 + 6 - 2/45*l**5 - 2/27*l**3 + 0*l**2 - 1/9*l**4. Factor h(s).
-2*s**2*(s + 1)**2/9
Let p(t) be the second derivative of -2*t**6/15 - t**5 - 7*t**4/3 - 2*t**3 - 21*t. Factor p(h).
-4*h*(h + 1)**2*(h + 3)
Suppose 2 = -5*m + 12. Let x(p) be the first derivative of m + 0*p - 1/12*p**3 + 1/4*p**2 - 1/16*p**4. Factor x(s).
-s*(s - 1)*(s + 2)/4
Let w(a) be the third derivative of -a**5/12 + 25*a**4/12 + 55*a**3/6 + 8*a**2 + 4. Factor w(u).
-5*(u - 11)*(u + 1)
Let r(m) = m**3 - 7*m**2 + 6*m + 3. Let u(b) = b - 1. Let y be u(7). Let q be r(y). Find o such that -3*o**q + 5*o + 0 - 2*o + o**2 + o**4 - 2 = 0.
-1, 1, 2
Factor 1/3*f**2 - 5/3*f + 1 + 1/3*f**3.
(f - 1)**2*(f + 3)/3
Determine s so that -4/3*s**3 - 10/3*s**4 + 4/3*s + 10/3*s**2 + 0 = 0.
-1, -2/5, 0, 1
Let j = 1/30 - -1/6. Let -1/5*z**2 + 0*z + 0 - 2/5*z**3 - j*z**4 = 0. What is z?
-1, 0
Factor 2/3*b**2 + 0*b - 2/3.
2*(b - 1)*(b + 1)/3
Suppose -2 + 6 = 2*v. Let d = v - 0. Factor 1/2*g**d + 0*g + 0 - 5/4*g**3.
-g**2*(5*g - 2)/4
Suppose 0 = -50*c + 48*c + 4. What is t in -2/3*t - 2/3*t**c + 4/3 = 0?
-2, 1
Let m(v) = -v**3 + 23*v**2 + 11*v - 61. Let q(p) = 8*p**2 + 4*p - 20. Let s(i) = 4*m(i) - 14*q(i). What is u in s(u) = 0?
-3, 1
Let r(m) = -2*m**4 - 7*m**3 - 44*m**2 - 57*m - 18. Let a(q) = -q**4 - 4*q**3 - 22*q**2 - 28*q - 9. Let c(t) = -9*a(t) + 4*r(t). Factor c(v).
(v + 1)**2*(v + 3)**2
Let c(x) = -2*x**4 + 15*x**2 - x**4 + 3*x + 6*x**4 + 19*x**3 + 1. Let s(z) = -10*z**4 - 56*z**3 - 44*z**2 - 8*z - 2. Let p(y) = -8*c(y) - 3*s(y). Factor p(j).
2*(j + 1)**3*(3*j - 1)
Let m(z) be the second derivative of -z**7/98 + z**6/70 + 3*z**5/140 - z**4/28 + 2*z. Factor m(u).
-3*u**2*(u - 1)**2*(u + 1)/7
Let t(v) = 2*v**3 + 7*v**2 - 5*v - 2. Let i be t(-4). Factor 1/5*q + 1/5 - 1/5*q**3 - 1/5*q**i.
-(q - 1)*(q + 1)**2/5
What is v in -469*v**2 - 6 + 6*v + 466*v**2 + 3 = 0?
1
Let y(f) = -3 + 6*f + 5*f**2 - 3*f**2 + 3. Let a(c) = -c. Let g(w) = -4*a(w) - y(w). Factor g(q).
-2*q*(q + 1)
Let j(p) be the second derivative of -p**5/130 + p**4/78 + p**3/39 - p**2/13 + 12*p. Factor j(y).
-2*(y - 1)**2*(y + 1)/13
Let b(t) be the third derivative of t**5/20 + 3*t**4/8 + t**3 - 8*t**2. Factor b(m).
3*(m + 1)*(m + 2)
Determine c so that -20*c + 8*c**2 + 107*c**3 + 7*c**2 - 102*c**3 = 0.
-4, 0, 1
Let a be ((-2)/6*1)/(-1). Let b be ((-2)/(-15))/(2/10). Determine k, given that 1/3*k + b*k**2 + 0 + a*k**3 = 0.
-1, 0
Let b(w) be the first derivative of 4*w**6/13 + 106*w**5/65 + 3*w**4 + 82*w**3/39 - 8*w/13 + 6. Determine m, given that b(m) = 0.
-2, -1, -2/3, 1/4
Factor -1 - d - 1/4*d**2.
-(d + 2)**2/4
Let n(k) = -k + 7. Suppose 4*v - 25 = -1. Let g be n(v). Factor -3*d + 3*d + d**2 + 0*d - g.
(d - 1)*(d + 1)
Let w(i) = i + 12. Let j be w(-10). Factor -5*d**3 - 2*d + 15*d**j - d - 7*d**3.
-3*d*(d - 1)*(4*d - 1)
Factor 1/2*b**4 - 2 - 1/2*b**2 - 1/2*b**5 - 4*b + 5/2*b**3.
-(b - 2)**2*(b + 1)**3/2
Let b(w) be the first derivative of w**4/8 + 2*w**3/3 + 5*w**2/4 + w - 6. Factor b(x).
(x + 1)**2*(x + 2)/2
Let m(v) be the second derivative of v**9/7560 - v**7/630 + v**5/60 - v**4/12 - v. Let l(q) be the third derivative of m(q). Suppose l(u) = 0. What is u?
-1, 1
Let z be 81/4 + 4/(-16). Let m be ((-8)/z)/((-6)/15). Let x(b) = -3*b**2 - 6*b + 5. Let r(q) = q**2 + q - 1. Let o(a) = m*x(a) + 4*r(a). Factor o(c).
(c - 1)**2
Let u(f) be the first derivative of f**5/10 + f**4 + 4*f**3 + 8*f**2 - 2*f - 4. Let i(y) be the first derivative of u(y). Find b, given that i(b) = 0.
-2
Let d be -4 - -7 - (2 - 0). Let a = -169/2 + 89. Factor -a*l - d - 7/2*l**2.
-(l + 1)*(7*l + 2)/2
Let n(v) be the third derivative of 0*v**3 + 0 + 1/210*v**7 + 0*v**4 + 1/60*v**5 + v**2 + 1/60*v**6 + 0*v. Factor n(j).
j**2*(j + 1)**2
What is c in 2*c**3 + 3*c**3 - 2*c**2 - 5*c**4 + c**4 + 0*c**2 + c**5 = 0?
0, 1, 2
Let n be 5*4/80 + 2/(-8). Factor n - 3/2*j**3 - 3/2*j + 3*j**2.
-3*j*(j - 1)**2/2
Let o(x) be the third derivative of -x**6/300 - 2*x**5/75 + x**4/12 - 4*x**2 + 13. Determine u, given that o(u) = 0.
-5, 0, 1
Let l(z) be the second derivative of z**7/1365 + z**6/390 - z**5/130 - z**4/39 + 4*z**3/39 - 3*z**2 + z. Let h(y) be the first derivative of l(y). Factor h(f).
2*(f - 1)**2*(f + 2)**2/13
Let g = 1/69 + 91/69. Let i(k) be the third derivative of 1/2*k**4 - g*k**3 + 0*k + 2*k**2 - 1/10*k**5 + 0 + 1/120*k**6. Let i(y) = 0. What is y?
2
Let o = -9/7 - -73/35. Let v(m) be the first derivative of 1/10*m**4 + 0*m + 2 + o*m**2 + 8/15*m**3. Let v(s) = 0. What is s?
-2, 0
Let d(y) be the third derivative of -y**5/15 - y**4/2 - 4*y**3/3 - 4*y**2. Find o such that d(o) = 0.
-2, -1
Let g(z) be the first derivative of -z**4 - 92*z**3/21 - 40*z**2/7 - 16*z/7 - 6. Factor g(n).
-4*(n + 1)*(n + 2)*(7*n + 2)/7
Let d(y) be the third derivative of y**6/1020 - y**5/170 + y**4/68 - y**3/51 - 5*y**2. Factor d(r).
2*(r - 1)**3/17
Let c be -4 - 60/3*-1. Factor 2*t**2 + 20 - 10 - c*t + 0*t**2 + 22.
2*(t - 4)**2
Let j(x) be the first derivative of -4*x**3/3 + 16*x**2 - 64*x - 12. Find c, given that j(c) = 0.
4
Let l = -597 + 37609/63. Let a = l + 44/63. Factor 0 - 2/9*s - a*s**2.
-2*s*(3*s + 1)/9
Let m(a) be the second derivative of -a**6/360 - a**5/120 + a**4/12 + a**3/6 + a. Let c(p) be the second derivative of m(p). Let c(x) = 0. What is x?
-2, 1
Let l(k) = -6*k - 9. Let j be l(-2). Factor -6/5*d**2 + 0*d - 4/5*d**j + 2/5.
-2*(d + 1)**2*(2*d - 1)/5
Let r = 14 + -14. Let n(v) be the third derivative of 0*v**3 - 2*v**2 - 1/30*v**5 + r*v + 0 - 1/12*v**4. Factor n(x).
-2*x*(x + 1)
Let m(p) be the third derivative of p**5/270 + p**4/108 - 6*p**2. Factor m(z).
2*z*(z + 1)/9
Let b(s) be the second derivative of -s**5/80 + s**4/16 + s**3/24 - 3*s**2/8 - 22*s. Factor b(t).
-(t - 3)*(t - 1)*(t + 1)/4
Let o(w) be the third derivative of w**7/42 - 5*w**6/24 + 3*w**5/4 - 35*w**4/24 + 5*w**3/3 - 4*w**2. Factor o(y).
5*(y - 2)*(y - 1)**3
Suppose -3*s + 10 = 2*s. Factor -18*i**s + 0 - 3 - 3*i**4 - i + 13*i + 12*i**3.
-3*(i - 1)**4
Solve 2*d + d**3 + 6*d**2 + 3*d - 5*d = 0.
-6, 0
Let w(d) be the third derivative of 0*d**4 - 2*d**2 - 1/300*d**6 + 0*d**3 - 1/150*d**5 + 0*d + 0. What is n in w(n) = 0?
-1, 0
Let s be (-4)/10 - (-180)/150. Suppose 6/5*f - 2/5*f**3 + 0 + s*f**2 = 0. Calculate f.
-1, 0, 3
Let r be (-87)/(-42) - (-7)/14. Solve r - 12/7*g + 2/7*g**2 = 0.
3
Let u(h) be the first derivative of 0*h**2 + 0*h**3 + 1/48*h**4 - 1/16*h**5 + 1 + h. Let k(a) be the first derivative of u(a). Determine p, given that k(p) = 0.
0, 1/5
Suppose -y = 4*j + y - 10, -y = -2*j - 1. Let v(g) be the first derivative of -1/4*g**4 - g**3 - g - 3/2*g**2 + j. Factor v(b).
-(b + 1)**3
Let s(j) be the third derivative of -1/108*j**4 + 0*j - 6*j**2 - 2/27*j**3 + 0 + 1/270*j**5. Factor s(r).
2*(r - 2)*(r + 1)/9
Factor -2*p**5 - 40*p**3 - 2*p**4 + 48*p**3 - 2*p**5 - 2*p**4.
-4*p**3*(p - 1)*(p + 2)
Let h(c) be the second derivative of -c**6/40 - 3*c**5/20 - 3*c**4/8 - c**3/2 - 3*c**2/8 - 12*c. Factor h(g).
-3*(g + 1)**4/4
Let u(w) be the second derivative of -1/15*w**4 - 1/50*w**5 - 2*w + 0*w**2 + 0 - 1/15*w**3. Factor u(v).
-2*v*(v + 1)**2/5
Let o = 704 - 704. Solve -2/3*h**3 + h**4 - 1/3*h**5 + 0 + o*h**2 + 0*h = 0.
0, 1, 2
Let n(j) be the first derivative of -10*j**3/39 + 2*j**2/13 + 2. What is d in n(d) = 0?
0, 2/5
Let f(q) be the third derivative of 0 + 1/80*q**6 + 3*q**2 + 0*q - 1/40*q**5 + 0*q**4 + 0*q**3. Factor f(s).
3*s**2*(s - 1)/2
Let o(c) = -2*c - 9. Suppose -m + 20 = -4*u - 4, -4*u - 5*m = 24. Let i be o(u). Factor -4/7*v**2 + 2/7*v + 0 + 2/7*v**i.
2*v*(v - 1)**2/7
Let q(n) be the second derivative of n**5/90 + n**4/54 - 5*n**3/27 + n**2/3 - 7*n. Factor q(r).
2*(r - 1)**2*(r + 3)/9
Let f(j) = 2*j**2 + 101*j - 92. Let m(a) = a**2 + 34*a - 31. Let s(q) = 4*f(q) - 11*m(q). Suppose s(r) = 0. Calculate r.
1, 9
Let u be 6/(3 + 1 + 6). Determine f, given that -3/5*f**5 + 6/5*f**4 + 0*f**2 + 0 - u*f**3 + 0*f = 0.
0, 1
Let t be (-4)/(-2) - 40/(-5). Let d be (-25)/t*(-4)/25. Factor -3/5*f + 2/5*f**3 + 1/5*f**5 + 3/5*f**4 - d*f**2 - 1/5.
(f - 1)*(f + 1)**4/5
Let k(a) be the first derivative of a**4 - 13*a**3/3 + 3*a**2/2 - 22. Determine g so that k(g) = 0.
0, 1/4, 3
Let z be (40/16)/((-2)/(-8)). What is n in 10*n**2 - 3*n**4 - z*n**2 + 3*n**3 = 0?
0, 1
Suppose 0 = 5*y - 13*y - 288. Let k = 39 + y. Let 1/4