 - 77)**2/15
Let r(p) = -1 + 28*p**2 - 2 + p**3 - 27*p**2. Let u(i) = i**3 + 2*i**2 - 2. Let g(y) = -2*r(y) + 3*u(y). Factor g(j).
j**2*(j + 4)
Let v = 87 - -53. Let l = -138 + v. Factor -2/9*z**3 + 2/3 + 2/9*z**l + 10/9*z.
-2*(z - 3)*(z + 1)**2/9
Let h = 7321 + -21961/3. Factor -h*o**4 - 1/3*o + 5/6*o**3 + 7/6*o**2 + 0.
-o*(o - 2)*(o + 1)*(4*o - 1)/6
Let i(p) be the second derivative of p**6/75 + 14*p**5/25 + 131*p**4/15 + 308*p**3/5 + 1089*p**2/5 - 34*p. Factor i(o).
2*(o + 3)**2*(o + 11)**2/5
Let h(r) = 3*r**2 - 414*r - 14700. Let u(g) = g**2 - 416*g - 14700. Let m(j) = 2*h(j) - 3*u(j). Suppose m(x) = 0. What is x?
-70
Let m(o) be the third derivative of 0*o**4 + 0*o**3 + 0 - 1/20*o**5 + 0*o - 14*o**2. What is g in m(g) = 0?
0
Let a = 50 - 47. Factor 7*x**4 + 3*x**a + 3*x**4 - 6*x**5 - 7*x**3.
-2*x**3*(x - 1)*(3*x - 2)
Let q(b) be the first derivative of -b**6/42 - b**5/7 - 9*b**4/28 - b**3/3 - b**2/7 + 212. Factor q(u).
-u*(u + 1)**3*(u + 2)/7
Let a(h) be the first derivative of h**7/1050 - h**6/150 - h**5/60 - 16*h**2 + 5. Let n(q) be the second derivative of a(q). What is z in n(z) = 0?
-1, 0, 5
Let d(a) be the third derivative of -a**6/24 - 11*a**5/12 - a**2 + 3*a. Factor d(n).
-5*n**2*(n + 11)
Factor 22/3*y**2 - 4*y - 4*y**3 + 0 + 2/3*y**4.
2*y*(y - 3)*(y - 2)*(y - 1)/3
Let r(l) be the second derivative of l**6/45 + l**5/30 - 13*l**4/18 - 25*l**3/9 - 4*l**2 - 2*l + 13. Find v such that r(v) = 0.
-3, -1, 4
Let b(t) be the second derivative of -t**4/42 + 10*t**3/7 + 64*t**2/7 - 40*t + 1. Factor b(z).
-2*(z - 32)*(z + 2)/7
Let l(m) be the third derivative of -m**7/280 + m**6/60 - m**5/40 - 11*m**3/3 - m**2. Let c(z) be the first derivative of l(z). Find n, given that c(n) = 0.
0, 1
Let n be (-15)/(-6)*(184/25 - 4). Factor -n*s**3 - 9/5*s**2 + 6/5*s + 0.
-3*s*(2*s + 1)*(7*s - 2)/5
Let f(s) be the first derivative of s**4/5 - 544*s**3/15 + 9248*s**2/5 - 202. Let f(u) = 0. What is u?
0, 68
Factor -3/5*q - 3*q**2 - 6/5*q**3 + 6/5.
-3*(q + 1)*(q + 2)*(2*q - 1)/5
Suppose 0 = -0*q - 2*q + 5*c + 19, 2*q + 4*c = -8. Factor 26*x**2 - 27*x**q + 0*x + 0*x.
-x**2
Let q be 12/(240/(-25))*(-8)/5. Let -16/7*b - 2/7 - 2*b**q = 0. What is b?
-1, -1/7
Let a = 2318/63 - 256/7. Let x(f) be the first derivative of 2/3*f + a*f**3 - 2/3*f**2 - 6. Solve x(v) = 0.
1
Let v = 28 - 22. Let s(g) = -g**3 - g**2 - g + 1. Let r(u) = 2*u**3 + 30*u**2 - 42*u + 26. Let j(h) = v*s(h) + r(h). Factor j(p).
-4*(p - 2)**3
Let h(n) be the second derivative of 4*n**6/105 - 2*n**5/5 + 25*n**4/42 - 2*n**3/7 - 2*n - 296. Factor h(b).
2*b*(b - 6)*(2*b - 1)**2/7
Let q(g) be the third derivative of -g**8/10080 - g**7/2520 + 17*g**5/60 - 22*g**2. Let s(x) be the third derivative of q(x). Factor s(m).
-2*m*(m + 1)
Let b(f) = f**3 - 13*f**2 + 14*f - 12. Let j be b(12). Let v be j/(-9) + (-51)/(-18). Factor 0 + v*t**3 - 3/2*t**2 + 1/2*t - 1/2*t**4.
-t*(t - 1)**3/2
Solve 0 + 32/5*f**3 - 64/5*f - 128/5*f**2 + 96/5*f**4 - 36/5*f**5 = 0 for f.
-2/3, 0, 2
Suppose 6*x = -0 + 12. Determine a so that -3*a - 7*a**x + 0 + 2 + 2*a**2 = 0.
-1, 2/5
Let h = 10 + -4. Let c(o) = 21*o**4 + 0*o - o**3 - o - 22*o**4. Let m(p) = 7*p**4 + 6*p**3 - 3*p**2 + 4*p. Let a(u) = h*c(u) + m(u). Factor a(i).
i*(i - 2)*(i + 1)**2
Suppose -2*u - 1739 = i - 1754, -2*i = -3*u + 12. Determine q so that 0 + 6*q + 0*q**2 - 2/3*q**i = 0.
-3, 0, 3
Let m(j) = j - 5. Let k be m(7). Factor 3 - 5*v**2 + v**k - v**2 + 2*v**2.
-3*(v - 1)*(v + 1)
Let m(o) be the first derivative of o**6/6 - 4*o**5/5 + 3*o**4/4 + 4*o**3/3 - 2*o**2 - 46. Factor m(y).
y*(y - 2)**2*(y - 1)*(y + 1)
Let w(u) be the third derivative of u**6/480 + 33*u**5/80 + 1089*u**4/32 + 11979*u**3/8 + 5*u**2 + 3. Factor w(g).
(g + 33)**3/4
Factor -3/5*u**3 - 18/5*u + 0 - 21/5*u**2.
-3*u*(u + 1)*(u + 6)/5
Let x(n) be the first derivative of n**5/300 - 5*n**2 - 2. Let r(j) be the second derivative of x(j). Find b such that r(b) = 0.
0
Let v(h) be the third derivative of -5*h**8/48 - 5*h**7/42 + 3*h**6/8 + 5*h**5/12 - 5*h**4/12 - 27*h**2 - 4. Determine t so that v(t) = 0.
-1, 0, 2/7, 1
Let c = 99 - 88. Factor 12*q**2 + 155*q + 68 + c*q**2 - 178 - 8*q**2.
5*(q + 11)*(3*q - 2)
Let x = 506 - 10119/20. Let l(b) be the third derivative of 0 - 3/8*b**4 - 3/70*b**7 - 6*b**2 + 1/112*b**8 + 1/10*b**5 + 0*b + 1/2*b**3 + x*b**6. Factor l(u).
3*(u - 1)**4*(u + 1)
Let s(o) be the first derivative of -o**7/175 + 21*o**6/200 - 3*o**5/5 + 5*o**4/8 + 3*o**2/2 - 9*o + 3. Let h(y) be the second derivative of s(y). Factor h(j).
-3*j*(j - 5)**2*(2*j - 1)/5
Let d(n) = -2*n**4 + n**3 + n**2 + n - 1. Let c(f) = -10*f**3 + 94*f**2 + 198*f + 102. Let o(g) = c(g) + 2*d(g). Factor o(k).
-4*(k - 5)*(k + 1)**2*(k + 5)
Let p(v) = v**2 - 3*v - 7. Let a be p(5). Let q = -20 + 25. Factor -t**4 + 5*t + t**2 - t**a - 9*t + q*t.
-t*(t - 1)*(t + 1)**2
Let f(t) be the second derivative of 1 + 1/48*t**4 - 1/4*t**2 + 1/120*t**6 - 6*t + 3/80*t**5 - 1/8*t**3. Factor f(w).
(w - 1)*(w + 1)**2*(w + 2)/4
Solve 0*u**2 + 21*u - 18*u**2 - 2*u**3 + 8*u**3 - 4*u**2 - 5*u**3 = 0 for u.
0, 1, 21
Let p(v) be the third derivative of -v**8/42 - 16*v**7/105 - 5*v**6/12 - 19*v**5/30 - 7*v**4/12 - v**3/3 + 55*v**2. Determine c, given that p(c) = 0.
-1, -1/2
Let r be (3/(-2))/(30/(-40)). Let a(n) be the third derivative of 0 - 5*n**r + 0*n**3 + 0*n + 1/15*n**5 - 1/6*n**4 - 1/120*n**6. Solve a(u) = 0.
0, 2
Let b(t) = t**3 - 15*t**2 + 57*t + 1. Let n be b(7). Suppose -n*g = -0*g. Factor 9/4*o**2 + 3/2*o + 3/4*o**3 + g.
3*o*(o + 1)*(o + 2)/4
Let v(p) be the second derivative of p**5/70 + 73*p**4/42 - 199*p. Factor v(k).
2*k**2*(k + 73)/7
Let z(h) be the third derivative of h**5/360 + 31*h**4/24 + 961*h**3/4 + 176*h**2. What is b in z(b) = 0?
-93
Let k(y) = 2*y**2 - y - 1. Let o(w) = -39*w**2 + 9*w + 48. Let t(l) = 18*k(l) + o(l). Factor t(q).
-3*(q - 2)*(q + 5)
Let u(g) = 15*g + 213. Let z be u(-14). Let v(m) be the second derivative of 4/15*m**z + 3*m + 0*m**2 + 1/15*m**4 + 0. Factor v(b).
4*b*(b + 2)/5
Let f(v) be the first derivative of v**3/18 + 7*v**2/12 - 281. Solve f(b) = 0.
-7, 0
Let k be (-216)/16*(5 + -1). Let g = k - -57. Factor 0 - 2/7*i - 6/7*i**2 - 4/7*i**g.
-2*i*(i + 1)*(2*i + 1)/7
Let -165*b**3 + 22*b**2 + 28*b**4 + 4*b**4 - 12*b**4 + 165*b - 2*b**2 - 40 = 0. What is b?
-1, 1/4, 1, 8
Let c(r) = -r + 18. Let b be c(17). Let n be (2 - b)*(-2 - (-78)/27). Factor -n*m**3 + 0*m**2 - 2/9*m**5 - 8/9*m**4 + 0*m + 0.
-2*m**3*(m + 2)**2/9
Suppose 153 = 39*x + 36. Solve 0 - 4/7*i**2 - 2/7*i**x + 0*i = 0 for i.
-2, 0
Suppose 6*n - 26 = -8. Let f(x) be the first derivative of 0*x + 3 + 2/21*x**n + 1/7*x**2. Solve f(w) = 0 for w.
-1, 0
Let x be -2 + ((-1140)/(-75) - 13). Factor -2/5*w**4 - 1/5*w + x*w**5 + 0 + 0*w**3 + 2/5*w**2.
w*(w - 1)**3*(w + 1)/5
Let l = 7 + 33. Let c be 136/l + ((-12)/5 - -2). Determine d, given that -1/2*d - 2*d**c - 49/6*d**2 + 2/3 = 0.
-4, -1/3, 1/4
Let q(g) be the third derivative of -g**5/140 + g**4/56 + 3*g**3/7 + 19*g**2. Factor q(a).
-3*(a - 3)*(a + 2)/7
Let d(w) = 2*w**2 - w - 1. Let j(t) = -6*t**2 + 2*t. Let n(p) = -4*d(p) - j(p). Solve n(r) = 0.
-1, 2
Suppose 28*y = 27*y + 2. Suppose -4*x = -n - 4 - 0, -4*x - 8 = -4*n. Factor 9*t**3 + t**2 - 6*t**2 + x*t**2 + 0*t**y.
3*t**2*(3*t - 1)
Suppose 12*g - 8*g + 48 = 0. Let x = 12 + g. What is p in 0 - 1/2*p**2 + 0*p + x*p**3 + 1/2*p**4 = 0?
-1, 0, 1
Factor 11*x + 14*x**2 - 22*x**2 + 11*x**2 - 32*x + 18.
3*(x - 6)*(x - 1)
Let j = -1306 + 2613/2. Find y, given that -1/4*y**4 - j - 7/4*y - 9/4*y**2 - 5/4*y**3 = 0.
-2, -1
Let c = 83 + -77. Let 34*n**4 + 18*n**3 + c*n - 18*n**4 - 12*n**4 + 0*n + 20*n**2 = 0. What is n?
-3, -1, -1/2, 0
Let m(p) be the third derivative of -9*p**2 + 0*p**3 + 0*p - 1/6*p**5 + 0*p**4 + 0 + 1/24*p**6. Determine w, given that m(w) = 0.
0, 2
Let f(y) be the third derivative of 1/4*y**4 - 3*y**2 - 1/30*y**6 + 0 + y**3 + 7/40*y**5 + 0*y. Let h(l) be the first derivative of f(l). Factor h(w).
-3*(w - 2)*(4*w + 1)
Suppose 3*f = -0*f - 6. Let m = 0 - f. What is x in -3*x + 7*x - 4 - 2*x**m + 2*x = 0?
1, 2
Solve 12/7*j - 121*j**3 - 72/7 + 682/7*j**2 = 0 for j.
-2/7, 6/11
Suppose -3*u + 5 = -2*u - t, 3*u - t = 17. Factor 27*z - 2*z**2 - 7*z**2 + u*z**3 + 9*z**4 - 33*z.
3*z*(z - 1)*(z + 1)*(3*z + 2)
Let w be 970/90 - (-2)/9. Let k = w - -13.