t o(t) be the third derivative of 0*t + t**2 + 1/150*t**6 - 1/840*t**8 + h*t**3 + 0*t**5 + 0 + 0*t**7 - 1/60*t**4. Factor o(i).
-2*i*(i - 1)**2*(i + 1)**2/5
Suppose 2*f + 2 = i, 0 = 4*i - 8*f + 9*f - 8. Factor -5/3*k - 2/3 - 4/3*k**i - 1/3*k**3.
-(k + 1)**2*(k + 2)/3
Let c(o) be the second derivative of -o**4/18 - o**3/3 - 2*o**2/3 - 2*o. Factor c(h).
-2*(h + 1)*(h + 2)/3
Let g(z) be the first derivative of z**3/2 + 45*z**2/4 + 21*z - 23. Find x such that g(x) = 0.
-14, -1
Let i be 16/(-48)*9/(-5). Factor -1/5*q**2 + 4/5 + i*q.
-(q - 4)*(q + 1)/5
Let k(a) be the third derivative of a**5/90 + a**4/18 + 19*a**2. Factor k(s).
2*s*(s + 2)/3
Factor 0 - 3/2*j + 3/2*j**2.
3*j*(j - 1)/2
Suppose -5*f = -f + 4. Let p be (12 + -6)*f/(-2). Determine n so that -p*n**3 + n**3 - 2*n**2 + 4*n**3 = 0.
0, 1
Let p(y) = -2*y - 12. Let j be p(-7). Find h, given that 0 + h**5 - 7/3*h**4 + h**j - 2/3*h + h**3 = 0.
-2/3, 0, 1
Let t(q) = q**4 - 7*q**3 + 5. Let u(r) = -6*r**3 + 4. Let j = 1 - -1. Suppose -d - j*s = 3 + 4, 0 = s + 1. Let p(l) = d*u(l) + 4*t(l). Factor p(m).
2*m**3*(2*m + 1)
Let f(b) be the third derivative of b**5/210 + b**4/21 + 4*b**3/21 - b**2. What is y in f(y) = 0?
-2
Let x = -2/13 - -19/39. Factor -1/3*p**4 + 1/3*p**5 + 0 + 0*p + 1/3*p**2 - x*p**3.
p**2*(p - 1)**2*(p + 1)/3
Let a = -957/7 + 137. Let m be ((-6)/(-14) - 0)/(15/10). Factor 0*t + 0 + a*t**3 + m*t**2.
2*t**2*(t + 1)/7
Factor 0 + 8/5*d - 8/5*d**2 - 6/5*d**3.
-2*d*(d + 2)*(3*d - 2)/5
Let d(s) be the second derivative of -1/2*s**2 + 0 + 1/12*s**4 - s + 0*s**3. Let d(j) = 0. What is j?
-1, 1
Let v(i) = 1 - 7 + 4*i - 2*i. Let m be v(5). Solve -24*q**3 + q**2 - 8*q + 6*q**4 + 3*q**m + 1 + 21*q**2 = 0 for q.
1/3, 1
Let l = 430 - 3051. Let o = l + 13168/5. Find v, given that -o*v**4 + 42/5*v**3 + 1/5 + 27/5*v**5 - v - 2/5*v**2 = 0.
-1/3, 1/3, 1
Suppose 12*q + 3*q + q**3 - 4*q**2 + q - 3*q**3 = 0. What is q?
-4, 0, 2
Let g(b) be the first derivative of b**5/25 - b**4/10 - 13. Factor g(f).
f**3*(f - 2)/5
Let q(x) be the second derivative of -x**6/90 + 7*x**3/6 + 2*x. Let r(a) be the second derivative of q(a). Determine v, given that r(v) = 0.
0
Let p be (-5)/(-10)*(7 + -1). Factor -102*k + 99*k - 2*k**5 - k**5 + 6*k**p.
-3*k*(k - 1)**2*(k + 1)**2
Let i(w) = -w - 11. Let z be i(-15). Factor -z*b + 6 + 2/3*b**2.
2*(b - 3)**2/3
Let k(j) be the first derivative of 7*j**6/15 + 18*j**5/25 - 4*j**4 - 16*j**3/3 + 48*j**2/5 + 32*j/5 - 44. Find n such that k(n) = 0.
-2, -2/7, 1, 2
Let u(d) be the first derivative of d**4/14 - 4*d**3/21 - 3*d**2/7 - 29. Factor u(k).
2*k*(k - 3)*(k + 1)/7
Suppose 6 = -p + 3*p. Suppose p*n = 5*v - 24, 5*n = -3*v + 3*n + 3. Factor -w - 3*w - w**2 + v*w**2.
2*w*(w - 2)
Factor -11*f - 10*f**2 + 13*f + 10 + 20*f**3 - 17*f - 5*f**5.
-5*(f - 1)**3*(f + 1)*(f + 2)
Determine l so that -3/4 - l - 1/4*l**2 = 0.
-3, -1
Suppose 0 = 4*j + 4 - 12. Determine h, given that -1/3*h**3 - 4/3*h**j - 4/3*h + 0 = 0.
-2, 0
Let p be 60/(-25)*(-20)/6. Factor p*s**2 - 6*s + 0*s**2 + 3*s**3 - 9*s**4 + s**2 + 3*s**5.
3*s*(s - 2)*(s - 1)**2*(s + 1)
Factor -5*d**4 - 6*d**4 + 15*d**4 - 2*d**5.
-2*d**4*(d - 2)
Let g = -2715/14 - -194. Let f(r) be the first derivative of 2/7*r**2 - 2/7*r**3 + 0*r + g*r**4 + 1. Find z, given that f(z) = 0.
0, 1, 2
Let c(i) be the first derivative of 3 + 3/2*i**2 - 4*i**3 - 12/5*i**5 + 0*i + 9/2*i**4 + 1/2*i**6. Let c(j) = 0. What is j?
0, 1
Let o(h) = -2*h**2 + h + 15. Let x be o(0). Suppose 3*k + 6 = x. Suppose -1/3*a**4 + 1/3*a**2 + 0*a - 1/3*a**5 + 1/3*a**k + 0 = 0. Calculate a.
-1, 0, 1
Suppose 2*r + 3*r = -2*w, -w = -3*r. Factor 17*k**3 + w*k**3 - 8*k**2 + 19*k**3 - 16*k**4.
-4*k**2*(k - 2)*(4*k - 1)
Let c = -14 - -19. Let o = -11/23 + 261/161. Suppose 0 + 6/7*x**2 - 2/7*x + 10/7*x**3 - 6/7*x**4 - o*x**c = 0. What is x?
-1, 0, 1/4, 1
Let l(d) = -81*d**4 + 63*d**3 + 192*d**2 - 384*d. Let x(n) = -5*n**4 + 4*n**3 + 12*n**2 - 24*n. Let i(z) = 2*l(z) - 33*x(z). Factor i(v).
3*v*(v - 2)**2*(v + 2)
Let f = 86 + -3183/37. Let a = f + 79/185. Find q, given that -4/5*q**2 + 0*q + 0 - a*q**3 = 0.
-2, 0
Let f(t) be the first derivative of t**3/18 + t**2/12 - 8. Factor f(q).
q*(q + 1)/6
Determine o, given that 1/3*o**3 - 1/3 - 1/3*o + 1/3*o**2 = 0.
-1, 1
Let h(s) be the second derivative of 0*s**2 + 0 + 0*s**3 + 7*s + 1/36*s**4 - 1/60*s**5. Factor h(c).
-c**2*(c - 1)/3
Let s(i) = -i**3 - 15*i**2 - 51*i - 67. Let v(m) = -m**2 - m - 1. Let w(b) = 2*s(b) - 6*v(b). Solve w(x) = 0.
-4
Let 2 - 7*f**3 + 3*f + 6*f**2 - 8*f**2 + 5*f**3 - f = 0. What is f?
-1, 1
Let u(d) be the second derivative of 8*d - 5/42*d**4 + 2/7*d**2 + 0 - 1/7*d**3. Suppose u(s) = 0. Calculate s.
-1, 2/5
Suppose 2*u + 0 + 2 = -f, -4*f - 8 = -2*u. Let d = -5/13 - -28/39. Factor 1/3 - d*l**2 + u*l.
-(l - 1)*(l + 1)/3
Factor -1 - 1 - 11*m - 16*m**2 + m + 8*m**2.
-2*(m + 1)*(4*m + 1)
Let f(r) be the second derivative of 3*r + 0*r**2 - 1/36*r**4 - 1/18*r**3 + 0. Factor f(l).
-l*(l + 1)/3
Let k = -2 + 5. Suppose -k = 3*j - 12. Factor -1/3*v**j + 1/3 - 1/3*v**2 + 1/3*v.
-(v - 1)*(v + 1)**2/3
Factor 0*t**2 - 9 - 5*t**2 + 5*t**2 + 3*t**2 + 6*t.
3*(t - 1)*(t + 3)
Let a(l) be the first derivative of 1/8*l**2 + 4 - 1/20*l**5 + 1/6*l**3 - 1/4*l + 1/24*l**6 - 1/8*l**4. Factor a(w).
(w - 1)**3*(w + 1)**2/4
Let o(h) = 8*h**4 + 2*h**3 - 2*h**2 + 4*h. Let l(z) = 15*z**4 + 3*z**3 - 4*z**2 + 8*z. Let i(f) = -6*l(f) + 11*o(f). What is p in i(p) = 0?
-1, 0, 1, 2
Let v = -9 + 13. Suppose -2*a = 5*p + 3 + 3, -8 = v*p. Find y, given that -1/4*y**4 + 0*y + 0 - y**3 - y**a = 0.
-2, 0
Let u be (-1486)/444 + (1 - -1). Let x = -1/74 - u. Factor 0 + 1/3*w**4 + x*w - w**3 + 0*w**2.
w*(w - 2)**2*(w + 1)/3
Let i(t) be the second derivative of t**5/5 + t**4 - 10*t. Solve i(j) = 0.
-3, 0
Let n(l) be the second derivative of 0*l**2 + 1/24*l**4 - 2*l - 1/24*l**7 + 0*l**3 - 3/80*l**5 + 0 - 1/10*l**6. What is q in n(q) = 0?
-1, 0, 2/7
Let u = 904 + -8128/9. Factor 2*i**2 + u + 8/3*i.
2*(3*i + 2)**2/9
Let h(q) = 2*q**3 - 2*q**2 - 2*q - 1. Let n(m) = -m**2. Let g(y) = -h(y) + 3*n(y). Factor g(r).
-(r - 1)*(r + 1)*(2*r + 1)
Let j = 3 + 2. Let w(k) = -k**2 + 6*k - 4. Let u be w(j). Factor -u - 5*v + 2*v - v**3 + 0*v - 3*v**2.
-(v + 1)**3
Suppose -3*g - 2*w - 17 = 0, -3*g + 4*w - 47 = -0*g. Let q(p) = p**3 + 9*p**2 - p - 6. Let v be q(g). Solve -3*c**5 - c**4 + 2*c**4 - v*c**4 + 5*c**5 = 0.
0, 1
Solve -2/7*v - 12/7 + 2/7*v**3 + 12/7*v**2 = 0.
-6, -1, 1
Let b(m) be the second derivative of -m**6/120 - 7*m**5/80 - 5*m**4/16 - 13*m**3/24 - m**2/2 - 7*m. Factor b(v).
-(v + 1)**3*(v + 4)/4
Let x = 15 - 22. Let t(j) = -j**3 + 2*j**2 - j. Let r(y) = -2*y**3 + 4*y**2 - 2*y. Let n(a) = x*t(a) + 4*r(a). Factor n(m).
-m*(m - 1)**2
Let d(l) be the first derivative of -l**3/6 + 3*l**2/2 - 9*l/2 - 14. Factor d(p).
-(p - 3)**2/2
Let b(c) be the third derivative of 2*c**2 + 0 + 0*c**6 - 1/15*c**5 - 1/168*c**8 + 0*c + 1/12*c**4 + 0*c**3 + 2/105*c**7. Factor b(w).
-2*w*(w - 1)**3*(w + 1)
Let w(r) = r**3 - r + 1. Let m(z) = -3*z**3 + 6*z**2 + 9*z - 6. Let t(i) = -m(i) - 6*w(i). Suppose t(v) = 0. What is v?
-1, 0
Suppose 0 = -u - 2*l + 18, -5*l + 5 + 47 = 3*u. Let h be (4/(-14))/((-2)/u). Let -2*k**h + 4*k**4 - k**2 - 3*k**3 + 0*k**2 + 3*k**5 - k**4 = 0. Calculate k.
-1, 0, 1
Let y(x) be the third derivative of -x**6/180 + x**4/12 - x**3/2 + 2*x**2. Let k(c) be the first derivative of y(c). Factor k(r).
-2*(r - 1)*(r + 1)
Let g = 4 - 3. Suppose 7*r - 3*r - 8 = 0. Factor -2*s**2 + 4*s**2 + 3*s**3 + s - g + 3*s**r.
(s + 1)**2*(3*s - 1)
Let c be (-10)/35 - (-200)/14. Let j be c/9 - (-4)/(-18). Factor 2/3*t**2 + j*t + 2/3.
2*(t + 1)**2/3
Let 2*g**2 - 9*g**2 + 7*g**2 + 2*g**2 = 0. What is g?
0
Suppose -4*q - 5*a = -6, 8 = 2*q - q - 2*a. Factor 4/3*c**2 + 4/3*c**3 - 2/3*c**q - 2/3*c**5 - 2/3*c - 2/3.
-2*(c - 1)**2*(c + 1)**3/3
Let m = 19 + -7. Let j(z) = -z + 15. Let k be j(m). Find p such that 0 + 1/4*p**4 + 0*p - 1/4*p**2 + 0*p**k = 0.
-1, 0, 1
Suppose 5*f = 9*f - 16. Let z(h) be the second derivative of -h + 0 + 1/48*h**f + 1/12*h**3 + 1/8*h**2. Factor z(k).
(k + 1)**2/4
Let c(t) be the second derivative of -t**3/6 - 3*t**2 + 3*t. Let p be c(-8). What is r in -r**p + r**2 - 1 + r**2 = 0?
-1, 1
Suppose 0 = 3*j - 6, -6*q + 2*q - 2*j = -4. Suppose 2*b - 3 - 3 = c, 0 = c + 2. Let -2*