
-4, 0, 1
Factor -20*w**3 + 32*w - 121 + 4*w**4 + 4*w**5 - 4*w**2 - 113 + 218.
4*(w - 1)**3*(w + 2)**2
Let i(k) be the second derivative of -k**6/60 - 9*k**5/40 + k**4/24 + 3*k**3/4 + 78*k - 1. Factor i(q).
-q*(q - 1)*(q + 1)*(q + 9)/2
Let m(r) = r**2 - 50*r + 341. Let p be m(8). Let f(o) be the second derivative of 1/3*o**4 + 4*o**2 + p*o + 0 + 2*o**3. Factor f(t).
4*(t + 1)*(t + 2)
Let t(o) = -o - 1. Let b(w) = -8 - 22*w + 194*w**2 + 34 - 214*w**2. Let n be (-3 - 0)*30/9. Let v(k) = n*t(k) - b(k). Factor v(p).
4*(p + 2)*(5*p - 2)
Let s(f) = 3*f**3 - 12*f**2 + 2*f. Let t = 85 - 64. Let o(q) = 30*q**3 - 120*q**2 + 21*q. Let v(c) = t*s(c) - 2*o(c). Factor v(h).
3*h**2*(h - 4)
Let j(x) be the third derivative of 0 + 1/210*x**7 + 0*x**4 + 1/240*x**5 + 18*x**2 + 0*x**3 + 0*x + 1/96*x**6. Suppose j(w) = 0. Calculate w.
-1, -1/4, 0
Let k(t) be the second derivative of -49*t**6/120 + 63*t**5/40 - 109*t**4/48 + 3*t**3/2 - t**2/2 + 2*t - 50. Factor k(s).
-(s - 1)**2*(7*s - 2)**2/4
Suppose 9*i + 15*i = 6*i. Let r(n) be the second derivative of i - n + 1/48*n**4 + 1/24*n**3 + 0*n**2. Factor r(d).
d*(d + 1)/4
Let p(x) = x**2 + x + 1. Let z(b) = -b**3 + 7*b**2 - 20*b - 31. Let m(f) = -3*p(f) - z(f). Suppose m(a) = 0. Calculate a.
-1, 4, 7
Let q be (((-105)/(-14) + -7)*(0 + 0))/(-3). Determine d so that -2/11*d + 4/11*d**2 + 0 - 4/11*d**4 + q*d**3 + 2/11*d**5 = 0.
-1, 0, 1
Let r be -9 + 2 + (1 - 0). Let n = 19 + r. Suppose -3*s**5 - n - 4*s**4 + 13 - s**3 = 0. Calculate s.
-1, -1/3, 0
Let g(k) be the second derivative of k**4/12 + 29*k**3/3 + 841*k**2/2 + 54*k. Solve g(l) = 0 for l.
-29
Determine c, given that -1 + 7/6*c**2 + 1/6*c**3 - 1/6*c**4 - 1/6*c = 0.
-2, -1, 1, 3
Let t(z) = z**2 + 6*z + 8. Let b be t(-11). Let v be (-3)/((b/(-12))/7). Determine j, given that 1/2*j**3 - 1/2*j**v + 0 + 0*j**2 + 0*j = 0.
0, 1
Let y(v) be the third derivative of -v**7/525 - v**6/100 + v**4/15 + 84*v**2. Determine u so that y(u) = 0.
-2, 0, 1
Let v(m) = -2*m - 2. Let i be v(1). Let f be (-51)/(-12) + 1/i. Let 1 - f - 3*s + 2 - 1 + 2*s**2 = 0. Calculate s.
-1/2, 2
Let y(f) be the first derivative of 2*f**5/15 - f**4/18 - 2*f**3/9 + f**2/9 + 229. Find q, given that y(q) = 0.
-1, 0, 1/3, 1
Factor 16*j + 16/3*j**3 + 6 + 44/3*j**2 + 2/3*j**4.
2*(j + 1)**2*(j + 3)**2/3
Let s(v) be the first derivative of -40*v**6/3 - 24*v**5 + 275*v**4/4 + 160*v**3 + 90*v**2 - 947. Determine a so that s(a) = 0.
-2, -3/4, 0, 2
Let g = 1276 + -19138/15. Determine c so that g*c + 4/5 - 2/15*c**2 = 0.
-2, 3
Let p = 62 - 70. Let r be p/(-6) - 46/(-69). Find v, given that -2/3*v**r - 2/3*v + 2/3*v**3 + 2/3 = 0.
-1, 1
Let n = 2670310/13047 + -8/4349. Let o = n - 204. Solve -4/3 - o*p + 2/3*p**2 = 0 for p.
-1, 2
Let z(p) be the second derivative of p**5/25 + 11*p**4/15 + 14*p**3/3 + 10*p**2 + p + 2. Factor z(r).
4*(r + 1)*(r + 5)**2/5
Let s(g) be the first derivative of 0*g - 50/3*g**3 + 0*g**2 - 2/5*g**5 + 5*g**4 + 6. Let s(x) = 0. What is x?
0, 5
Let p be -7 + (-2529)/1800*-5. Let x(f) be the second derivative of 0*f**2 - p*f**5 - 8*f + 0*f**4 + 0 + 1/12*f**3. Determine k, given that x(k) = 0.
-1, 0, 1
Let t be 12/8 + -2 - (-14)/4. Suppose 11 = u + 4*f, -11 - 6 = -t*u - 4*f. Determine a, given that -2/11 + 6/11*a + 2/11*a**u - 6/11*a**2 = 0.
1
Let r(l) = -5*l**2 + 4*l. Let c(t) = t**2 - 2*t**2 - t**2 - t**2 + 3*t. Let w(d) = -8*c(d) + 5*r(d). Factor w(o).
-o*(o + 4)
Suppose -o + 3*o = 10. Let w = o + -1. Factor 4*m**w + 2*m**4 - 11*m**2 + 12*m + m**3 - 4*m**4 - 4 + m**4 - m**5.
-(m - 2)*(m - 1)**3*(m + 2)
Suppose -17*b + 99 = -88 + 102. Factor -46/9*w**4 - 6*w**3 - 14/9*w**b - 26/9*w**2 + 0 - 4/9*w.
-2*w*(w + 1)**3*(7*w + 2)/9
Let h(i) be the third derivative of -i**8/26880 + i**7/560 - 3*i**6/80 + 9*i**5/20 - i**4/24 - 27*i**2. Let o(c) be the second derivative of h(c). Factor o(s).
-(s - 6)**3/4
Let y(d) = 3*d**3 + 2*d**2 - 3*d - 10. Let h(v) = -13*v**3 - 7*v**2 + 10*v + 40. Let j(g) = 4*h(g) + 18*y(g). Suppose j(a) = 0. What is a?
-5, -1, 2
Let m(q) be the first derivative of -2*q**5/5 + 5*q**4 - 6*q**3 + 374. What is d in m(d) = 0?
0, 1, 9
Let r be 4 - -1 - 145/30. Let d(g) be the first derivative of 0*g**2 + 1/15*g**5 + 0*g + 1/9*g**3 + 6 + r*g**4. Find o, given that d(o) = 0.
-1, 0
Find a such that 11*a**2 - 4*a**2 - 3*a + 3*a**2 + 28*a = 0.
-5/2, 0
Let z be 5*(-5)/(-7 + 2). Let w(t) = 10*t**2. Let f(r) = -11*r**2 - r. Let b(v) = z*f(v) + 4*w(v). Factor b(g).
-5*g*(3*g + 1)
Suppose 0 + 52/11*i**3 - 26/11*i**4 - 10/11*i**5 + 0*i - 16/11*i**2 = 0. What is i?
-4, 0, 2/5, 1
Suppose 2*m = -s + 4, -11*s + 12*s = 4*m - 2. Determine l so that 5/2*l - 1/2 - 3/2*l**5 + 7/2*l**4 - l**3 - 3*l**s = 0.
-1, 1/3, 1
Let d(u) be the third derivative of u**7/630 + u**6/135 + 13*u**3/6 + 14*u**2. Let z(j) be the first derivative of d(j). Let z(f) = 0. Calculate f.
-2, 0
Let x(r) be the third derivative of -4*r**2 + 0*r + 0 + 2/9*r**3 - 1/180*r**5 + 1/360*r**6 - 1/18*r**4. Suppose x(t) = 0. What is t?
-2, 1, 2
Let p(w) be the second derivative of 10/3*w**3 - 1/6*w**6 + 0 - 3/4*w**5 + 0*w**2 + 0*w**4 + 6*w. What is k in p(k) = 0?
-2, 0, 1
Let o(f) be the second derivative of f**7/252 - 31*f**5/120 + 5*f**4/12 - 2*f + 121. Solve o(a) = 0 for a.
-6, 0, 1, 5
Suppose 4 = 5*l - 11. Suppose -2*y = 4*p - 18, 0 = l*y + 4 - 19. Determine u, given that -1/2 - 1/4*u**p + 3/4*u = 0.
1, 2
Let u(y) be the first derivative of 0*y + 10/3*y**2 + 41 + 5/12*y**4 - 25/9*y**3. Factor u(c).
5*c*(c - 4)*(c - 1)/3
Let v(l) be the first derivative of -l**4/4 - l**3 + 14*l**2 - 380. Factor v(n).
-n*(n - 4)*(n + 7)
Let w = 11 + -7. Suppose o = -3*m - 4, -2*o = -w*m + 8 - 20. Let -4*x**3 - 3*x**3 - 4 + 2*x - 4*x**4 + 3*x**3 + 4*x**2 + 4*x**o + 2*x**5 = 0. Calculate x.
-1, 1, 2
Let s(a) = -9*a**2 - 21*a + 21. Let h(t) be the first derivative of -t**3/3 - t**2 + 2*t - 16. Let m(k) = -21*h(k) + 2*s(k). Factor m(d).
3*d**2
Let -10*p + 28/3*p**3 + 16/3*p**2 + 2/3*p**5 + 0 - 16/3*p**4 = 0. What is p?
-1, 0, 1, 3, 5
Suppose -47*r = 95*r - 2556. Determine d so that -8/3 - 44/3*d - 4/3*d**4 - r*d**2 - 25/3*d**3 = 0.
-2, -1/4
Let z be ((-9)/(-12))/((-1)/(-16)). Let w = z - 10. Determine l, given that 3*l - 7*l + 3*l**w + 3 - 2*l = 0.
1
Let b(y) = 8*y**2 + 14*y. Let k(a) = -4*a**2 - 6*a. Let d(f) = -3*b(f) - 5*k(f). Let d(n) = 0. Calculate n.
-3, 0
Let k(w) be the first derivative of w**6/150 - 2*w**5/25 - 7*w**4/30 - 17*w**2 + 32. Let a(h) be the second derivative of k(h). Let a(c) = 0. What is c?
-1, 0, 7
Let s = -8 + 14. Let h(w) = 5*w - 16. Let g be h(4). Factor -2*y**5 + 10*y + 8*y**4 - 5*y**3 - g - 4*y**2 + 3*y**3 - s*y**3 + 0*y**5.
-2*(y - 2)*(y - 1)**3*(y + 1)
Let v(o) = o**3 - 4*o**2 + 3*o + 3. Let u(t) = t**3 - 4*t**2 + 3*t + 4. Let l(k) = -3*u(k) + 4*v(k). Suppose l(z) = 0. Calculate z.
0, 1, 3
What is z in -643*z + 473*z - 2*z**2 + 175 - 3*z**2 = 0?
-35, 1
Let g(a) = a**2 - 10*a + 7. Let b be g(9). Let k be ((-24)/18)/(b/3). Solve -9*p**3 - 2*p**k + 5*p**2 + 10*p**3 = 0 for p.
-3, 0
Let c be 6/(-10)*135/(-3). Suppose -5*i - 3*b = -c, -6*b + 4 = -4*i - 2*b. Factor z**3 + 15*z - i + 3*z**2 - 10*z - 6*z.
(z - 1)*(z + 1)*(z + 3)
Let l(h) be the second derivative of 0 + 3/8*h**5 + 6*h**2 + 16*h - h**3 - 3/4*h**4 - 1/20*h**6. Factor l(r).
-3*(r - 2)**3*(r + 1)/2
Let x(v) be the third derivative of v**7/120 - 19*v**6/360 + v**5/15 + v**4/6 - v**3/2 + v**2. Let p(o) be the first derivative of x(o). Factor p(t).
(t - 2)*(t - 1)*(7*t + 2)
Suppose 238*h + 182 = 658. Determine b so that -2/7*b**3 - 4/7 + 6/7*b**h + 2/7*b - 2/7*b**4 = 0.
-2, -1, 1
Let a(r) be the first derivative of -r**4/20 + 7*r**3/15 - r**2 - 38. Let a(u) = 0. What is u?
0, 2, 5
Find b, given that -6/7*b**3 - 204/7*b + 0 - 114/7*b**2 = 0.
-17, -2, 0
Let i(l) = 6*l - l**2 - l - 9*l - l - 2. Let h(r) = 2*r**2 + 11*r + 4. Let n(g) = -6*h(g) - 15*i(g). Factor n(q).
3*(q + 1)*(q + 2)
Let u(h) be the third derivative of -h**7/735 + h**6/84 - 4*h**5/105 + h**4/21 + h**2 - 38*h. Factor u(v).
-2*v*(v - 2)**2*(v - 1)/7
Suppose 0 = -2*y + p - 3*p + 12, -4*y + 5*p - 12 = 0. Find m, given that -3*m + 6*m + 5*m - 8 - m**2 - m**y = 0.
2
Let r(q) be the first derivative of -q**7/280 - q**6/40 - 3*q**5/40 - q**4/8 - 11*q**3/3 + 12. Let s(l) be the third derivative of r(l). Factor s(t).
-3*(t + 1)