 derivative of b(x). What is k in w(k) = 0?
-1/2
Let v(i) be the second derivative of 2*i**7/21 + 4*i**6/15 - 8*i**5/5 - 16*i**4/3 + 32*i**3/3 + 64*i**2 - i. Suppose v(g) = 0. What is g?
-2, 2
Suppose 4*o + 3*x = -43, -4*o + 3*x - 8 = -x. Let t(j) = -j - 4. Let l be t(o). Solve -4/5*k**2 + 2/5 + 0*k + 0*k**l + 2/5*k**4 = 0 for k.
-1, 1
Let g(n) = -7*n**5 + 2*n**4 - 7*n**3 + 4*n**2 + 4. Let o(f) = f**5 + f**4 + f**3 - f**2 - 1. Let a(w) = -g(w) - 4*o(w). Factor a(b).
3*b**3*(b - 1)**2
Let h(r) = -5*r**3 + r + 8. Let k(t) = -9*t**3 + 2*t + 14. Let u(z) = -7*h(z) + 4*k(z). Factor u(f).
-f*(f - 1)*(f + 1)
Let k be 2/(-12) - 58/12. Let n = k - -11. Solve 2*x - x + 4*x**2 - n*x**2 + x**2 = 0.
0, 1
Let w(s) = -20*s**2 - 8. Let y(d) = -13*d**2 - 5. Let a(z) = -5*w(z) + 8*y(z). Let h(k) = 5*k**2 - k. Let q(f) = -3*a(f) - 2*h(f). Find j such that q(j) = 0.
-1, 0
Let -4*w**4 + w**3 + w**2 - w - 2*w**4 + 3*w**4 + 2*w**4 = 0. Calculate w.
-1, 0, 1
Let k(a) = a**2 + 5*a + 2. Let b be k(-5). Determine r so that -r**3 + 3*r**3 - 4*r - r**2 + b*r**4 - r**2 + 2*r = 0.
-1, 0, 1
Let x(f) = f**3 + 10*f**2 + 8*f - 5. Let i be x(-9). Suppose 25*d**3 - 3*d + 3*d - i*d**2 - 27*d**3 = 0. What is d?
-2, 0
Suppose 5*h - 102 = 248. Let b = 212/3 - h. Factor -1/3 + b*t**3 - 2/3*t + 0*t**2 + 1/3*t**4.
(t - 1)*(t + 1)**3/3
Factor -1 + 4*g**3 + 5 - 18*g + 14*g**3 - 3*g**2 - g**2.
2*(g - 1)*(g + 1)*(9*g - 2)
Let k(b) = -b**3 + 7*b**2 - 3*b - 3. Let l(f) = f**2 - 1. Let c(u) = k(u) - 4*l(u). Suppose c(z) = 0. Calculate z.
1
Let w(o) be the first derivative of o**5/5 - 2*o**3 - 4*o**2 + 2*o + 4. Let k(i) be the first derivative of w(i). Factor k(q).
4*(q - 2)*(q + 1)**2
Let r(a) be the first derivative of -a**4/4 + a**3/3 + a**2/2 - a + 5. Factor r(k).
-(k - 1)**2*(k + 1)
Let v(q) = -17*q**2 + 30*q - 17. Let w(l) = -26*l**2 + 44*l - 26. Let f(r) = -8*v(r) + 5*w(r). Factor f(a).
2*(a - 3)*(3*a - 1)
Let d(z) = -z + z - 6 - z + 0*z. Let h be d(-8). Suppose 2/5*u**h - 2/5*u**4 + 0*u - 2/5*u**5 + 2/5*u**3 + 0 = 0. Calculate u.
-1, 0, 1
Factor 24/5*q + 0 + 4*q**2 + 4/5*q**3.
4*q*(q + 2)*(q + 3)/5
Let l be 5*-4*(-6)/40. Factor 5*u**4 - l*u**4 + 2*u**4 - 4*u**2.
4*u**2*(u - 1)*(u + 1)
Let i(j) be the first derivative of j**7/420 + j**6/240 + j**2/2 - 4. Let h(q) be the second derivative of i(q). Factor h(f).
f**3*(f + 1)/2
Let s(r) = -3*r**5 - r**4 + 4*r**3 - r + 1. Let v(o) = -10*o**5 - 3*o**4 + 13*o**3 - o**2 - 3*o + 4. Let t(k) = 7*s(k) - 2*v(k). Suppose t(c) = 0. Calculate c.
-1, 1
Let k(f) = f - 6. Let u be k(9). Suppose -3*a = -u - 3. Determine s so that -2*s - a - 4*s**2 + 3*s**2 + 1 = 0.
-1
Let u(p) be the first derivative of 3*p**5/5 + 9*p**4/4 + 3*p**3 + 3*p**2/2 - 4. Factor u(z).
3*z*(z + 1)**3
Let g(n) be the first derivative of 0*n - 3 + 2/7*n**2 - 2/21*n**3. Determine p, given that g(p) = 0.
0, 2
Let h(l) be the second derivative of -l**5/5 + l**4/3 + 4*l**3 + 22*l. Factor h(k).
-4*k*(k - 3)*(k + 2)
Let c(f) = 7 + 0*f**2 + f**5 + f**2 - 5*f**3 - 3 - 5*f**4 - 2. Let g(i) = 6*i**4 + 6*i**3 - 3. Let h(o) = -3*c(o) - 2*g(o). Find k such that h(k) = 0.
-1, 0, 1
Let w be 38/14 + (-10)/(-35). Find p such that -2 - w*p**3 + 2*p - p**3 + 3*p**3 + 2*p**2 - p**3 = 0.
-1, 1
Let v = 1 + -5. Let q be v/(-3) - (2 - 1). Factor -1/3*b**3 + q*b + 0*b**2 + 0.
-b*(b - 1)*(b + 1)/3
Determine y so that 1/10*y + 1/10*y**3 + 0 - 1/5*y**2 = 0.
0, 1
Let t(k) = 3*k**4 + 2*k**3 - 6*k**2 - 5*k + 5. Let y(h) = -3*h**4 - 3*h**3 + 6*h**2 + 6*h - 6. Let f(b) = -6*t(b) - 5*y(b). Factor f(j).
-3*j**2*(j - 2)*(j + 1)
Let b be (-1)/(-4)*88/66. Let w(a) be the second derivative of 0*a**2 + 0 + 1/6*a**3 - a + b*a**4. Suppose w(d) = 0. Calculate d.
-1/4, 0
Solve 0*j**3 - 4*j**2 + 16*j**4 - 12*j**5 - 2*j**2 - 2*j**2 + 4*j**3 = 0.
-2/3, 0, 1
Let b(v) be the second derivative of v**6/1980 - v**4/132 - v**3/2 - 6*v. Let o(y) be the second derivative of b(y). Determine x, given that o(x) = 0.
-1, 1
Let y(m) = -31*m + 1. Let o be y(-1). Suppose -3*x + 37 = -2*l, o = 2*x - l + 9. Solve -4*k**5 + 6*k**5 - x*k**3 + 9*k**4 + 3*k**2 - 5*k**5 = 0 for k.
0, 1
Let g be (6/10 + -1)/((-18)/27). Find p, given that g - 3/5*p**2 + 0*p = 0.
-1, 1
Factor -25*p**2 + 74*p + 41*p - 25*p + 40.
-5*(p - 4)*(5*p + 2)
Factor -1/2*k**4 + 1/2*k + 3/2*k**2 - 1/2*k**3 - 1.
-(k - 1)**2*(k + 1)*(k + 2)/2
Let r(x) be the second derivative of x**5/80 + x**4/48 - x**3/24 - x**2/8 - 8*x. Factor r(k).
(k - 1)*(k + 1)**2/4
Suppose 16 = 4*a - 4*b - 4, 0 = -a - 2*b - 4. Factor 8*r**2 - r - 6*r**2 - r**a.
r*(r - 1)
Let x(s) be the third derivative of s**8/168 + s**7/105 - s**6/30 - s**5/15 + s**4/12 + s**3/3 + s**2. Factor x(w).
2*(w - 1)**2*(w + 1)**3
Let s(y) = 4*y**4 + 3*y**3 + 6*y**2 + y. Let v(c) = 23*c**4 + 18*c**3 + 35*c**2 + 6*c. Suppose -3*w + 99 + 3 = 0. Let o(n) = w*s(n) - 6*v(n). Factor o(p).
-2*p*(p + 1)**3
Let o = 26 + -24. Solve 0*d + 0 - 1/3*d**3 + 2/3*d**o = 0.
0, 2
Suppose -t - t + 14 = 0. Solve -m**2 + 3*m**2 - 3*m + 0*m**3 - 2*m**4 - 4*m**3 + t*m = 0.
-2, -1, 0, 1
Let a = 134 - 134. Let b(o) be the third derivative of -1/20*o**5 + a*o - 2*o**2 - 3/4*o**4 + 0 - 9/2*o**3. Find i, given that b(i) = 0.
-3
Let s(g) be the first derivative of -2/5*g**5 + 1/4*g**4 + 0*g**3 + 0*g + 0*g**2 + 1/6*g**6 - 8. Factor s(t).
t**3*(t - 1)**2
Determine x so that 3*x**3 - 3*x + 6*x**2 + 3 + 5 - 14 = 0.
-2, -1, 1
Let x(h) be the first derivative of h**4/20 - 2*h**3/15 + 14. Factor x(j).
j**2*(j - 2)/5
Let i(v) be the third derivative of -v**6/120 + v**4/8 - v**3/6 + 2*v**2. Let j(n) be the first derivative of i(n). Suppose j(d) = 0. What is d?
-1, 1
Let g(c) be the second derivative of 0 - 1/6*c**4 - c - 1/60*c**5 - 2/3*c**3 - 4/3*c**2. Suppose g(o) = 0. What is o?
-2
Let p(u) be the second derivative of u**6/105 - u**5/70 - u**4/14 + u**3/21 + 2*u**2/7 + 9*u. Factor p(d).
2*(d - 2)*(d - 1)*(d + 1)**2/7
Let b be (-6)/(-21) + 1/28*13. Suppose 9/4*u - b + 3/4*u**3 - 9/4*u**2 = 0. What is u?
1
Let n(p) be the second derivative of p**5/40 - p**4/12 - p**3/12 + p**2/2 - 13*p. Factor n(i).
(i - 2)*(i - 1)*(i + 1)/2
Let u(m) = 3*m**2 - 2*m - 1. Let v = 0 - 4. Let w(k) = 5*k**2 - 4*k - 2. Let j(z) = v*w(z) + 7*u(z). What is t in j(t) = 0?
-1
Factor 4/5 - 2/15*u**2 + 2/3*u.
-2*(u - 6)*(u + 1)/15
Let y(x) be the first derivative of -3 + 0*x + 1/12*x**3 + 0*x**2. Determine z, given that y(z) = 0.
0
Suppose 0 = -4*f - 3*d + 5, -5*f - 2*d = -2 - 6. Let v = 12 + -10. Factor -v*j**2 - 2*j**2 + 3*j**f - j**3 + 1 + 0*j + j.
-(j - 1)*(j + 1)**2
Let m(y) = 20*y**3 - 20*y**2 + 25*y. Let w(v) = -5*v**3 + 5*v**2 - 6*v. Let r(i) = 6*m(i) + 25*w(i). Factor r(u).
-5*u**2*(u - 1)
Suppose -4*z + 4 = -t, -7*t = -4*z - 3*t - 8. Suppose 12/7*w - 12/7*w**z + 3/7*w**3 + 0 = 0. Calculate w.
0, 2
Let 7 + 3*w**2 - 16 + 6 = 0. Calculate w.
-1, 1
Let j = -11 + 9. Let k be (-4)/(-8) + j/8. Suppose 1/2 + k*u**2 - 3/4*u = 0. Calculate u.
1, 2
Let t(g) be the second derivative of g**6/10 + 3*g**5/20 - g**4 - 2*g**3 + 10*g. Factor t(b).
3*b*(b - 2)*(b + 1)*(b + 2)
Let k(p) = 3*p**4 + 3*p**3 - 6*p**2 - 9*p + 12. Let j(h) = -h**3 + h**2 + h. Let a(v) = 3*j(v) - k(v). Let a(z) = 0. What is z?
-2, 1
Let k(n) be the first derivative of n**6/6 - 4*n**5/5 + 5*n**4/4 - 2*n**3/3 + 8. Factor k(l).
l**2*(l - 2)*(l - 1)**2
Let b(m) be the second derivative of 5*m**4/36 - 17*m**3/18 + m**2 - 22*m. Factor b(o).
(o - 3)*(5*o - 2)/3
Let a = 4 - -1. Factor x**2 + x**2 - 2*x**4 - x**a - 2*x**3 + 3*x**5.
2*x**2*(x - 1)**2*(x + 1)
Suppose 0 = 4*a - q - 76, -3*a - 4*q = a - 56. Let n be (-6)/a*(0 - 0). Suppose -3*h + h**3 + n*h + 4*h + 2*h**2 = 0. Calculate h.
-1, 0
Solve -7/4*h**5 - 1/2*h**3 + 0*h + 0*h**2 + 0 + 9/4*h**4 = 0 for h.
0, 2/7, 1
Let n(v) be the first derivative of 2/5*v**5 + 0*v - 1 + 0*v**3 + 0*v**2 + 1/5*v**4. Factor n(p).
2*p**3*(5*p + 2)/5
Let j(u) = 19*u + 1. Let i be j(1). Suppose 2*q = -c - 4, -q + 5*c = 2*q - i. Factor 0 - 2/3*o**3 + 0*o + q*o**2.
-2*o**3/3
Let t be (-20)/(-3) - (-6)/(-9). Factor -2*i**2 + t + 27*i + 0 - 31*i.
-2*(i - 1)*(i + 3)
Let c(u) be the first derivative of u**4/12 + 2*u**3/3 - 32*u/3 + 3. Find f such that c(f) = 0.
-4, 2
Let r(u) = -u**5 + u**3 + u**2 + u - 1. Let o(t) = -9*t**5 + 5*t**4 + t**3 + 11*t**2 + 8*t - 8. Let w(h) = 3*o(h) - 24*r(h). What is g in w(g) = 0?