 + 1)*(f + 5)**2/2
Factor -454/3 + 2/3*q**2 + 452/3*q.
2*(q - 1)*(q + 227)/3
Let x(z) be the second derivative of z**10/60480 - z**9/7560 + z**8/2688 - z**7/2520 - z**4/6 + 8*z. Let u(g) be the third derivative of x(g). Factor u(y).
y**2*(y - 2)*(y - 1)**2/2
Suppose -4*w + 22 = -3*l - 23, 0 = -4*w + l + 39. Let c be (w/6)/(4/8). Determine y, given that -3*y**2 + 4*y**c - 4*y**4 + y**2 + 2*y**2 - 4*y + 4*y**2 = 0.
-1, 0, 1
Let l(t) be the first derivative of 15/2*t**4 - 20*t**3 - t**5 - 7 + 20*t**2 + 0*t. Factor l(w).
-5*w*(w - 2)**3
Let h(m) be the first derivative of -2*m**3/15 - 12*m**2/5 - 64*m/5 - 193. Solve h(a) = 0.
-8, -4
Factor f + 3*f**2 - 4*f - 3*f - 6*f**2.
-3*f*(f + 2)
Let v(t) be the third derivative of -11*t**2 + 0 + 2/9*t**4 + 0*t + 16/3*t**3 + 1/270*t**5. Factor v(q).
2*(q + 12)**2/9
Suppose v - 3*v + 8 = 0. Let w = 1323 - 978. Suppose -w*p**2 - 167*p**4 - 12 - 103*p**v + 108*p - 21*p**4 + 63*p**5 + 477*p**3 = 0. What is p?
2/7, 1/3, 1, 2
Suppose 3 = -4*f + 3*f. Let l be ((-2)/f)/(32/12). Find w, given that -1/2*w**2 + 1/4*w**3 - l*w + 1/2 = 0.
-1, 1, 2
Let h be 21/14 + -1 - (0 + 0). Let k(r) be the first derivative of 0*r**4 + 2/3*r**3 + 0*r + 1/6*r**6 + 4 - 2/5*r**5 - h*r**2. Factor k(f).
f*(f - 1)**3*(f + 1)
Let c(k) be the second derivative of -k**6/30 + 4*k**5/15 - k**4/2 - 17*k**2 - 21*k. Let d(l) be the first derivative of c(l). Factor d(v).
-4*v*(v - 3)*(v - 1)
Let s(g) be the first derivative of -g**6/21 + 4*g**5/7 - 33*g**4/14 + 80*g**3/21 - 16*g**2/7 - 362. Let s(d) = 0. What is d?
0, 1, 4
Let t(v) be the third derivative of 1/350*v**7 + 1/200*v**6 + 4*v**2 + 0*v**3 + 0*v + 0*v**4 + 0*v**5 + 0. Factor t(d).
3*d**3*(d + 1)/5
Find o, given that -3*o**3 - 21*o - 29*o - 36*o - 28*o - 112*o**2 + 5*o**3 = 0.
-1, 0, 57
Let o(w) be the first derivative of -3*w**5/50 + w**4/20 + 3*w**3/10 + 4*w - 10. Let m(q) be the first derivative of o(q). Factor m(j).
-3*j*(j + 1)*(2*j - 3)/5
Let z be 2/11 - ((-20618)/(-1716) + -12). Factor z*d**4 - 2/3*d**2 - 1/3*d**3 + 0 + 4/3*d.
d*(d - 2)**2*(d + 2)/6
Let i be 35/10 + (-3)/2. Suppose -5*d + 9 + 7 = -2*k, 5*k = 2*d + i. Solve -16*h - 2*h**d + 16*h + 16*h**2 - 32 = 0 for h.
-2, 2
Let v(r) = 132*r**3 - 162*r**2 + 63*r + 21. Let o(p) = -19*p**3 + 23*p**2 - 9*p - 3. Let q(m) = -27*o(m) - 4*v(m). Factor q(g).
-3*(g - 1)**2*(5*g + 1)
Let w(y) be the second derivative of -y**5/90 - 2*y**4/27 - 4*y**3/27 - 194*y. Factor w(l).
-2*l*(l + 2)**2/9
Suppose -3*c = -k - 54, 2*k + 2*c = c - 94. Let v = -237/5 - k. Find u such that v*u**2 + 0 + 3/5*u = 0.
-1, 0
Factor 205*a**4 - 6*a**2 + 3*a**5 - a**3 - 2*a**3 - 199*a**4.
3*a**2*(a - 1)*(a + 1)*(a + 2)
Let w(q) be the first derivative of -q**3/15 - 3*q**2/2 + 126*q/5 + 352. Determine r so that w(r) = 0.
-21, 6
Let m(w) = w - 18. Let k be m(21). Let z(l) be the second derivative of 3/10*l**5 - 2*l + 0*l**k - 1/6*l**4 + 0*l**2 - 2/15*l**6 + 0. What is h in z(h) = 0?
0, 1/2, 1
Let o(t) be the third derivative of 1/33*t**4 + 0 + 0*t**3 - 1/660*t**6 + 1/110*t**5 + 22*t**2 + 0*t. Determine u so that o(u) = 0.
-1, 0, 4
Let m(i) be the second derivative of -i**6/180 - i**5/30 + 7*i**3/2 + 32*i. Let h(k) be the second derivative of m(k). Factor h(j).
-2*j*(j + 2)
Let t be 4 + -1 + 6*7/42. Factor 44*m**4 + 7 + m**4 - 85*m + 3 - 125*m**3 - 15*m**t + 170*m**2.
5*(m - 2)*(m - 1)**2*(6*m - 1)
Let w(n) be the first derivative of -4/5*n - 27 - 7/5*n**2 - 6/5*n**3 - 1/2*n**4 - 2/25*n**5. Factor w(g).
-2*(g + 1)**3*(g + 2)/5
Let i(x) be the first derivative of x**5/15 - x**4/6 - x**3/9 + x**2/3 - 83. Suppose i(z) = 0. Calculate z.
-1, 0, 1, 2
Suppose 6*i + 26 = 38. Let j(t) be the second derivative of -i*t + 0*t**2 - 1/4*t**3 - 1/16*t**4 + 0. Determine p, given that j(p) = 0.
-2, 0
Let h = 1 - -1. Let w(a) = -a**3 + 3*a**2 + 5*a - 2. Let o be w(4). Let -2*v**3 + v**3 + 2*v**3 + v**3 + o*v**h = 0. What is v?
-1, 0
Let f be (-32)/(-48)*(-6)/4 + 6. Suppose -z + f*b = 25, -z + 5*b = 4*z + 25. Factor 0 - 2/5*i**2 + z*i.
-2*i**2/5
Suppose t = -n + 5, 96*n - 95*n + 13 = 5*t. Let a(c) be the first derivative of -3/2*c**n + 2 + 4*c - 1/3*c**3. Suppose a(j) = 0. Calculate j.
-4, 1
Let t(a) be the first derivative of 5*a**5 - 55*a**4/2 - 145*a**3 - 80*a**2 + 140*a - 422. Solve t(p) = 0 for p.
-2, -1, 2/5, 7
Let b(v) be the third derivative of v**6/24 + v**5/2 + 15*v**4/8 - 116*v**2. Factor b(n).
5*n*(n + 3)**2
Let y(o) be the first derivative of 5/2*o**2 + 0*o - 1/12*o**4 + 1/60*o**5 + 1/6*o**3 - 9. Let s(k) be the second derivative of y(k). Let s(w) = 0. What is w?
1
Let r = 1/201 + 395/1407. Let j be 18/15*35/147. Find i, given that j - 2/7*i + r*i**3 - 2/7*i**2 = 0.
-1, 1
Let p(y) = -5*y**3 + 5*y**2 + 9. Let l(j) = -j**3 + j**2 + 2. Let u(z) = 18*l(z) - 4*p(z). Factor u(h).
2*h**2*(h - 1)
Let k(l) = 16*l**2 - 28*l + 12. Let o(c) = 16*c**2 - 28*c + 12. Let u(a) = -a**2 + 4*a + 3. Let w be u(-1). Let d(m) = w*k(m) + 3*o(m). Factor d(q).
4*(q - 1)*(4*q - 3)
Let d(s) be the second derivative of 2*s**2 + 1/12*s**4 + 0 - 2*s + 2/3*s**3. Let d(p) = 0. Calculate p.
-2
What is n in 6*n**3 + 20*n**2 + 0*n**3 - n**3 + 20*n - 5*n = 0?
-3, -1, 0
Let k(c) = 2*c**4 + 3*c**3 - 4*c**2 - c + 1. Let x(d) = -d**4 + d - 1. Let h(b) = 3*k(b) + 3*x(b). Factor h(p).
3*p**2*(p - 1)*(p + 4)
Suppose 0 + 24/7*b + 243/7*b**4 + 54*b**3 - 204/7*b**2 = 0. What is b?
-2, 0, 2/9
Let z(j) be the second derivative of -9*j**7/280 + 7*j**6/40 - 2*j**5/5 + j**4/2 - 10*j**3/3 + j. Let f(y) be the second derivative of z(y). Factor f(n).
-3*(n - 1)*(3*n - 2)**2
Let b(n) = n**2 + n - 7. Let x(g) = 2. Let f(u) = b(u) + 3*x(u). Let y(c) = -5*c**2 + 2*c - 1. Let z(d) = -4*f(d) - y(d). Factor z(k).
(k - 5)*(k - 1)
Let d(i) be the second derivative of -i**5/50 - 17*i**4/30 - i - 3. Factor d(a).
-2*a**2*(a + 17)/5
Suppose 0*h - 5 = 5*h. Let a be 0/(-11) - (h - 1). Factor 4*s**3 - 4*s - 5*s**2 + 11*s**a - 4*s**2 - 2*s**3.
2*s*(s - 1)*(s + 2)
Let b be ((-18)/(-15))/(28/35). Let v(t) = -t**2 - 7*t - 9. Let g be v(-4). Determine n, given that b*n + 0 - 3/2*n**5 - 3*n**2 + g*n**4 + 0*n**3 = 0.
-1, 0, 1
Let z(a) = -8*a**2 - 46*a - 77. Let c(n) = 17*n**2 + 94*n + 153. Let t(r) = 3*c(r) + 7*z(r). Factor t(f).
-5*(f + 4)**2
Let y(u) = -6*u + 5. Let i be y(4). Let s be (-6 + i/(-4))/((-1)/4). Determine h so that -143*h**2 - 42*h - 259/2*h**3 + 343/2*h**s + 147*h**4 - 4 = 0.
-1, -2/7, 1
Let u(p) be the first derivative of 27/8*p**4 + 7/2*p**3 + 3/2*p**2 + 0*p + 1/4*p**6 - 11 + 3/2*p**5. Let u(t) = 0. Calculate t.
-2, -1, 0
Let w(f) be the first derivative of -1/16*f**4 - 3/8*f**2 + 5/12*f**3 - 9/4*f + 1. Factor w(z).
-(z - 3)**2*(z + 1)/4
Suppose -21 = 2*b + 5*a, 2 = -4*b + 3*a - 1. Let z(s) = -s - 3. Let f be z(b). Solve -10/9*w**2 - 2/9*w**4 - 8/9*w**3 + f - 4/9*w = 0.
-2, -1, 0
Let f be (48/(-18))/((-4)/6). Suppose -2*q = -f - 2. Solve -9*c + c**q + 8*c - c**2 - 2 + 3 = 0.
-1, 1
Factor -2*v**3 - 7*v**5 + 6*v**5 - v**5 + 4*v**5.
2*v**3*(v - 1)*(v + 1)
Let m(k) = -3*k**2 - 128*k - 1323. Let s(v) = -6*v**2 - 257*v - 2646. Let g(j) = 5*m(j) - 2*s(j). Factor g(x).
-3*(x + 21)**2
Let y = 3730/2799 - -2/2799. Find l such that -2/3*l**4 + 0*l**3 + y*l + 2*l**2 + 0 = 0.
-1, 0, 2
Let b be (-116)/203 - (1 + (-386)/210). Let n(x) be the second derivative of 0*x**2 - 2/75*x**6 - b*x**3 - 1/3*x**4 - 4/25*x**5 + x + 0. Factor n(d).
-4*d*(d + 1)**2*(d + 2)/5
Let m = -102 + 96. Let x be 4/m + 26/(-12) + 3. What is u in 1/3 - x*u**3 + 1/2*u + 0*u**2 = 0?
-1, 2
Let b be 72/(-2 - 4)*(-1)/3. Suppose -4*n - 5*x + 3*x = 8, 16 = n - b*x. Factor 4/9*o + 2/9*o**2 + n.
2*o*(o + 2)/9
Suppose 4*d + 2*k - 33 = 79, 72 = 2*d - 3*k. Determine l, given that -3*l**2 + 0*l + 5*l + 17*l**2 - d + 5*l**3 + 6*l**2 = 0.
-3, -2, 1
Let s(f) be the third derivative of 11*f**5/60 - f**4/10 - 2*f**3/15 - 43*f**2. Factor s(c).
(5*c - 2)*(11*c + 2)/5
Let b(f) be the second derivative of 0 - 1/18*f**5 - 4/27*f**4 + 4/27*f**3 + 0*f**2 + 11*f. Factor b(c).
-2*c*(c + 2)*(5*c - 2)/9
Suppose -5*x = 20, 5*s = s + 2*x + 16. Suppose 4*g + s*g - 10*g**3 - 2*g**3 - 4*g**2 + 2*g + 4*g**5 + 4*g**4 = 0. What is g?
-2, -1, 0, 1
Let g(q) = -q**3 + 8*q**2 - 10*q + 23. Let s be g(7). Let m(x) be the second derivative of -1/2*x**s + 0 - 5/24*x**4 + 7/12*x**3 + 6*x. Factor m(b).
-(b - 1)*(5*b - 2)