t r(d) = 3*d**2 + 1. Let g(f) = 4*j(f) - r(f). Factor g(q).
(q + 1)*(q + 3)
Let f(l) be the second derivative of -l**4/12 - l**3 + 7*l**2/2 - 24*l. Factor f(i).
-(i - 1)*(i + 7)
Let w(d) be the third derivative of 0 + 0*d**3 - 1/72*d**4 - 1/315*d**7 + 0*d**6 - 2*d**2 + 1/90*d**5 + 0*d + 1/1008*d**8. Let w(y) = 0. Calculate y.
-1, 0, 1
Let p(q) = 21*q**4 - 39*q**3 - 18*q**2 - 18. Let b(g) = 6*g**4 - 11*g**3 - 5*g**2 - 5. Let n(s) = -18*b(s) + 5*p(s). Factor n(u).
-3*u**3*(u - 1)
Suppose -25 = 59*y - 64*y. Let h(x) be the first derivative of -x**4 - 2/5*x**y + 0*x**2 - 2/3*x**3 + 0*x + 3. Factor h(z).
-2*z**2*(z + 1)**2
Factor 4 - 3*r + 10*r**2 + 4*r**3 - 14*r**2 - r.
4*(r - 1)**2*(r + 1)
Suppose -2*x = -x + 9. Let g = 14 + x. Factor -3*t**4 + 7*t**4 + 2*t**g + t**2 - 2*t - 5*t**2.
2*t*(t - 1)*(t + 1)**3
Let c = -523/10 - -52. Let j = 19/30 + c. Suppose 1/3 + 2/3*l + j*l**2 = 0. Calculate l.
-1
Factor -4/5*v - 4/5*v**2 + 8/5.
-4*(v - 1)*(v + 2)/5
Let p(c) be the first derivative of 1/15*c**3 + 1/5*c - 1 - 1/5*c**2. Factor p(j).
(j - 1)**2/5
Let q(r) be the second derivative of -3*r**5/20 + r**4/4 + r**3/2 - 3*r**2/2 - 13*r. Solve q(a) = 0.
-1, 1
Factor 3*h - 5*h**2 + 4*h**2 + 1 + 2*h**2 + 1.
(h + 1)*(h + 2)
Let v(f) = f**3 - f**2 - 2*f + 2. Let p be v(0). Determine h, given that 21/5*h**p + 16/5*h + 9/5*h**3 + 4/5 = 0.
-1, -2/3
Let s = 2/43 + 33/215. Factor -1/5*p**5 + 0 + 1/5*p**3 - 1/5*p**4 + 0*p + s*p**2.
-p**2*(p - 1)*(p + 1)**2/5
Suppose -5 = 6*a - 17. Let r(t) be the second derivative of 0 + a*t - 1/10*t**4 + 1/3*t**3 - 2/5*t**2 + 1/75*t**6 - 1/50*t**5. Factor r(g).
2*(g - 1)**3*(g + 2)/5
Let i(j) = -5*j**3 - 17*j**2 - 7*j + 7. Let r(s) = -3*s**3 - 11*s**2 - 5*s + 5. Let b(x) = 5*i(x) - 7*r(x). Factor b(z).
-4*z**2*(z + 2)
Let t(z) be the second derivative of 3*z**6/140 + z**5/10 + 4*z**4/21 + 4*z**3/21 - 9*z**2/2 + 5*z. Let a(h) be the first derivative of t(h). Factor a(x).
2*(x + 1)*(3*x + 2)**2/7
Let o(c) = c - 5. Let x be o(5). Let t be -3*((-4)/6 - x). Find p such that -2*p**t - 4*p**5 - 2*p + 0*p**2 + 4*p**3 + 2*p**3 + 2*p**4 = 0.
-1, -1/2, 0, 1
Let j(g) be the second derivative of g**7/91 + 4*g**6/195 + g**5/130 + 7*g. Factor j(n).
2*n**3*(n + 1)*(3*n + 1)/13
Let x be (-3)/(-2) + (-2)/(-4). Suppose -4*c + x*c = -10. Factor 7*i - 2*i + c - 3 - 2*i + i**2.
(i + 1)*(i + 2)
Suppose 4*d = -4*c + 16, 5*c - 16 = 2*d - 3. Let v be (-68)/(-51)*c/10. Factor 2/5*q**3 + 0 - 2/5*q - 2/5*q**4 + v*q**2.
-2*q*(q - 1)**2*(q + 1)/5
Suppose 0 = -3*j + 8 + 4. Suppose j + 2 = 3*a. Factor -2*d**2 + 0*d - 3*d**a + 7*d**2 + 2*d.
2*d*(d + 1)
Let g be (14/4)/((-6)/(-24)). Suppose -k = -7 + 4. Factor b + 10*b**k - g*b**2 + b + 2*b.
2*b*(b - 1)*(5*b - 2)
Let v(b) be the second derivative of b**7/105 + 4*b**6/75 + 2*b**5/25 - b**4/15 - b**3/3 - 2*b**2/5 + 12*b. Factor v(t).
2*(t - 1)*(t + 1)**3*(t + 2)/5
Let u(x) = -2*x - 1. Let d be u(1). Let w = d - -5. Factor -1/3*t**4 + 0*t + 1/3*t**3 - 1/3*t**5 + 0 + 1/3*t**w.
-t**2*(t - 1)*(t + 1)**2/3
Let h be 58/5 + 6/(-10). Let b = h + -7. Factor -2/9*i - 4/9*i**2 + 14/9*i**3 - 8/9*i**b + 0.
-2*i*(i - 1)**2*(4*i + 1)/9
Suppose -1906 + 1906 = -11*z. Factor z*m**3 + 0*m - 3/5*m**2 + 0 + 3/5*m**4.
3*m**2*(m - 1)*(m + 1)/5
Let q(p) = -5*p**5 - 7*p**4 - 8*p**3 - 2*p**2. Let s(l) = 21*l**5 + 27*l**4 + 33*l**3 + 9*l**2. Let k(f) = 9*q(f) + 2*s(f). Suppose k(x) = 0. Calculate x.
-2, -1, 0
Let z(o) be the first derivative of -7*o**5/5 - o**4 + o**3 - 5*o + 4. Let p(v) = -3*v**4 - 2*v**3 + v**2 - 2. Let w(c) = 5*p(c) - 2*z(c). Factor w(a).
-a**2*(a + 1)**2
Let a(c) be the third derivative of c**10/604800 + c**9/241920 - c**5/15 + c**2. Let f(w) be the third derivative of a(w). Determine t, given that f(t) = 0.
-1, 0
Let d(f) be the second derivative of -f**6/165 + f**4/66 - 16*f. What is s in d(s) = 0?
-1, 0, 1
Factor f**2 - 32 + 32 + f**2.
2*f**2
Factor 0 + 1/3*m - 1/3*m**3 + 1/3*m**4 - 1/3*m**2.
m*(m - 1)**2*(m + 1)/3
Let n be (-36)/(-8) - (-2)/4. Let b(m) be the third derivative of -1/30*m**n + 0*m**3 + 0 - 2*m**2 + 0*m**4 + 0*m. Let b(q) = 0. What is q?
0
Let 4*y**4 + 48*y**2 + 102 + 160*y + 84*y**2 - 38 + 40*y**3 = 0. What is y?
-4, -1
Let h(g) be the second derivative of -1/15*g**3 + 1/105*g**7 + 4*g + 0 - 2/75*g**6 + 0*g**2 + 0*g**5 + 1/15*g**4. Factor h(x).
2*x*(x - 1)**3*(x + 1)/5
Let y(w) be the first derivative of -2*w**6/3 + 8*w**5/5 + 2*w**4 - 32*w**3/3 + 14*w**2 - 8*w + 19. Find f, given that y(f) = 0.
-2, 1
Let n(r) be the first derivative of r**5/25 + r**4/10 + r**3/15 + 2*r - 3. Let x(s) be the first derivative of n(s). Factor x(l).
2*l*(l + 1)*(2*l + 1)/5
Let o(i) = -i**2 - 5*i + 6. Let h be o(-6). Suppose h - 5/2*r**4 + 5/2*r**2 - 2*r**5 + 1/2*r + 3/2*r**3 = 0. What is r?
-1, -1/4, 0, 1
Let s(l) = -3*l + 81. Let q be s(26). Determine m so that 75/7*m**5 + 12/7*m**q + 0*m + 0 - 60/7*m**4 + 0*m**2 = 0.
0, 2/5
Let h(i) be the second derivative of -i**4/44 - 5*i**3/33 - 3*i**2/22 - 8*i. Factor h(s).
-(s + 3)*(3*s + 1)/11
Let v(t) = 6*t**3 - 5*t**2 - 17. Let k be 70/6 - 3/(-9). Let y(m) = k + 0*m**3 + 2*m**2 - 6 - 2*m**3. Let b(s) = 6*v(s) + 17*y(s). Factor b(r).
2*r**2*(r + 2)
Let l(i) = -2 + 3*i - 4 + 3*i**2 - 3*i + 3*i. Let n(p) = -p**2 - p + 1. Let x(g) = l(g) + 6*n(g). Determine s, given that x(s) = 0.
-1, 0
Let z(k) = -5*k + 4*k**2 - 5*k**2 - 2*k + 2. Let b be z(-7). Find m, given that m**2 - m - m - 3*m**b = 0.
-1, 0
Factor -2/15*j**2 - 2/15 - 4/15*j.
-2*(j + 1)**2/15
Let c = 11 - 131/12. Let o(q) be the second derivative of 1/40*q**5 + 0 + 0*q**4 + 0*q**2 - 3*q - c*q**3. Solve o(t) = 0 for t.
-1, 0, 1
Suppose -4*j = -q - 12, -4*q = -4*j + 2 + 10. Let z(m) be the third derivative of 0 + 1/270*m**6 - 1/27*m**3 + q*m**4 + 0*m - 4*m**2 + 1/90*m**5. Factor z(u).
2*(u + 1)**2*(2*u - 1)/9
Let s(j) be the third derivative of j**10/50400 + j**9/6720 + j**8/3360 - j**5/20 + 3*j**2. Let p(m) be the third derivative of s(m). Factor p(t).
3*t**2*(t + 1)*(t + 2)
Factor -l**2 + 0*l**4 + 3*l**3 + 43*l**5 - 3*l**4 + 0*l**3 - 42*l**5.
l**2*(l - 1)**3
Let c(h) = h**3 + 8*h**2 + 4. Let d be c(-8). Let -5 + 46*r**2 - 98*r**5 - 238*r**d + 3 - 134*r**3 + 32*r - 6 = 0. Calculate r.
-1, 2/7
Let z = 308/107 + -58545/749. Let i = -75 - z. Determine w so that -i*w**2 + 2/7*w + 0 = 0.
0, 1
Let t(r) = -r**2 - 3. Let x(c) = c + 1. Let s be (1/3*0)/2. Suppose -4*j + 8 = -s. Let q(n) = j*t(n) + 4*x(n). Let q(h) = 0. What is h?
1
Let q(t) = -2*t + 10. Let s be q(4). Determine a, given that -8/3*a**2 - 8/3*a**3 + 0 + 0*a + 10/3*a**4 + s*a**5 = 0.
-2, -2/3, 0, 1
Determine s so that 28/3*s + 49/3*s**4 - 4/3 - 15*s**2 - 28/3*s**3 = 0.
-1, 2/7, 1
Suppose 0 = 4*k - 42 + 30. Let n(o) be the third derivative of 1/120*o**5 + 2*o**2 + 0*o + 0*o**k + 0 + 0*o**4. Factor n(d).
d**2/2
Let f(p) = p**3 + 4*p**2 - 4*p + 7. Let q be f(-5). Factor -n**2 + 2*n + n**4 - n - q*n + n**3.
n*(n - 1)*(n + 1)**2
Let x(b) be the third derivative of b**5/30 + b**4/12 - 2*b**3 + 22*b**2. Factor x(h).
2*(h - 2)*(h + 3)
Let p(k) be the second derivative of k**6/60 - k**5/20 + k**3/6 - k**2/4 + 3*k. Factor p(g).
(g - 1)**3*(g + 1)/2
Let j be (-3 + 2)*(-44 + -2). Let f be (-3)/5 - j/(-10). Factor -4*t**f + 0*t + t**4 - 3*t**3 + 3*t + 3*t**2.
-3*t*(t - 1)*(t + 1)**2
Let f(m) be the first derivative of 2*m**6/5 - 7*m**5/10 + m**4/3 - 5*m + 8. Let w(i) be the first derivative of f(i). Factor w(c).
2*c**2*(2*c - 1)*(3*c - 2)
Suppose -4*b = 5*y - 31, 0 = 3*y + 2*b - 5 - 14. Factor 8*k + 0*k**2 + 3*k**2 - y*k**2 - 8 + 2*k**2.
-2*(k - 2)**2
Let g = 213 - 415/2. Let b = -65/14 + g. Find z, given that -2/7 - 6/7*z**3 + b*z + 2/7*z**2 = 0.
-1, 1/3, 1
Let r(m) be the third derivative of 2/3*m**3 - 1/10*m**5 + 1/105*m**7 + 0 - 1/60*m**6 + 1/12*m**4 + 5*m**2 + 0*m. Solve r(h) = 0.
-1, 1, 2
Suppose w + 6 = -4*g + 3, 5*g = -5*w. Let h(t) = -t**2 - t + 1. Let f(i) = -7*i**2 - 4*i + 6. Let r(x) = w*f(x) - 6*h(x). What is m in r(m) = 0?
0, 2
Let b = -34 + 24. Let m = -19/2 - b. Factor -1/2*f - 3/2*f**2 + 0 - 3/2*f**3 - m*f**4.
-f*(f + 1)**3/2
Let l(u) be the second derivative of -u**7/70 - u**6/25 - 3*u**5/100 + 2*u - 15. Find f, given that l(f) = 0.
-1, 0
Let i = -6 + 1. Let y be 210/567*(-3)/i. Find h, given that 4/9*h**2 + 0 + 2/9*h**3 + y*h = 0.
-1, 0
Let u(i) = 2*i**4 - 32*i**3 + 2