0 + 1/6*n**5 + 1/2*n**4 + 0*n - 2/3*n**2.
n**2*(n - 1)*(n + 2)**2/6
Let i(n) be the third derivative of -n**8/896 + n**7/560 + 3*n**6/320 - n**5/32 + n**4/32 + 6*n**2. Determine y so that i(y) = 0.
-2, 0, 1
Let u(q) = 7*q - 2. Let n be u(1). Let -2*m**2 - 2*m**2 - n*m + 5*m = 0. What is m?
0
Suppose -344*d + 332*d + 48 = 0. Suppose 0*p - 2/11*p**2 - 32/11*p**5 - 16/11*p**3 + 0 - 40/11*p**d = 0. Calculate p.
-1/2, -1/4, 0
Suppose 3*n - 506 = -x + 6*x, 0 = 3*n - x - 526. Let o = -881/5 + n. Factor 2/5*d**2 + 2/5 + o*d.
2*(d + 1)**2/5
Let f(s) = s**3 - s**2. Let y(u) = -9*u**2 - 3*u. Let t(w) = -3*f(w) + y(w). Factor t(o).
-3*o*(o + 1)**2
Let l(v) be the second derivative of -v**6/1260 + v**5/210 - v**4/84 - 7*v**3/6 + 4*v. Let w(y) be the second derivative of l(y). Determine t so that w(t) = 0.
1
Suppose 0 = 2*y - 6 - 0. Suppose 0 = y*j - 6. Let 4*i**j - 4*i**2 + 5*i**2 - 3*i**2 = 0. What is i?
0
Let t(z) be the second derivative of z**4/3 + 2*z**3/3 - 22*z. Factor t(c).
4*c*(c + 1)
Let b(z) be the first derivative of 5*z**4/16 - 5*z**3/12 - 5*z**2/2 + 5*z + 40. Factor b(n).
5*(n - 2)*(n - 1)*(n + 2)/4
Suppose -5*q + 2*x = -2, 3*q + 3*x = -x + 22. Factor -12*l - 4*l**5 - 32*l**3 - 15*l**4 + 0*l**5 - 3*l**4 - 28*l**2 - q + 0*l**4.
-2*(l + 1)**4*(2*l + 1)
Let b(m) be the second derivative of -m**6/3 + 23*m**5/20 - 31*m**4/20 + 16*m**3/15 - 2*m**2/5 - 5*m. What is k in b(k) = 0?
2/5, 1/2, 1
Factor -19*y - 2*y - 14*y**2 + 9 - 1 - 3*y.
-2*(y + 2)*(7*y - 2)
Let b(i) = 3*i - 5. Let j be b(3). What is f in 0 + 5 + 20*f**3 + 18*f**2 - 5 + 4*f + 6*f**j = 0?
-2, -1, -1/3, 0
Let s = -2 - -26. Factor 22*q**2 + 2*q**4 - 4*q + 0*q**4 - s*q**2 + 4*q**3.
2*q*(q - 1)*(q + 1)*(q + 2)
Determine g, given that 0 + 9/4*g**2 + 0*g + 3/4*g**3 - 9/4*g**4 - 3/4*g**5 = 0.
-3, -1, 0, 1
Suppose -k - 5*m = 3 - 2, -4*m = 4. Let d(c) be the second derivative of -2/27*c**k - 1/27*c**3 + 0*c**2 + 0 - 1/30*c**5 + 3*c. Solve d(a) = 0 for a.
-1, -1/3, 0
Let z(b) be the third derivative of b**6/660 + b**5/660 - b**4/264 + 19*b**2 + 3*b. Factor z(j).
j*(j + 1)*(2*j - 1)/11
Let s(o) be the third derivative of -o**7/840 + o**6/120 - o**4/6 + 2*o**3/3 - 4*o**2. Let c(k) be the first derivative of s(k). Factor c(z).
-(z - 2)**2*(z + 1)
Let h be 10/(-260)*-13*16/3. Factor -5/3*x**2 + h*x + 1/3*x**3 - 4/3.
(x - 2)**2*(x - 1)/3
Suppose 49 - 70 = -3*z. Let s(x) be the third derivative of -1/735*x**z + 1/210*x**6 - 1/42*x**4 + 0*x + 1/21*x**3 + 0*x**5 + 3*x**2 + 0. Factor s(u).
-2*(u - 1)**3*(u + 1)/7
Let h(r) = -17*r**2 + 17*r. Let a be (-2)/3*-2*3. Let k(f) = -8 + 8 + a*f**2 - 4*f. Let g(j) = -2*h(j) - 9*k(j). Factor g(t).
-2*t*(t - 1)
Let j = 7 - 40. Let w = j + 233/7. Solve -4/7*y + 2/7*y**2 + w = 0 for y.
1
Let j = 2020/3039 - -2/1013. Let g = 236/3 - 78. Let j*t**2 - g*t**4 + 2/3*t + 0 - 2/3*t**3 = 0. What is t?
-1, 0, 1
Let w be 35/25 - (-6)/10. Let g(h) be the second derivative of -2/21*h**4 + 0 + 3/7*h**w - 3*h + 1/21*h**3. What is j in g(j) = 0?
-3/4, 1
Let s = -3 - -21. Find u, given that -47*u**2 + 3*u + 9*u + 49*u**2 + s = 0.
-3
Suppose -a + 0*a + 2 = 0. Let o = a - 2. Factor 5*d + 4 + 5*d + o*d**2 - 14*d**2.
-2*(d - 1)*(7*d + 2)
Let x(v) = 2*v**5 - 18*v**4 + 56*v**3 - 72*v**2 + 31*v. Let r(p) = p. Let b(o) = -2*r(o) - 2*x(o). Find s such that b(s) = 0.
0, 1, 2, 4
Let x(n) be the second derivative of -3*n**5/100 - 3*n**4/4 - 27*n**3/10 - 39*n**2/10 - 25*n - 1. Let x(o) = 0. What is o?
-13, -1
Let t = 53 - 129. Let u = 155/2 + t. Factor 3*j + 3/2*j**2 + u.
3*(j + 1)**2/2
Let c(s) be the first derivative of -2*s - 2*s**2 - 2/3*s**3 - 6. Factor c(x).
-2*(x + 1)**2
Let i(d) be the first derivative of d**6/180 - d**5/150 - d**4/90 - d**2/2 + 1. Let y(z) be the second derivative of i(z). Factor y(l).
2*l*(l - 1)*(5*l + 2)/15
Let j = 881 + -879. Let t(p) = p**2 + 2. Let u be t(0). Factor -j*y - 1/2*y**u - 2.
-(y + 2)**2/2
Let t = 167/2 + -81. Factor 0 - w - 7/2*w**2 - t*w**3.
-w*(w + 1)*(5*w + 2)/2
Suppose 2*z + 20 + 10 = 0. Let y(a) = 3*a**2 - 27*a - 15. Let g(m) = -m**2 + 7*m + 4. Let r(t) = z*g(t) - 4*y(t). Factor r(v).
3*v*(v + 1)
Let b(p) be the second derivative of -p**6/300 - p**5/150 + 11*p**2/2 - 7*p. Let g(r) be the first derivative of b(r). Solve g(j) = 0 for j.
-1, 0
Let n(d) be the first derivative of -d**5/10 + d**4/6 + 3*d + 3. Let v(p) be the first derivative of n(p). Factor v(k).
-2*k**2*(k - 1)
Let t(z) = -2*z**3 + z**2 + z + 1. Let s be t(-1). Let k = 4 + -1. Solve -3*w**3 - 2*w**2 - 2*w**3 + s*w**k = 0.
-1, 0
Let z(j) be the first derivative of -j**4/28 + j**3/3 - 11*j**2/14 + 5*j/7 + 58. Let z(g) = 0. What is g?
1, 5
Let f be (6 + -4)*5/2. Suppose 6*o - 2*o - f*n - 28 = 0, 4*o - n = 12. Solve -2*y**2 - y**2 + 2*y**o = 0 for y.
0
Let o(z) be the third derivative of z**8/336 - z**7/105 - z**6/60 + 2*z**5/15 - 7*z**4/24 + z**3/3 + 9*z**2. Factor o(u).
(u - 1)**4*(u + 2)
Let u(x) = -x. Let o(v) = -v**2 - 2*v. Let t be 1 + 1 - (2 + -2). Let p(s) = t*u(s) - o(s). Find j such that p(j) = 0.
0
Let s(f) be the second derivative of 2/147*f**7 + 4/105*f**6 + 0*f**2 + 0 + 1/35*f**5 - 4*f + 0*f**3 + 0*f**4. Suppose s(h) = 0. What is h?
-1, 0
Factor -1/3*f - 1/3*f**3 + 2 - 4/3*f**2.
-(f - 1)*(f + 2)*(f + 3)/3
Let m be (-21)/(-3) + (-1)/1. Suppose -5*c = -5*n, -n + m = c - 0*n. Factor 3*u**4 - 9*u**4 + 3*u**5 - u**5 + 6*u**c - 2*u**2.
2*u**2*(u - 1)**3
Let s be 6/15*(-20)/(-28). Let y be (-10 - -2)*1/(-2). Factor 4/7 - 10/7*u - s*u**y + 6/7*u**2 + 2/7*u**3.
-2*(u - 1)**3*(u + 2)/7
Let b be 22/(30/(-7) + 4). Let d be b/(-21) - (-2)/(-3). Factor 1/2*u**4 - 1 + 5/2*u - 1/2*u**d - 3/2*u**2.
(u - 1)**3*(u + 2)/2
Let i(d) be the second derivative of -3*d**5/20 + d**4/2 + d**3/2 - 3*d**2 - 7*d. Suppose i(h) = 0. What is h?
-1, 1, 2
Let i(x) = -1. Let u(h) = -h**2 - 4. Let n(g) = 15*i(g) - 3*u(g). Factor n(j).
3*(j - 1)*(j + 1)
Let t(j) be the third derivative of j**5/120 - j**3/3 - 21*j**2. Let t(n) = 0. Calculate n.
-2, 2
Let p = -1987/6 - -330. Let o = -5/12 - p. Determine d, given that 3/2*d - o - 3/4*d**2 = 0.
1
Factor 4/5*h + 2/5*h**2 + 2/5.
2*(h + 1)**2/5
Let c(s) = -3*s**2 - 7*s - 4. Let z(n) = -30*n**2 - 69*n - 39. Let a(b) = -21*c(b) + 2*z(b). Determine v so that a(v) = 0.
-2, -1
Suppose 22 - 1 = -3*v. Let s = v - -11. Factor 4*t**4 + t**2 - 4*t**4 - t**s.
-t**2*(t - 1)*(t + 1)
Solve -64 + 63 - y**4 - y**2 + 3*y**2 = 0.
-1, 1
Let w = -36 - -36. Find m, given that 1/2*m**3 + 1/4*m**4 + 0*m + 1/4*m**2 + w = 0.
-1, 0
Let r(c) = -7*c + 254. Let l be r(36). Suppose 0 + 1/2*t**l - 1/2*t**4 + 0*t**3 + 0*t = 0. What is t?
-1, 0, 1
Solve -2/17*n - 8/17*n**2 + 0 - 2/17*n**5 - 12/17*n**3 - 8/17*n**4 = 0.
-1, 0
Let k = -1 + 1. Suppose k = -8*h + 4*h + 8. Solve 2*f**2 + h - 1 + 4*f + 1 = 0 for f.
-1
Let -5*r**2 + 7*r**2 - r**4 + 0*r**2 - 2*r**5 + 2*r**3 - r**4 = 0. What is r?
-1, 0, 1
Let v = -47/6 - -8. Determine p so that -1/2*p**3 + 1/2*p**2 + 0 + v*p**4 - 1/6*p = 0.
0, 1
Suppose 12*w**3 + 2*w**5 + 3*w**3 - 25*w**4 + 45*w**2 + 3*w**5 = 0. Calculate w.
-1, 0, 3
Suppose -2*b + 0*b = n - 7, -5*n - 4*b + 29 = 0. Find j such that -n*j - 3 + j + 5 + 2*j**2 = 0.
1
Find c such that -3/2*c**2 + 3/2*c - 3/2*c**3 + 3/2 = 0.
-1, 1
Let p(l) be the third derivative of 1/210*l**5 + 0*l + 0 + 3*l**2 + 0*l**3 - 1/84*l**4. Factor p(c).
2*c*(c - 1)/7
Let l(i) be the first derivative of -i**6/180 + i**5/20 - 2*i**3/3 + 4. Let q(t) be the third derivative of l(t). Factor q(o).
-2*o*(o - 3)
Factor 3*k**2 - 3*k**3 - 3*k**4 + 2*k**4 + k**4 + 3*k - 3*k**4.
-3*k*(k - 1)*(k + 1)**2
Factor -1/2*b**3 + 0 + 1/2*b + 1/2*b**4 - 1/2*b**2.
b*(b - 1)**2*(b + 1)/2
Suppose -b = -5*x + 4, b - 8 = 3*x + 3*b. Suppose x = -0*v + 3*v. Solve -6*g**2 - 6*g**3 + 3*g**4 - 2*g - 5*g**4 + v*g**2 = 0.
-1, 0
Let a(n) be the second derivative of n**4/20 - n**3/10 + 2*n. Factor a(p).
3*p*(p - 1)/5
Suppose -8/3 - 2*g**2 - 16/3*g = 0. What is g?
-2, -2/3
Solve -13/4*p + 3/4 + p**2 = 0.
1/4, 3
Factor -2*q**2 - 9*q + 26 - q**2 - 14.
-3*(q - 1)*(q + 4)
Let k(q) = -q**2 + 7*q + 3. Let i be k(7). Suppose 7*z - i*z = 4. What is l in -z - 4*l + 4*l**2 - 3*l**2 + 5 = 0?
2
Suppose 4*y - 8*y = 0. Let d(i) be the third derivative of 1/6*i**4 + 2*i**2 + 1/30*i**5 + 0*i + y + 0*i**3 - 1/60*i**6. Factor d(l).
-2*l*(l - 2)*(l + 1)
Let v = -17 + 19. Fin