+ 2*c**3/27 - 2*c. Factor l(t).
2*t*(t + 1)*(t + 2)/9
Let l(p) be the second derivative of p**6/40 - p**5/20 + 2*p**2 - 2*p. Let s(u) be the first derivative of l(u). What is a in s(a) = 0?
0, 1
Solve -22/5*p**3 + 4/5 - 43/5*p**2 + 21/5*p**4 + 4/5*p = 0.
-1, -2/7, 1/3, 2
Suppose -y - 2*y + 3 = -3*o, 5*o = -5*y + 5. Let r(h) be the first derivative of -2/3*h + o*h**2 + 2/9*h**3 - 2. Factor r(u).
2*(u - 1)*(u + 1)/3
Let h(x) be the first derivative of -4*x**3/9 + 8*x**2/3 + 11. Factor h(y).
-4*y*(y - 4)/3
Factor -1/6 + 1/3*d**2 + 7/12*d.
(d + 2)*(4*d - 1)/12
Let o(s) = 2*s**4 + 18*s**3 + 22*s**2 + 8*s. Suppose 2*c = 4*c + 2. Let a(i) = i**4 - i**3 - i**2. Let b(q) = c*o(q) - 2*a(q). Factor b(n).
-4*n*(n + 1)**2*(n + 2)
Let v(k) = -8*k**2 + 14*k - 10. Let m(c) = -c**2 + 51 + 7*c**2 + 3*c**2 - 69*c + 32*c**2. Let y(l) = 2*m(l) + 11*v(l). Factor y(g).
-2*(g - 2)*(3*g - 2)
Let y(j) be the second derivative of -j**5/5 - 2*j**4 - 22*j**3/3 - 12*j**2 - 11*j. Solve y(z) = 0 for z.
-3, -2, -1
Let m be 32/56*35/6. Let -4/3 - 8/3*n**2 - m*n - 2/3*n**3 = 0. Calculate n.
-2, -1
Let o = -61 + 65. Factor -1/2*v**5 + 0 - 5/2*v**o - v - 9/2*v**3 - 7/2*v**2.
-v*(v + 1)**3*(v + 2)/2
Let t be ((369/(-3))/3)/1. Let b = 124/3 + t. Factor 2/3*d**2 + b*d**3 + 0 + 1/3*d.
d*(d + 1)**2/3
Let v(c) be the second derivative of 0 - 2*c - 2/3*c**3 - c**2 - 1/6*c**4. Let v(s) = 0. What is s?
-1
Let c = 52 + -49. Let 2/5*f**5 + 2/5 - 4/5*f**c + 2/5*f**4 - 4/5*f**2 + 2/5*f = 0. Calculate f.
-1, 1
Let c(z) be the first derivative of -6*z**5/5 + 19*z**4/6 - 62*z**3/27 - z**2/9 + 4*z/9 - 21. Let c(g) = 0. Calculate g.
-2/9, 1/3, 1
Factor 12*t**5 - 11*t**5 - 12*t**4 - 132*t - 11*t**2 + 49*t**2 + 72 + 33*t**3.
(t - 6)**2*(t - 1)**2*(t + 2)
Let r be -4 - 1/(2/4). Let n(a) = a**3 + 6*a**2. Let t be n(r). Factor t + 0*h + 2/9*h**2.
2*h**2/9
Suppose -2*t - 3*t = 2*o - 21, -2*o = 3*t - 11. Let p(y) be the third derivative of 1/6*y**4 + 0 + 0*y - 1/3*y**3 + 2*y**2 - 1/30*y**t. Factor p(b).
-2*(b - 1)**2
What is t in 0*t + 0 + 0*t**2 - 1/5*t**4 + 0*t**3 = 0?
0
Let r(o) be the third derivative of o**6/630 + o**5/210 + 3*o**3/2 + 7*o**2. Let m(x) be the first derivative of r(x). Factor m(n).
4*n*(n + 1)/7
Factor 9/2*n**2 - n + 0 - 2*n**3.
-n*(n - 2)*(4*n - 1)/2
Suppose m - 114 = -3*o, o - 31 = 2*m - 0*m. Determine k so that 5 + 41*k**3 - 21*k**4 + 15*k - 3 - o*k**2 - 4 + 4*k**5 = 0.
1/4, 1, 2
Let l(y) be the first derivative of -y**4/2 - 8*y**3/3 + 5*y**2 - 32. Solve l(o) = 0.
-5, 0, 1
Suppose -3*s + 219 + 105 = 4*t, 3*s - 324 = 5*t. Let v be (-3)/(-2)*48/s. Factor 4/3*m + 0 + v*m**2.
2*m*(m + 2)/3
Let o(t) be the first derivative of 2 + 0*t + 2/3*t**3 - t**2. Factor o(l).
2*l*(l - 1)
Determine g so that 32*g**3 - 80*g**3 + 16*g**2 + 12*g**4 + 7*g**5 + 13*g**5 = 0.
-2, 0, 2/5, 1
Let z(a) be the second derivative of 0*a**3 - 2*a - 1/21*a**7 - 3/10*a**5 + 0*a**2 - 1/6*a**4 + 0 - 1/5*a**6. Suppose z(w) = 0. What is w?
-1, 0
Let c = 9 - 6. Determine l so that 6*l**3 + l**c + 2*l**2 + 0*l**2 = 0.
-2/7, 0
Factor -4*h**2 + 4*h**3 - 1 + 4 + 6*h**4 + 2*h**5 - 4 - 1 - 6*h.
2*(h - 1)*(h + 1)**4
Let z(q) be the third derivative of -q**6/180 - 2*q**2. Factor z(d).
-2*d**3/3
Let z(r) = r**3 + r**2 - r + 1. Let q(w) = -3*w**4 - 24*w**3 - 21*w**2 + 15*w - 15. Let g(b) = -q(b) - 15*z(b). Factor g(v).
3*v**2*(v + 1)*(v + 2)
Let b(c) be the third derivative of c**7/1260 - c**6/720 - 4*c**2. Solve b(k) = 0 for k.
0, 1
Let g(n) be the second derivative of 2*n**7/3 + 38*n**6/15 + 8*n**5/5 - 4*n**4/3 - 6*n. Solve g(k) = 0 for k.
-2, -1, 0, 2/7
Let w(v) be the first derivative of 1/160*v**6 - 2*v**2 + 0*v**3 + 1 + 0*v**4 - 1/80*v**5 + 0*v. Let t(y) be the second derivative of w(y). Factor t(r).
3*r**2*(r - 1)/4
Let o(p) be the first derivative of 4*p**3/21 - 4*p**2 + 28*p + 10. What is a in o(a) = 0?
7
Factor -1/3*o**4 + 2/3*o**3 + 0*o + 0 - 1/3*o**2.
-o**2*(o - 1)**2/3
Let d(x) be the first derivative of x**6/2 + 8*x**5/5 - 3*x**4/2 - 8*x**3/3 + 3*x**2/2 - 24. Find p such that d(p) = 0.
-3, -1, 0, 1/3, 1
Let l(q) = 5*q**5 + 7*q**4 - 5*q**3 - q**2. Let p(k) = 4*k**5 + 6*k**4 - 4*k**3 - k**2. Let h be 365/(-75) + (-6)/45. Let j(w) = h*l(w) + 6*p(w). Factor j(b).
-b**2*(b - 1)**2*(b + 1)
Factor -12*z**4 - 7*z**2 + 14*z**2 + 3*z**5 - 7*z**2 - 6*z**2 + 15*z**3.
3*z**2*(z - 2)*(z - 1)**2
Let r(t) = -t**3 + t - 1. Let u(b) = -6*b + 6*b - 4*b + 2*b**3 + 3 - 3*b**2 + 5*b**2. Let w(o) = -3*r(o) - u(o). Factor w(k).
k*(k - 1)**2
Let o(s) be the second derivative of -s**4/108 - s**3/54 + s**2/3 - 22*s. Let o(z) = 0. Calculate z.
-3, 2
Suppose -2*i + 15 = 3*i. Factor -b**i - b**3 + 2*b**5 + 0*b**5 + 0*b**3.
2*b**3*(b - 1)*(b + 1)
Find c such that 0 + 16/3*c**2 + 7/6*c**5 - 9*c**4 + 16*c**3 + 0*c = 0.
-2/7, 0, 4
Let l(i) = -17*i - 48. Let p be l(-3). Factor 0 + 0*c**2 + 0*c + 3/4*c**5 + 3*c**3 - p*c**4.
3*c**3*(c - 2)**2/4
Factor 3*f - 1/2*f**2 - 9/2.
-(f - 3)**2/2
Suppose -4 = -y - 0*y. Factor 6*v**3 + 10*v**2 + 6 - 6 - y*v.
2*v*(v + 2)*(3*v - 1)
Factor 19 - 319*o + 21*o**2 + 367*o + 8.
3*(o + 1)*(7*o + 9)
Let h(n) be the second derivative of -n**4/2 - 2*n**3/3 - 3*n**2 + 3*n. Let j = -3 - -2. Let v(u) = u**2 + 1. Let p(i) = j*h(i) - 4*v(i). Factor p(x).
2*(x + 1)**2
Factor 46*l**2 + 36*l**2 - 76*l**2 - 3*l + 3*l**3 - 6.
3*(l - 1)*(l + 1)*(l + 2)
Let s = -12747463/45 + 283290. Let v = -112/9 + s. What is r in 4/5*r - 4/5 - 2/5*r**3 - 1/5*r**4 + v*r**2 = 0?
-2, 1
Let w(o) = -2*o**3 - o. Let r be 1 - (-1 - -3) - 0. Let f(v) = -v. Let x(d) = r*w(d) + 3*f(d). Factor x(j).
2*j*(j - 1)*(j + 1)
Let z(h) be the third derivative of -h**7/140 + h**6/30 - h**5/20 + h**3/12 + 45*h**2. Factor z(g).
-(g - 1)**3*(3*g + 1)/2
Let z(u) be the third derivative of -u**5/40 + 3*u**4/16 + u**3 - 19*u**2. Determine h, given that z(h) = 0.
-1, 4
Let s(l) = -l**4 + l**3 - l**2 + 1. Let p(w) = -7*w**4 - 5*w**3 - 7*w**2 + 3. Let x(v) = p(v) - 3*s(v). Suppose x(o) = 0. Calculate o.
-1, 0
Let q(z) be the third derivative of -z**5/60 - z**4/12 - 24*z**2. Factor q(b).
-b*(b + 2)
Let m be 23/((-161)/6)*-1. Let z = 877/7 + -125. Factor -6/7*h**2 + z*h**3 - 2/7 + m*h.
2*(h - 1)**3/7
Suppose -3 = -3*c - 0*c. Let s be 50/40 + (1 - c). Find z such that -3/4*z**4 + 1/4 + 7/2*z**3 + 1/2*z**2 - 9/4*z**5 - s*z = 0.
-1, 1/3, 1
Factor -3/5*g**2 + 6*g - 15.
-3*(g - 5)**2/5
Suppose 5*u - w - 17 = -5*w, -3*u = -3*w + 6. Let c be u/(3/(-2) + 2). Find h, given that 0*h + 0 + 1/3*h**c = 0.
0
Let n be (1 - 2)/(2/(-6)). Factor 3*t**2 + 2*t**n + 0*t**3 + 4 + 5*t**2 + 10*t.
2*(t + 1)**2*(t + 2)
Let p be 10/(-90) + 62/234. Solve 0*g**3 + 0 - 4/13*g**4 - 2/13*g + 4/13*g**2 + p*g**5 = 0.
-1, 0, 1
Let b(h) be the second derivative of h**4/12 - 2*h**3/3 + 3*h**2/2 - 23*h. Suppose b(x) = 0. Calculate x.
1, 3
Find l, given that -20/3*l**2 + 10/3*l + 2/3*l**5 - 2/3 + 20/3*l**3 - 10/3*l**4 = 0.
1
Let s(f) = -f**3 - f**2 - 1. Let v(z) = -2*z**3 + 18*z**2 - 4*z + 6. Let b(p) = 6*s(p) + v(p). Suppose b(m) = 0. Calculate m.
0, 1/2, 1
Factor -5*q**2 + 5*q**2 - 2*q**4 - 2*q**5 + 4*q**5.
2*q**4*(q - 1)
Suppose n + 2*n = 9. Let t(p) = -9*p - 3. Let v be t(-3). Find q, given that 20*q - 5*q**2 - q**2 - v*q + 28*q**n = 0.
-2/7, 0, 1/2
Let z = -2 + 3. Let k = 3 - z. Factor -3*h**4 - 5*h**3 - k*h - h**3 + h**4 - 6*h**2.
-2*h*(h + 1)**3
Suppose b - 2*h = 2*b + 25, -3*b = h + 50. Let p be (1 + 0)*(-5)/b. Let 2/3 - w**2 + p*w = 0. What is w?
-2/3, 1
Let a(w) be the third derivative of -w**8/60480 + w**6/2160 - w**5/60 - w**2. Let q(u) be the third derivative of a(u). Determine m so that q(m) = 0.
-1, 1
Let d = -115/3 + 39. Let n(r) be the second derivative of d*r**4 + 12/35*r**6 + 0*r**2 + r + 0 - 57/70*r**5 - 4/21*r**3. Factor n(i).
2*i*(3*i - 2)**2*(4*i - 1)/7
Suppose 3*q - s + 7 = 0, -3*s + 8 + 1 = -3*q. Let v be (-58)/(-14) - q/(-14). Suppose 0*z + 8/7*z**2 + 8*z**3 + 14*z**v + 0 = 0. Calculate z.
-2/7, 0
Suppose 0 - 9/8*m**3 - 9/4*m + 33/8*m**2 = 0. Calculate m.
0, 2/3, 3
Let n = 293/2 - 146. Factor -n*w**2 + 1/2*w + 0 + 1/2*w**4 - 1/2*w**3.
w*(w - 1)**2*(w + 1)/2
Let t = -1511 + 187387/124. Let j = 2/31 + t. Factor -3/4*k**2 - j*k**3 + 0*k + 1.
-(k - 1)*(k + 2)**2/4
Find v such that 1/2*v + 0 + 1/8*v**3 - 5/8*v**2 = 0.
0, 1, 4
Suppose 8 = -4*h + 4*j, 4*j - 32 = -3*h - h. Let l(c) be the first 