k).
-3*k**2*(k + 1)/7
Let y(r) be the second derivative of -r**4/21 - 2*r**3/21 + 15*r. Suppose y(f) = 0. Calculate f.
-1, 0
Let w(c) = -c**2 - 4*c - 3. Let n(s) = -s**2 - 5*s - 4. Suppose 0*m - 4*m + 24 = 0. Let d(o) = m*w(o) - 5*n(o). Factor d(x).
-(x - 2)*(x + 1)
Let a(t) be the second derivative of t**4/30 - 7*t**3/15 - 8*t**2/5 - 14*t. Factor a(b).
2*(b - 8)*(b + 1)/5
Suppose -2*w - 2*w + 8 = 0. Let o(j) be the first derivative of -32/5*j**5 + 11/2*j**4 - 4/3*j**3 - 1 + 0*j**w + 7/3*j**6 + 0*j. Factor o(m).
2*m**2*(m - 1)**2*(7*m - 2)
Factor 0 + 9/2*a - 3/2*a**2.
-3*a*(a - 3)/2
Let j = 6 - 6. Let x(l) = l**2 - l + 6. Let f be x(j). Factor -f*w + 6*w**2 + 4 - 2*w**2 + 0*w**2 - 2*w**2.
2*(w - 2)*(w - 1)
Let i(s) = 7*s**2 + s + 5. Suppose 3*r - u - 3*u = 15, -4*u = 0. Let c(y) = -4*y**2 - y - 3. Let m(o) = r*c(o) + 3*i(o). Factor m(a).
a*(a - 2)
Let o(s) = -s**4 + s**3 - s**2 + s - 1. Let j(x) = 10*x**4 - 7*x**3 + 4*x**2 - 4*x + 4. Let i(d) = -j(d) - 4*o(d). Find l, given that i(l) = 0.
0, 1/2
Let d(l) be the second derivative of -5*l**4/12 + 5*l**3/3 + 20*l**2 - 40*l. Factor d(p).
-5*(p - 4)*(p + 2)
Let h(v) be the second derivative of v**6/360 - v**4/24 + v**3/9 - v**2 + v. Let z(j) be the first derivative of h(j). Find c, given that z(c) = 0.
-2, 1
Let b(z) be the first derivative of -z**5/40 + z**4/16 - z**2/2 - 4. Let m(a) be the second derivative of b(a). Factor m(s).
-3*s*(s - 1)/2
Suppose 3*n + 0 + 15/2*n**2 - 27*n**3 = 0. What is n?
-2/9, 0, 1/2
Let n(q) be the first derivative of 2*q**6/15 + 12*q**5/25 + 3*q**4/5 + 4*q**3/15 + 7. Factor n(m).
4*m**2*(m + 1)**3/5
Let c be 2*1*(-23)/(-138). Suppose c*r**3 + 2/3*r + 0 - r**2 = 0. Calculate r.
0, 1, 2
Let f(a) be the second derivative of 0 + 3*a - 1/2*a**3 + 3/20*a**5 + 1/2*a**4 - 3*a**2. Factor f(n).
3*(n - 1)*(n + 1)*(n + 2)
Let k = -25 + 7. Let n be k/35 - (-48)/60. Find v such that n*v - 2/7*v**2 + 4/7 = 0.
-1, 2
Let d be (-1932)/(-315) + 2/(-15). Let i(b) be the second derivative of 2*b + 0*b**2 - 1/105*b**d + 0*b**3 - 2/35*b**5 + 0 - 2/21*b**4. Solve i(m) = 0.
-2, 0
Let i(y) be the second derivative of y**6/30 + y**5/5 + 5*y**4/12 + y**3/3 + 6*y. Determine n so that i(n) = 0.
-2, -1, 0
Let c(h) be the second derivative of h**6/345 + 4*h**5/115 + 8*h**4/69 + 19*h. Let c(v) = 0. Calculate v.
-4, 0
Factor 0 + 2/3*b - 2/3*b**3 + 0*b**2.
-2*b*(b - 1)*(b + 1)/3
Suppose 0 = 5*f + 20, -3*k = 2*k + 2*f - 32. What is v in -v**2 + k - 4*v**2 + 4*v**3 - 3*v**2 - 4*v = 0?
-1, 1, 2
Factor 30*v**2 - 16*v - 50/3*v**3 + 8/3.
-2*(v - 1)*(5*v - 2)**2/3
Suppose 2*c = -5*u + 10, -8*c = -u - 4*c - 20. Factor 8*w - 2*w + u*w**2 - 2*w**2 - 3 - w**2.
-3*(w - 1)**2
Let j(r) be the second derivative of 1/3*r**3 + 0 + 1/10*r**5 + 0*r**2 - 1/3*r**4 - r. Factor j(a).
2*a*(a - 1)**2
Let y = 31 + -26. Let r(h) be the second derivative of 0 + 0*h**2 - 1/2*h**4 + 3/10*h**y + 3*h + 1/3*h**3 - 1/15*h**6. Factor r(g).
-2*g*(g - 1)**3
Let h = 461/10 - 46. Let g(c) be the first derivative of 0*c + 1/2*c**3 + 3/8*c**4 + 2 + h*c**5 + 1/4*c**2. Let g(y) = 0. Calculate y.
-1, 0
Let h = -142 + 145. Let l be (-4)/(-10) + (2 - 2). Suppose 1/5 - 1/5*d**5 - l*d**2 + 1/5*d**4 - 1/5*d + 2/5*d**h = 0. What is d?
-1, 1
Let k(n) be the second derivative of -2/7*n**2 - 1/21*n**3 + 1/70*n**5 + 2*n + 1/21*n**4 + 0. Factor k(d).
2*(d - 1)*(d + 1)*(d + 2)/7
Factor 4*i**4 - i**3 - 2*i**5 + 4*i**2 - 6*i**4 + 3*i**5 - 2*i**2.
i**2*(i - 2)*(i - 1)*(i + 1)
Let j(a) be the second derivative of -3/28*a**4 + 0*a**2 + 0*a**5 + 1/70*a**6 + 1/7*a**3 - 3*a + 0. Factor j(y).
3*y*(y - 1)**2*(y + 2)/7
Let 64 - 19*c**2 + 32*c - 16*c**2 + 39*c**2 = 0. What is c?
-4
Factor -2/5*y**2 + 2/5 + 8/5*y**3 - 8/5*y.
2*(y - 1)*(y + 1)*(4*y - 1)/5
Let h = -47 + 47. Let c(r) be the second derivative of h + 0*r**2 - 1/24*r**4 + r - 3/80*r**5 + 1/24*r**3. Factor c(g).
-g*(g + 1)*(3*g - 1)/4
Let m(r) = r**3 + 4*r**2 - 48*r - 192. Let w be m(-4). Solve w*t - 2/9*t**2 + 8/9 = 0.
-2, 2
Let i(n) be the second derivative of -n**6/120 + n**5/40 + n**4/4 - n**3/2 - 3*n. Let g(z) be the second derivative of i(z). Factor g(s).
-3*(s - 2)*(s + 1)
Let d be (3 - (-3)/(-1)) + 2. Suppose 17*v**2 - 17*v**2 - d*v**4 - v**3 - v**5 = 0. Calculate v.
-1, 0
Suppose 11*l - 24 = 3*l. Determine t, given that 18/5*t**2 - 2*t**l - 4/5 - 14/5*t**4 + 2*t = 0.
-1, 2/7, 1
Let r be (-1)/3*0 + -5. Let q(b) = b + 7. Let a be q(r). What is c in 2/5 - 1/5*c**3 + 3/5*c**4 + 1/5*c - c**a = 0?
-1, -2/3, 1
Determine h, given that -5*h - 14*h**2 + 5*h**3 + 10*h + 24*h**2 = 0.
-1, 0
Let o be (3/30)/(4/6). Let y(z) be the second derivative of 0*z**2 + 0 - 3*z + 0*z**3 + o*z**5 - 1/6*z**4 - 1/30*z**6. Find r such that y(r) = 0.
0, 1, 2
Let c be 5/(40/16) - -1. Factor 1/4*y**c - 3/4*y**2 - 1/4*y + 1/4 + 1/2*y**4.
(y - 1)*(y + 1)**2*(2*y - 1)/4
Let f(s) be the second derivative of -s**9/83160 + s**8/18480 - s**6/1980 + s**5/660 + s**4/3 + s. Let x(n) be the third derivative of f(n). Factor x(h).
-2*(h - 1)**3*(h + 1)/11
Let y be ((-81)/(-90))/((-72)/(-15)). Let b(j) be the second derivative of 0*j**2 - 1/8*j**3 + y*j**4 + 2*j + 0. Let b(w) = 0. What is w?
0, 1/3
Let k(t) be the third derivative of -t**9/15120 - t**8/20160 + t**7/2520 + t**6/2160 + t**4/24 + 2*t**2. Let o(u) be the second derivative of k(u). Factor o(d).
-d*(d - 1)*(d + 1)*(3*d + 1)/3
Let f(a) = a**2 - a + 1. Let n(x) = 3*x**4 - 6*x**3 - x**2 + x - 1. Let c(h) = -f(h) - n(h). Factor c(p).
-3*p**3*(p - 2)
Determine o so that 3/8*o**2 - 3/2*o + 9/8 = 0.
1, 3
Let a be -4*(33/(-20) - 16/(-40)). Let k(n) be the second derivative of 1/70*n**a + 1/14*n**4 + 1/7*n**3 + 0 + 1/7*n**2 - n. Factor k(f).
2*(f + 1)**3/7
Let p = 10 - 6. Let o be -2 - -1 - (0 - p). Factor -k - 5*k**o + 2*k**3 + 6*k**2 - 2*k.
-3*k*(k - 1)**2
Let q = 8 + -5. Let o(x) be the first derivative of 0*x - 1/3*x**q - 1 + 0*x**2. Suppose o(p) = 0. What is p?
0
Let g = -154/3 + 643/12. Solve -g*t**5 - 3/4*t**4 + 1/4 - 5/4*t + 1/2*t**2 + 7/2*t**3 = 0.
-1, 1/3, 1
Let j(g) = -12*g - 4. Let q be j(-2). Let h = -37/2 + q. Find n such that -9/4*n**5 - 3*n**4 + 0 + h*n**3 + 3/4*n + 3*n**2 = 0.
-1, -1/3, 0, 1
Let g(p) be the third derivative of -p**8/336 + p**7/105 - p**5/30 + p**4/24 + 9*p**2. What is c in g(c) = 0?
-1, 0, 1
Let d be (-1)/(-2) - (-4)/(-12). Let l(x) be the third derivative of -d*x**3 + 0*x + 0 + x**2 + 0*x**4 + 1/60*x**5. Factor l(y).
(y - 1)*(y + 1)
Let f be ((-72)/(-12) + -8)*3/(-4). Let 0 - 3/4*s**4 + 3/2*s - f*s**3 + 3/4*s**2 = 0. Calculate s.
-2, -1, 0, 1
Let q be (-18)/6 + 1157/(-7). Let c = -168 - q. What is n in -2/7 - c*n**2 + 4/7*n = 0?
1
Let o(n) be the second derivative of -n**8/560 - n**7/70 - n**6/20 - n**5/10 - n**4/8 + n**3/6 - 3*n. Let f(c) be the second derivative of o(c). Factor f(r).
-3*(r + 1)**4
Suppose 2*y + 0*y - 4 = 0. Factor -27*s**y + 9*s**3 - 6*s + 0*s**3 - 11*s**2 - 8 + 50*s.
(s - 2)**2*(9*s - 2)
Let c(n) = -n - 1. Let k be c(-1). Factor k*h + 4*h - 2*h + 4 - 2*h**2.
-2*(h - 2)*(h + 1)
Suppose -4*f - 3 = -3*i - 0, 3 = -5*i + 4*f. Let z be (42/(-6 - i))/(-2). Let g**2 - 3 + 3*g - 3 - 5*g + z = 0. What is g?
1
Suppose -2*r + 68 = 4*o, 4*o + 8 - 74 = -r. Suppose 5*y = 2*g + 2, 4*g - o = -5*y + 10. Factor 3*j**4 - j**5 - 5*j + y*j**3 - 2*j**2 - 2*j**4 + 4*j + 1.
-(j - 1)**3*(j + 1)**2
Suppose 13 + 9 = a. Suppose -5*m = 5*q + 5, -2*q - 4*m = -4*q + a. Factor -6*z**3 + z + 3 + 3*z**4 + 0*z - 6*z**2 + q*z**5 + 0 + 2*z.
3*(z - 1)**2*(z + 1)**3
Let p(z) = 2*z - 7. Let m be p(5). Let c(f) be the first derivative of 3 + 0*f - 1/3*f**2 + 5/9*f**m. Factor c(i).
i*(5*i - 2)/3
Let c(x) be the second derivative of -3*x + 0 + 0*x**2 + 1/18*x**4 + 0*x**3 - 1/10*x**5 - 1/63*x**7 + 1/15*x**6. Find j such that c(j) = 0.
0, 1
Let d be (1 - -1) + -1 + 0. Suppose -2*o + d = l, 3*l = -3*o + 8*l + 8. Find j, given that -6*j**2 - 4 + 3*j**2 + o - 6*j = 0.
-1
Let o = -7 + 12. Let a = -1 + o. Factor -5*n + 3*n**3 + 5*n - n**a + n - 3*n**2.
-n*(n - 1)**3
Suppose -4*d + 23 = -5*v, -4*d - v - 2 = -7. Let z be (-16)/(-6)*1/d. Factor 0 + 2*j**4 + 16/3*j**3 + 14/3*j**2 + z*j.
2*j*(j + 1)**2*(3*j + 2)/3
Let v(h) be the second derivative of -1/165*h**6 + 1/110*h**5 - 9*h + 0 + 1/66*h**4 - 1/33*h**3 + 0*h**2. Solve v(q) = 0 for q.
-1, 0, 1
Let t = 122/11 + -11. Let g(d) be the first