= -k**2 - 100*k + 500. Let l(b) = b**2. Let n(z) = 6*l(z) + v(z). Find d, given that n(d) = 0.
10
Let l = 71 - 69. Let q(t) be the first derivative of -1/9*t**3 + l + 1/3*t**2 + 0*t. What is f in q(f) = 0?
0, 2
Let f(s) be the first derivative of -s**6/2 + 12*s**5/5 - 9*s**4/2 + 4*s**3 - 3*s**2/2 - 4. Factor f(u).
-3*u*(u - 1)**4
Factor -p**2 - 10 - 15*p - 8*p**2 + 4*p**2.
-5*(p + 1)*(p + 2)
Find r such that -1/2*r**3 - 1/2*r**2 - 1/6*r + 0 - 1/6*r**4 = 0.
-1, 0
Let u = 953 + -85769/90. Let s(q) be the second derivative of 0*q**4 + 0*q**3 + 0*q**5 - u*q**6 + 0 - 3*q + 0*q**2 + 1/126*q**7. Factor s(c).
c**4*(c - 1)/3
Let l(o) be the first derivative of 4*o**3/3 - 4*o + 1. Factor l(x).
4*(x - 1)*(x + 1)
Factor -3/4 + 3/4*y**2 + 9/8*y.
3*(y + 2)*(2*y - 1)/8
Let m(z) be the first derivative of -3 + 1/4*z**3 + 3*z - 3/16*z**4 + 1/20*z**5 - 1/8*z**2. Let r(y) be the first derivative of m(y). Factor r(b).
(b - 1)**2*(4*b - 1)/4
Factor -2*f**4 - 7*f**4 + f**4 + 4*f**2 + 4*f**4.
-4*f**2*(f - 1)*(f + 1)
Suppose 4*u = t + 219, -2*u - 5*t = -t - 96. Let n = 274/5 - u. Solve -n - 1/5*x**2 - 3/5*x**3 + 8/5*x = 0 for x.
-2, 2/3, 1
Determine d, given that 9 - 3*d**3 - 15 - 3*d**4 + 5*d - 2*d + 9*d**2 = 0.
-2, -1, 1
Suppose -6 = -6*w + 3*w. Let v = 5 - w. Solve -q + q**2 + 0*q**3 - 4*q + 5*q**v - 3*q**4 + 0*q**2 + 2 = 0 for q.
-1, 2/3, 1
Let i(o) be the second derivative of -o**5/30 + o**4/4 - 2*o**3/3 - 2*o**2 + 2*o. Let j(x) be the first derivative of i(x). Factor j(n).
-2*(n - 2)*(n - 1)
Factor 5*g**2 + 10 + 16 - 6 - 20*g.
5*(g - 2)**2
Let g = 568 + -566. Suppose 2*x + 0 + 14*x**g - 14*x**4 + 45/2*x**3 - 49/2*x**5 = 0. Calculate x.
-1, -2/7, 0, 1
Let i(g) be the first derivative of -g**6/80 + g**5/15 - 7*g**4/48 + g**3/6 + g**2 - 4. Let a(x) be the second derivative of i(x). Solve a(s) = 0.
2/3, 1
Suppose -2*r + 6 = 0, -4 = -o - r + 3. Factor 0*t + 1/2*t**2 + 3/2*t**o + 0 - 3/2*t**3 - 1/2*t**5.
-t**2*(t - 1)**3/2
Let c(x) be the first derivative of -3*x**5/5 - 15*x**4/2 - 33*x**3 - 60*x**2 - 48*x + 5. Solve c(j) = 0 for j.
-4, -1
Let m(l) = -2*l + 1. Let a be m(-1). Factor -2*p**4 + p**3 - 36*p + 12*p - 26*p**2 - 14*p**3 - 8 + p**a.
-2*(p + 1)**2*(p + 2)**2
Let j(p) be the second derivative of p**5/90 + p**4/18 + p**3/9 + p**2/9 - p. Find s such that j(s) = 0.
-1
Let z = -123/4 + 31. Suppose z*j**2 - 1/4 + 0*j = 0. Calculate j.
-1, 1
Let w(f) be the first derivative of 16*f**2 + 3 + 42/5*f**5 - 3*f**6 - 7/2*f**4 - 34/3*f**3 - 8*f. Determine v, given that w(v) = 0.
-1, 2/3, 1
Let k(u) be the third derivative of 7*u**9/648 - u**8/36 - u**7/420 + u**6/27 + u**5/45 - u**3 + 3*u**2. Let o(g) be the first derivative of k(g). Factor o(n).
2*n*(n - 1)**2*(7*n + 2)**2/3
Let q(c) be the second derivative of 5/24*c**4 - 3*c + 1/6*c**3 + 0*c**2 + 3/40*c**5 + 0. What is m in q(m) = 0?
-1, -2/3, 0
Let q(f) = -f**2 - 8*f + 12. Let b be q(-10). Let k = 8 + b. Find h such that k - 2/3*h**3 + 1/3*h + 0*h**2 + 0*h**4 + 1/3*h**5 = 0.
-1, 0, 1
Let w(l) be the first derivative of l**4/6 + l**3/3 + l - 2. Let g(t) be the first derivative of w(t). Solve g(o) = 0.
-1, 0
Let t(a) be the second derivative of 0 - 2/45*a**5 + 7/54*a**4 - 1/9*a**2 + a - 2/27*a**3. Find x, given that t(x) = 0.
-1/4, 1
Let c = -5 + 8. Suppose c = a - 7. Suppose 2*o**3 - 4*o**3 + 6 - 2 - a*o + 8*o**2 = 0. What is o?
1, 2
Let u = -4045 - -40483/10. Let i = 251/70 - u. Factor 0 - 4/7*n**3 - i*n**4 + 0*n - 2/7*n**2.
-2*n**2*(n + 1)**2/7
Let v(u) = 2*u**2 - 3*u + 3. Let s(o) = -4*o**2 + 7*o - 7. Let k(h) = 3*s(h) + 7*v(h). What is g in k(g) = 0?
0
Let d(p) = -70*p**3 - 85*p**2 - 15*p + 55. Let k(g) = 5*g**3 + 6*g**2 + g - 4. Let u(l) = 4*d(l) + 55*k(l). Factor u(o).
-5*o*(o + 1)**2
Let c(t) be the first derivative of 1/600*t**6 - 1/2*t**2 + 0*t + 1 + 0*t**5 - 1/120*t**4 + 0*t**3. Let m(h) be the second derivative of c(h). Factor m(o).
o*(o - 1)*(o + 1)/5
Let o = -1333/18 + 223/3. Let i(s) be the second derivative of o*s**4 - 1/30*s**5 + 4/3*s**2 - 8/9*s**3 + 0 + s. Suppose i(g) = 0. What is g?
1, 2
Let t(a) be the first derivative of a**4/14 + 20*a**3/21 + 4*a**2 + 48*a/7 + 25. Factor t(d).
2*(d + 2)**2*(d + 6)/7
Let s(i) = 2*i**2 - i - 8. Let u be s(-2). Find y, given that -2/5*y**3 + 2/5*y**u + 1/5*y + 1/5*y**5 - 1/5*y**4 - 1/5 = 0.
-1, 1
Determine b so that -6/13 + 2/13*b**2 + 4/13*b = 0.
-3, 1
Let a(r) be the second derivative of -r**4/20 - 3*r**3/10 - 3*r**2/5 + 21*r. Let a(n) = 0. Calculate n.
-2, -1
What is g in 0 - 1/2*g**4 + 1/2*g**2 + 0*g**3 + 0*g = 0?
-1, 0, 1
Suppose 3*f = 2*f - 4. Let a be (-4)/32*18 - f. Factor 5/4*t**4 + a*t - 7/4*t**3 - 3/4*t**2 - 1/2.
(t - 1)**2*(t + 1)*(5*t - 2)/4
Suppose 3*o - 85 + 25 = 0. Suppose -2*t = 5*r, -2*r + 9 = -5*t - o. Let 1/3*x - 4/3*x**r + 0 = 0. What is x?
0, 1/4
Let x(b) be the first derivative of -2*b**3/15 + 3*b**2/5 - 14. What is s in x(s) = 0?
0, 3
Let z(l) be the first derivative of 4*l**3/3 - 6*l**2 + 27. Solve z(u) = 0.
0, 3
Suppose -69 = 5*l + y, -3*y = 1 - 4. Let o = l + 16. Solve -4/5 - 2/5*b + 2/5*b**o = 0.
-1, 2
Let f(u) = 6*u - 4. Let l be f(1). Let x = 1 + -1. Factor -2*v**3 + l*v**2 - 4*v**2 - 2*v**2 + x*v**3.
-2*v**2*(v + 2)
Let g(c) be the first derivative of c**5/20 - c**4/12 - c**3/6 + c**2/2 + 3*c + 4. Let b(u) be the first derivative of g(u). Find d, given that b(d) = 0.
-1, 1
Let x(h) = -h**2 + 4 - 59*h + 0 + 68*h. Let g be x(9). Find l, given that 9*l**3 - 10*l**3 + g*l + 21*l**2 - 4*l**5 - 11*l**5 - 4 - 29*l**4 = 0.
-1, 2/5, 2/3
Let l(t) = -t**2 + 4*t + 7. Let c be l(6). Let b be (-1*(3 + -2))/c. Factor 2/5*k + 1/5*k**2 + b.
(k + 1)**2/5
Let s = 4 - 1. Suppose 4*b = f + 14, -4*b - s*f + 2 = 2*f. Factor -8*r**b + 6*r**4 - 4*r**3 + 2*r**3 + 2*r**2 + 2*r.
2*r*(r - 1)**2*(3*r + 1)
Let c be 182/195*1*(-8)/(-28). Factor 0*y**2 + 2/15*y**5 + 0 + 2/15*y**3 + c*y**4 + 0*y.
2*y**3*(y + 1)**2/15
Let f(j) = j**3 + j. Let b(k) = 2*k**3 - 3*k**2 - 1. Let h(r) = b(r) - 3*f(r). Find y such that h(y) = 0.
-1
Let g(a) be the first derivative of -2*a**5/5 - a**4/2 + 6*a**3 - 11*a**2 + 8*a + 3. Suppose g(r) = 0. Calculate r.
-4, 1
Solve -3/4*p**4 + 1/4*p**3 - 1/4*p + 5/4*p**2 - 1/2 = 0 for p.
-1, -2/3, 1
Let p(z) be the second derivative of -z**7/210 + z**6/60 - z**4/12 + z**3/6 - z**2 + 3*z. Let d(w) be the first derivative of p(w). Factor d(y).
-(y - 1)**3*(y + 1)
Let k(t) be the second derivative of -t**6/20 + 3*t**4/16 + t**3/4 + t**2/2 - 6*t. Let r(u) be the first derivative of k(u). Factor r(n).
-3*(n - 1)*(2*n + 1)**2/2
Let u(w) be the third derivative of 0*w + 2/3*w**3 + 9*w**2 - 1/30*w**5 + 1/12*w**4 + 0. Factor u(s).
-2*(s - 2)*(s + 1)
Let b(a) be the first derivative of -a**5/30 + a**4/6 + a**2/2 - 3. Let y(v) be the second derivative of b(v). Solve y(j) = 0.
0, 2
Let y(d) be the first derivative of d**6/45 - d**5/18 + d**4/27 - d + 1. Let k(m) be the first derivative of y(m). Factor k(q).
2*q**2*(q - 1)*(3*q - 2)/9
Let y(f) = 2*f**2 + f - 1. Let g(c) = c**2 - 1. Let l(m) = 3*g(m) - 2*y(m). Factor l(x).
-(x + 1)**2
Let v(m) be the third derivative of m**5/150 + m**4/30 - 8*m**2. Factor v(y).
2*y*(y + 2)/5
Let o(k) be the third derivative of -k**8/560 + k**7/175 + k**6/100 - k**5/25 - k**4/40 + k**3/5 - 26*k**2. Suppose o(t) = 0. What is t?
-1, 1, 2
Let m be 2 + ((-27)/6)/3. Let y(n) be the second derivative of -1/48*n**4 + 0 - 1/6*n**3 + 2*n - m*n**2. Solve y(q) = 0 for q.
-2
Let c(y) = -3 - 4 + 2*y - 3*y - 3*y. Let w be c(-3). Let -3/2*p**3 + 1/4*p - 2*p**4 + 0 - 3/4*p**w + 0*p**2 = 0. Calculate p.
-1, 0, 1/3
Let k(r) = r**2 - 18*r + 67. Let d be k(5). Suppose -2*i**d - 2/7*i**3 - 30/7*i - 18/7 = 0. Calculate i.
-3, -1
Suppose 2*y = -g - 3*y + 45, -3*y = -15. Suppose 0 = -d - 4*d + g. Solve 4*f**3 - 13/3*f**2 - 4/3*f**d + 2*f - 1/3 = 0.
1/2, 1
Let c(t) = -t**2 + 4*t + 2. Let l be c(4). Let o = -3/14 - -5/7. Factor -2 - 4*g - 5/2*g**l - o*g**3.
-(g + 1)*(g + 2)**2/2
Suppose -5*m + 10 = -0. Let s be m/4*0/3. Determine o so that 0*o**2 + 1/2*o**3 + 0 + s*o = 0.
0
Factor 2/5*h - 2/5*h**3 - 3/5*h**4 + 3/5*h**2 + 0.
-h*(h - 1)*(h + 1)*(3*h + 2)/5
Let y = 4 + 2. Let q be ((-110)/y)/(-5) + -3. Factor 0 + 2/3*f - q*f**2.
-2*f*(f - 1)/3
Suppose -3*g - 3 = 3. Let f be ((-25)/(-15))/(g/(-6)). Factor 4*o**3 + 3*o**2 - 3*o**2 + 18*o**4 + 14*o**f.
2*o**3