*o**5 + 5*o**2. Find q such that m(q) = 0.
-2, 0, 1
Let i be ((-160)/(-100))/(2/5). Let f(p) be the first derivative of 0*p - 3/16*p**i - 3/8*p**2 + 3 + 1/2*p**3. Factor f(k).
-3*k*(k - 1)**2/4
Let z(n) be the third derivative of -1/24*n**4 + 0*n**3 - 1/60*n**5 + 0*n + 0 - 2*n**2. Factor z(a).
-a*(a + 1)
Let r(x) = 5*x**3 + 17*x**2 - 28*x + 3. Let y(z) = -10*z**3 - 35*z**2 + 55*z - 5. Let k(p) = -5*r(p) - 3*y(p). What is i in k(i) = 0?
-5, 0, 1
Suppose a + 0 = 2. Factor -7*g + 3*g - 3*g**2 - 2 + g**a.
-2*(g + 1)**2
Suppose -3*v - 8 = -x, 0*v = x - 4*v - 10. Factor 2*z**x + 0*z**2 - 4*z**2 + 3 - 5 - 5*z.
-(z + 2)*(2*z + 1)
Let v(x) = 2 - 8*x**2 + 12*x**2 + 3*x**4 - 2*x**4 - x**3. Let y(c) = -3*c**4 + 2*c**3 - 9*c**2 - 5. Let q(i) = -5*v(i) - 2*y(i). Factor q(j).
j**2*(j - 1)*(j + 2)
Factor -6/5*z**2 - 6/5*z - 2/5*z**3 - 2/5.
-2*(z + 1)**3/5
Let n = -3 - -6. Let o(x) be the third derivative of 4/3*x**n + 0 + 2*x**2 + 77/30*x**5 - 49/60*x**6 + 0*x - 8/3*x**4. Solve o(g) = 0.
2/7, 1
Suppose -3*y + 5 = -1. Let k(p) be the first derivative of 3/5*p**5 - p + 3/2*p**y - 1/2*p**4 - 2/3*p**3 - 1/6*p**6 - 1. Factor k(q).
-(q - 1)**4*(q + 1)
Let -11/3*d - 1/3*d**2 + 0 = 0. What is d?
-11, 0
Let x(v) be the third derivative of -v**5/20 + 5*v**4/4 - 25*v**3/2 + 2*v**2. Factor x(d).
-3*(d - 5)**2
Let s(b) be the first derivative of -b**5/10 - b**4/12 + 2*b**3/3 - b**2 + 3. Let i(x) be the second derivative of s(x). Factor i(f).
-2*(f + 1)*(3*f - 2)
Let o = -67 - -739/11. Let m = 19/44 - o. Factor -1/4*y + 0 - m*y**2.
-y*(y + 1)/4
Let d(p) = -p**3 - p**2 + p - 1. Let t(i) = -2*i**3 - 2*i**2 + 2*i - 4. Let r(n) = -6*d(n) + 2*t(n). Suppose r(w) = 0. Calculate w.
-1, 1
Let s(k) be the first derivative of 0*k**3 - 2 + 0*k**4 + 0*k**5 - 1/2*k**2 + 0*k - 1/600*k**6. Let g(d) be the second derivative of s(d). Solve g(c) = 0.
0
Let w(s) be the second derivative of 2*s + 1/6*s**4 - 1/3*s**3 + 0*s**2 + 0. Factor w(n).
2*n*(n - 1)
Suppose 5*i - 3*i - 2*j = 14, -4*i = 3*j. Let h be i/12 + (-2 - -2). Solve 1/4*p**2 + h*p**3 - 1/4*p - 1/4 = 0 for p.
-1, 1
Suppose 4*t - 5*n = 69, 0 = -2*t - 0*n + n + 33. Let b = t - 13. Let 0 + 3/2*d - b*d**2 + 3/2*d**3 = 0. What is d?
0, 1
Let h(c) be the first derivative of 2/3*c - 1/9*c**3 - 2 - 1/6*c**2. Factor h(q).
-(q - 1)*(q + 2)/3
Let t(b) be the first derivative of -4 + 3*b**2 + 135*b**4 + 224*b**6 + 1392/5*b**5 + 0*b + 31*b**3. Let t(w) = 0. What is w?
-2/7, -1/4, 0
Let l = -2428/85 - -144/5. Determine p, given that 10/17*p - 14/17*p**2 + l = 0.
-2/7, 1
Let h(b) = 2*b - 5*b**2 - 6*b + 1 + 6*b**2. Let a(f) = -f**2 + 5*f - 1. Let x be (-2 + 5)/(0 + 1). Let v(n) = x*h(n) + 2*a(n). Factor v(s).
(s - 1)**2
Let l(u) be the second derivative of -3/20*u**5 + 0 - 1/6*u**3 + u + 0*u**2 + 1/30*u**6 + 1/4*u**4. Factor l(a).
a*(a - 1)**3
Let j = -164 - -164. Let n(i) be the second derivative of i - 1/21*i**3 + j + 0*i**2 - 1/70*i**5 - 1/21*i**4. Factor n(v).
-2*v*(v + 1)**2/7
Let x(h) be the first derivative of -6*h + 3/4*h**4 + 15/2*h**2 + 2 - 4*h**3. Factor x(d).
3*(d - 2)*(d - 1)**2
Suppose 0 = -n + 2, 5*n - 22 = 2*k - 6*k. Let -k*l + 3 - 9/4*l**2 = 0. What is l?
-2, 2/3
Let n(k) be the second derivative of k**5/110 + k**4/33 + k**3/33 - 40*k. Let n(a) = 0. Calculate a.
-1, 0
Let d = -1/55 - -59/220. Factor 0 + 1/4*l**2 - d*l**3 + 1/2*l.
-l*(l - 2)*(l + 1)/4
Let x(t) be the first derivative of -t**6/8 - t**5/20 + t**4/8 - 7. Solve x(i) = 0 for i.
-1, 0, 2/3
Let f(o) = 10*o**2 - 10*o - 10. Let r(z) = -11*z**2 + 10*z + 9. Let d(b) = 6*f(b) + 5*r(b). Factor d(j).
5*(j - 3)*(j + 1)
Let v(i) be the first derivative of 2/3*i**3 + 12*i**4 + 32/5*i**5 - 6*i**2 + 2*i - 4. Suppose v(q) = 0. What is q?
-1, 1/4
Let w(m) be the first derivative of -2/15*m**3 - 6/5*m - 3 + 4/5*m**2. Find u such that w(u) = 0.
1, 3
Let x be -3 + 3 + (58 - 3). Let p = x + -219/4. Factor p*k**2 + 0 + 1/4*k.
k*(k + 1)/4
Let m be (-2)/6 - 22/(-33). Find o, given that -1/3*o**2 + 0 + 1/3*o**5 + m*o**4 + 0*o - 1/3*o**3 = 0.
-1, 0, 1
Suppose 2 = -3*q + 14. Factor 3*u**4 - 3*u**4 + 2*u + 4*u**2 - 2*u**4 - q*u**3 + 2*u**5 - 2.
2*(u - 1)**3*(u + 1)**2
Suppose 12*v**2 - 4*v - 8*v**2 + 6*v**2 + 14*v**3 = 0. Calculate v.
-1, 0, 2/7
Find q such that -4*q**2 + 3 + 2*q**2 + 3*q + 3 - q**2 = 0.
-1, 2
Let k(j) be the third derivative of j**8/588 - j**6/70 + 2*j**5/105 + 4*j**2. Factor k(p).
4*p**2*(p - 1)**2*(p + 2)/7
Let j = 59 + -57. Let y be (1 + 0)/((-4)/(-2)). Factor 0*l + y*l**j - 1/2.
(l - 1)*(l + 1)/2
Let x(c) be the third derivative of c**5/90 - c**4/18 - 4*c**2. Factor x(k).
2*k*(k - 2)/3
Let m = -71218/1305 - 7/261. Let p = 55 + m. Let -2/5*v**2 + p + 0*v = 0. Calculate v.
-1, 1
Let v(n) be the third derivative of n**7/7 - 7*n**6/15 + 11*n**5/30 + n**4/6 - 5*n**2. Factor v(m).
2*m*(m - 1)**2*(15*m + 2)
Determine b so that 0 + 4/5*b**2 + 16/5*b = 0.
-4, 0
Let i = -31/63 + 5/7. Let l = 12 + -12. Suppose 0 + i*f**3 - 2/9*f**2 + l*f = 0. What is f?
0, 1
Let g be 1/8 - (-517)/88. Factor 10/3*q - g*q**3 - 2*q**2 - 2/3.
-2*(q + 1)*(3*q - 1)**2/3
Let n(s) be the second derivative of 3*s - 1/42*s**4 + 0 + 1/21*s**3 + 2/7*s**2. Factor n(y).
-2*(y - 2)*(y + 1)/7
Let g = 7 - 3. Suppose -3*d + 2 = -g*i - 29, 3 = -d - 2*i. Factor -8*n**4 - 4*n**3 - 2*n**2 - 2*n**d + 2*n**4 - 2*n**3.
-2*n**2*(n + 1)**3
Let o(p) = -4*p**2 + 6*p + 6. Let j(l) = -2*l + 0*l - 5 - l - 3*l + 5*l**2. Let s(n) = -4*j(n) - 3*o(n). Factor s(u).
-2*(u - 1)*(4*u + 1)
Suppose 2*q - 6 = -q. Let a = 52/3 + -17. Factor -a*u**q + u - 2/3.
-(u - 2)*(u - 1)/3
Let x(i) be the third derivative of i**6/360 + i**5/180 - 2*i**2 - 6. Factor x(s).
s**2*(s + 1)/3
Let l(q) be the second derivative of -q**7/42 - 4*q**6/15 - 5*q**5/4 - 19*q**4/6 - 14*q**3/3 - 4*q**2 + 40*q. Determine s, given that l(s) = 0.
-2, -1
Suppose -2*f - 3 = -9. Let p(u) be the second derivative of 2*u - 1/6*u**4 - 1/42*u**7 + 1/2*u**2 + 0 - 1/6*u**f + 1/10*u**5 + 1/30*u**6. Factor p(t).
-(t - 1)**3*(t + 1)**2
Let t = 31/5 - 6. Let k(l) be the first derivative of t*l**5 + l + 1 - 2/3*l**3 + 0*l**2 + 0*l**4. Factor k(u).
(u - 1)**2*(u + 1)**2
Let c(g) = -5*g**4 - 24*g**3 - 19*g**2 + 4*g - 4. Let d(k) = 20*k**4 + 95*k**3 + 75*k**2 - 15*k + 15. Let x(m) = -15*c(m) - 4*d(m). What is s in x(s) = 0?
-3, -1, 0
Let f(r) be the first derivative of -3*r**4/2 - 5*r**3 - 6*r**2 - 3*r + 22. Factor f(i).
-3*(i + 1)**2*(2*i + 1)
Let w be (-3)/(-3 + 2/1). Let o = -2 + 2. Solve 2*u + o*u + 2*u**2 - 2 - 6*u**3 + 4*u**w = 0 for u.
-1, 1
Let t be (-1)/(-1 + 25/(-5))*3. Suppose -1 + 3/2*d**2 + t*d = 0. Calculate d.
-1, 2/3
Factor -5*t**3 + t**4 + t + 3*t**2 + 4*t**3 + 4*t**3.
t*(t + 1)**3
Suppose 4*a = 1 + 7. Suppose 12 = 2*l + a*o, 0*l - 14 = l - 4*o. Find g such that g - 3*g + 0 + 1 + g**l = 0.
1
Let t(f) be the third derivative of f**9/120960 + f**8/40320 + f**5/30 + 2*f**2. Let w(s) be the third derivative of t(s). Factor w(r).
r**2*(r + 1)/2
Let q be 2/8 - 33/(-12). What is v in 2*v**q - 4*v - 2 + 2*v + 2*v**2 + 0*v = 0?
-1, 1
Let q be (-79)/40 + 6/3. Let b(c) be the second derivative of q*c**5 - 2*c + 0 + 1/8*c**4 + 1/4*c**3 + 1/4*c**2. Factor b(d).
(d + 1)**3/2
Let z(i) be the second derivative of -i + 1/24*i**4 - 1/3*i**3 + 0 + i**2. Factor z(f).
(f - 2)**2/2
Factor 10/3*z**2 -