2*l*(l + 2)*(3*l + 1)/5
Factor 3/8 - 3/4*p**3 - 1/4*p**2 + 5/8*p - 1/8*p**4 + 1/8*p**5.
(p - 3)*(p - 1)*(p + 1)**3/8
Let k(f) be the third derivative of -f**5/60 - f**4/24 + f**3/6 + 9*f**2. Let r(d) = -4*d + 3. Let n(u) = -k(u) + r(u). Solve n(v) = 0 for v.
1, 2
Let n(b) be the first derivative of -2*b**5/45 + b**4/9 - 2*b**3/27 + 3. What is o in n(o) = 0?
0, 1
Let x = 0 - 0. Let o(k) be the third derivative of k**2 + 0*k**4 + 1/240*k**5 + 0 + 0*k**3 + x*k - 1/480*k**6. Factor o(h).
-h**2*(h - 1)/4
What is n in -4/13*n - 10/13*n**2 + 0 + 22/13*n**3 - 8/13*n**4 = 0?
-1/4, 0, 1, 2
Factor -2/13*y**4 + 2/13*y - 2/13*y**3 + 2/13*y**2 + 0.
-2*y*(y - 1)*(y + 1)**2/13
Let g(x) be the third derivative of -x**7/11340 - x**6/3240 + x**5/270 + x**4/6 - 2*x**2. Let b(f) be the second derivative of g(f). Factor b(n).
-2*(n - 1)*(n + 2)/9
Let h(a) = -6*a**2 - 27*a + 6. Let r(q) = q**2 + 4*q - 1. Let f(w) = -4*h(w) - 27*r(w). What is p in f(p) = 0?
-1, 1
Let n(h) be the third derivative of -h**6/24 + 8*h**5/15 - 19*h**4/8 + 3*h**3 + 7*h**2. Factor n(o).
-(o - 3)**2*(5*o - 2)
Let r(k) = k**5 + k**4 - 4*k**3 - 2*k**2 - 2*k. Let j(y) = 8*y**5 + 8*y**4 - 33*y**3 - 17*y**2 - 17*y. Let u(o) = -6*j(o) + 51*r(o). Solve u(d) = 0 for d.
-2, 0, 1
Let h(w) be the second derivative of w**7/630 - w**6/60 + w**5/15 - 5*w**4/12 + 5*w. Let v(c) be the third derivative of h(c). Solve v(i) = 0 for i.
1, 2
Find g, given that -g**5 - 3*g**4 - 3 + 3*g - 2*g**3 + 1 + 2*g**2 + 3 = 0.
-1, 1
Let u(k) = -k**3 + 5*k**2 - k + 1. Let g be u(5). Let p = g + 8. Suppose 4*i**2 + 2/5 + 4*i**3 + 2/5*i**5 + 2*i + 2*i**p = 0. Calculate i.
-1
Let w = 18 - 15. Let t(h) be the first derivative of 0*h - 1/2*h**4 + h**2 + 0*h**w - 1. Suppose t(p) = 0. What is p?
-1, 0, 1
Factor -6 - 72*j**2 - 14 + 7*j**4 - 60*j - 30*j**3 + 7*j**2 - 12*j**4.
-5*(j + 1)**2*(j + 2)**2
What is x in 0*x + 1/8*x**2 - 1/2 = 0?
-2, 2
Let p(b) be the second derivative of b**4/12 - b**3/2 - 5*b. Factor p(f).
f*(f - 3)
Solve 0*r**4 + 0*r + 1/3*r**5 + 0*r**2 - 1/3*r**3 + 0 = 0 for r.
-1, 0, 1
Let t(g) be the first derivative of g**6/2 - 3*g**5 + 9*g**4/2 + 4*g**3 - 12*g**2 - 2. Determine p so that t(p) = 0.
-1, 0, 2
Let a be (-17 + 23)*4/6. Let t(s) be the third derivative of 1/30*s**3 - 1/300*s**5 + 0*s + 0 + 1/600*s**6 - a*s**2 - 1/120*s**4. Find j such that t(j) = 0.
-1, 1
Let j(z) = z**3 + z**2 - 1. Let b(w) = w**3 + 13*w**2 + 21*w + 11. Let l(u) = b(u) + 2*j(u). Let l(c) = 0. What is c?
-3, -1
Let z(r) = -r**4 - 4*r**3 + 11*r**2 + 10*r. Let h(f) = f**4 + 9*f**3 - 21*f**2 - 20*f. Let t(u) = -4*h(u) - 9*z(u). Find y such that t(y) = 0.
-1, 0, 2
Let w(i) be the third derivative of i**6/300 + i**5/50 + i**4/20 + i**3/15 + 5*i**2. Suppose w(q) = 0. Calculate q.
-1
Let -3/2*f**4 + 3 - 3/2*f**2 - 9/2*f + 9/2*f**3 = 0. Calculate f.
-1, 1, 2
Let t be (-1 - 0)/((-6)/24). Let d(j) be the third derivative of -j**2 + 0 + 1/210*j**5 + 0*j**3 + 0*j**t + 0*j. Let d(s) = 0. Calculate s.
0
Let u be (-1)/(-6)*(-226)/(-1). Let f = u + -37. Determine q, given that f*q**4 - 2/3*q**2 + 0*q**3 + 0*q + 0 = 0.
-1, 0, 1
Suppose 3*n = 0, -7*j + n = -3*j - 16. Let m(p) = -p + 4. Let a be m(j). Solve 0 - 2*f**4 + 0*f + a*f**2 + 4/5*f**3 = 0.
0, 2/5
Let m be (1 - 1)/(-4 + 5). Factor a**2 + m + a**3 + 5 - 5.
a**2*(a + 1)
Let l be (-22)/24 + (-1)/(-6)*6. Let f(k) be the first derivative of 2 + 0*k + l*k**4 + 0*k**2 + 1/9*k**3. Find n such that f(n) = 0.
-1, 0
Suppose 4*t = 1 + 11. Let m be (-252)/48*t/(-7). Solve -m*h + 1/2*h**4 + 7/2*h**2 + 1/2 - 9/4*h**3 = 0 for h.
1/2, 1, 2
Let a(t) = -483*t**5 + 707*t**4 + 527*t**3 + 87*t**2 + 7. Let v(i) = 241*i**5 - 354*i**4 - 264*i**3 - 44*i**2 - 4. Let o(z) = -4*a(z) - 7*v(z). Factor o(n).
5*n**2*(n - 2)*(7*n + 2)**2
Find l such that 4/9*l**2 + 2/9*l**3 - 4/9*l**4 + 0*l - 2/9*l**5 + 0 = 0.
-2, -1, 0, 1
Let z(i) be the first derivative of i**7/140 + i**6/40 - i**4/8 - i**3 + 4. Let y(f) be the third derivative of z(f). Factor y(d).
3*(d + 1)**2*(2*d - 1)
Let i(y) be the third derivative of y**7/280 - y**5/80 + 36*y**2. Factor i(f).
3*f**2*(f - 1)*(f + 1)/4
Let j(z) be the first derivative of z**9/1512 - z**7/105 + z**6/90 + z**5/20 - z**4/6 - z**3 + 2. Let r(m) be the third derivative of j(m). Factor r(k).
2*(k - 1)**3*(k + 1)*(k + 2)
Let b be (0 + 0 - 0)*-1. Let l(q) be the second derivative of 1/9*q**4 - 1/63*q**7 - 2/45*q**6 - q + 1/9*q**3 + 0 + b*q**2 + 0*q**5. Solve l(y) = 0 for y.
-1, 0, 1
Let s(f) = f**2 + 6*f - 2. Let m be s(-6). Let t be (-4)/(-6)*(-6)/m. Factor -8/5*u**3 + 12/5*u**t - 8/5*u + 2/5 + 2/5*u**4.
2*(u - 1)**4/5
Suppose 6*x = 3*x + 18. Solve -x*t**3 + 8*t**2 - 8*t**2 + 15*t**4 = 0.
0, 2/5
Let l be (16/20)/((-2)/(-10)). Suppose -14 = 3*n - 5*z, 0*n + l*n = 2*z. Let 2*k - 2*k + k**n - k = 0. What is k?
0, 1
Let c(i) = 3*i**3 - i**2 + 1. Let j be c(1). Let l(n) be the first derivative of -j + 0*n + 4/3*n**3 + n**2 - 1/3*n**6 + 0*n**4 - 4/5*n**5. Factor l(f).
-2*f*(f - 1)*(f + 1)**3
Let s be 0 + (2 - (0 + -3)). Let z(c) be the second derivative of -2/105*c**6 + 1/10*c**s + 0 - c + 0*c**2 - 1/21*c**7 + 0*c**3 + 1/21*c**4. Solve z(j) = 0.
-1, -2/7, 0, 1
Suppose -40 + 26 + 2*y**3 + 12*y**2 - 50 = 0. What is y?
-4, 2
Suppose 3 = -m + 3*n - 1, -3*m + n + 12 = 0. Suppose m*y = 4*b - 0*b - 6, 2*y + 8 = 3*b. Determine s so that 1/4*s - 1/4*s**4 + 0 + 1/4*s**y - 1/4*s**3 = 0.
-1, 0, 1
Let z(q) = 2*q**2 + 85*q - 41. Let j be z(-43). Find m such that -1/2*m + 0 - 1/4*m**j = 0.
-2, 0
Let s(u) = -u**3 + 6*u**2 + 8*u - 5. Let p be s(7). Factor -3*o - 5 - p*o**2 + 5 + 5*o**2.
3*o*(o - 1)
Let w(j) be the third derivative of -1/60*j**5 + 0 - 1/6*j**3 - 1/60*j**6 - 2*j**2 + 0*j + 1/6*j**4. Let u(v) be the first derivative of w(v). Factor u(a).
-2*(a + 1)*(3*a - 2)
Let w(v) be the first derivative of 1/5*v**4 + 0*v**3 + 0*v + 6 + 0*v**2. Determine i, given that w(i) = 0.
0
Suppose 5*b = 2*b + 6. Factor 4*s + 7*s + 4 + 3*s**2 - b*s + 2.
3*(s + 1)*(s + 2)
Let f(b) = -2*b**4 - b**2 + 5*b**2 - 7*b**4 - 5*b**3. Let q be -1 - -1*(-12)/(-2). Let h(r) = 5*r**4 + 3*r**3 - 2*r**2. Let s(a) = q*h(a) + 3*f(a). Factor s(v).
-2*v**2*(v - 1)*(v + 1)
Suppose -4*u + 7*g - 2*g = -7, 0 = -2*u + 2*g + 6. Determine o so that 2*o**4 + 10*o**5 + 4*o**3 - 2*o**4 - 6*o**4 - u*o**4 = 0.
0, 2/5, 1
Determine t, given that -2/3*t**3 + 2*t**2 + 0*t + 0 = 0.
0, 3
Let w = -224/209 - -10/19. Let n = w - -52/55. Find f, given that n - 1/5*f**2 - 1/5*f = 0.
-2, 1
Let c = 7 + -1. Let o(a) be the first derivative of 2*a**5 + 3/2*a**4 - 2/3*a**3 + 0*a + 2 - a**2 + 2/3*a**c. Find x, given that o(x) = 0.
-1, 0, 1/2
Suppose -2*a + 35 = 5*c, 0 = -3*a - c + 4*c. Let i(z) = z**2 - 5*z + 4. Let r be i(a). What is h in 0*h + 2/3*h**3 + 1/3*h**r + 0 + 1/3*h**2 = 0?
-1, 0
Let -4/3*j**2 - 1/3*j**3 - 2/3 - 5/3*j = 0. Calculate j.
-2, -1
Let b be (20/(-3))/(5/(-15)). Suppose -5*o = -x + 10, -2*x + b = -6*o + o. Suppose -9*d**4 - 2*d - 4*d**5 - 7*d**4 + x*d**5 + 12*d**3 = 0. What is d?
-1/3, 0, 1
Let n = -73 - -439/6. Let i(z) be the third derivative of -1/210*z**7 - 2*z**2 + 0*z**6 + 0 + 1/30*z**5 - n*z**3 + 0*z + 0*z**4. Factor i(w).
-(w - 1)**2*(w + 1)**2
Let r(j) be the first derivative of 2*j**3/3 + 1. Let z(h) = -h**2. Let q(v) = -3*r(v) - 7*z(v). What is d in q(d) = 0?
0
Let k = 5 + 3. Factor k*z - 8/5 - 10*z**2.
-2*(5*z - 2)**2/5
Let r(t) = -t**5 - 4*t**4 - 2*t**3 - 5*t**2 + 2*t. Let k(m) = -m**4 - m**3. Let j(w) = 5*k(w) - r(w). Let j(o) = 0. What is o?
-2, 0, 1
Let g(z) be the third derivative of -z**8/84 - 2*z**7/105 + z**6/15 + 2*z**5/15 - z**4/6 - 2*z**3/3 + 12*z**2. Find j such that g(j) = 0.
-1, 1
Let z(c) = -c**2 + 5*c + 10. Let o be z(7). Let w be o/(-16)*(-64)/(-12). Find b, given that 1/3*b**4 + 4/3*b + 2*b**2 + 1/3 + w*b**3 = 0.
-1
Let r(q) = q**3 + 5*q**2 + 3. Let i be r(-5). Let v = i - 2. What is f in 2*f**4 - 1 + v = 0?
0
Let a(o) = o - 4. Let z be 5 - (0 - (-2 + 3)). Let w be a(z). Factor 1/3 + 7/3*f**w - 5/3*f - f**3.
-(f - 1)**2*(3*f - 1)/3
Let c(x) be the first derivative of 0*x**4 + 0*x + 1/2*x**2 - 1/10*x**5 + 1/2*x**3 + 2. Factor c(h).
-h*(h - 2)*(h + 1)**2/2
Let i(o) be the third derivative of -o**7/1260 + o**6/180 - o**5/60 + o**4/36 + 2*o**3/3 - 3*o**2. Let m(r) be the first derivative of i(r). Factor m(x).
-2*(x - 1)**3/3
What i