 0*f = 0?
0, 2/7, 2
Let a(v) be the first derivative of -1/2*v**6 + 4*v**3 + 13 + 3*v**5 - 6*v**4 + 0*v + 0*v**2. Factor a(w).
-3*w**2*(w - 2)**2*(w - 1)
Let z be 8/14 - (-3638)/(-119). Let c(j) = -5*j - 150. Let b be c(z). Determine t, given that 20/3*t**2 + 80/3*t**3 - 5/3*t**4 - 20/3*t**5 + b + 0*t = 0.
-2, -1/4, 0, 2
Factor -294/5*n - 4*n**3 + 1/5*n**4 + 0 + 133/5*n**2.
n*(n - 7)**2*(n - 6)/5
Solve -174*s**2 - 7*s**3 + 43*s**3 - 10*s**3 + 3*s**4 - s**4 + 146*s**3 = 0 for s.
-87, 0, 1
Let y(q) = q**2 + 9*q + 1. Let a(i) = -15*i**2 - 255*i - 1220. Let g(x) = -a(x) - 10*y(x). Factor g(s).
5*(s + 11)*(s + 22)
Let t be 6 + 7 + 0 + -4. Determine u so that 50*u - 4*u**2 - t*u + 19 - 275 + 23*u = 0.
8
Let p(c) = 10*c**2 + 142*c - 940. Let i(n) = 14*n**2 + 189*n - 1254. Let q(a) = -8*i(a) + 11*p(a). Let q(s) = 0. What is s?
11, 14
Let x be -3*((-94 - -89) + (-21)/(-5)). Let t(d) be the second derivative of 7/50*d**5 - 52/15*d**3 - 11/10*d**4 + 0 - 27*d - x*d**2. Factor t(q).
2*(q - 6)*(q + 1)*(7*q + 2)/5
Let s(i) be the first derivative of 1/40*i**6 - 37/2*i**2 - 1/20*i**5 + 0*i**3 + 1 + 0*i**4 + 0*i. Let m(x) be the second derivative of s(x). Factor m(f).
3*f**2*(f - 1)
Let c(l) be the second derivative of l**5/140 + 601*l**4/28 + 361201*l**3/14 + 217081801*l**2/14 - 28*l + 23. Factor c(q).
(q + 601)**3/7
Suppose -215/8*x + 7/4 - 1055/4*x**3 + 275/4*x**4 + 125/8*x**5 + 281/2*x**2 = 0. What is x?
-7, 1/5, 2
Suppose 4*s = -2*i + 148, -s = 2*i - 27 - 13. Suppose 3*p**2 - 19*p + 15 - 25 - s - 28*p - 4*p**2 = 0. Calculate p.
-46, -1
Let r be (3 - -3 - 0) + -29*1/5. Let v(c) be the first derivative of 0*c**2 + r*c**3 - 20 + 0*c. Factor v(j).
3*j**2/5
Let o(d) be the third derivative of -d**8/1344 - d**7/420 + 3*d**6/160 + d**5/120 - d**4/12 + 730*d**2 + 2. Let o(j) = 0. What is j?
-4, -1, 0, 1, 2
Suppose -110 = 29*w - 51*w. Let 16*y**w - 47*y**5 - 10*y + 35*y**4 + 30*y**3 + 11*y**5 - 35*y**2 = 0. Calculate y.
-1, -1/4, 0, 1, 2
Suppose 7749*w - k = 7752*w - 5, 3*k = w - 15. Let y(r) be the first derivative of 3*r**2 - 10 + 4*r + 2/3*r**w. Solve y(p) = 0 for p.
-2, -1
Let j be 44/320*6*1680/1540. Suppose j*b**5 - 21/5*b**4 - 24/5*b + 0 + 4*b**2 + 37/10*b**3 = 0. Calculate b.
-1, 0, 4/3, 3
Determine r so that 462/5 + 42/5*r**2 + 507/5*r - 3/5*r**3 = 0.
-7, -1, 22
Find k, given that -2*k**4 - 61533*k - 1376*k - 70219*k - 259*k**3 - 836*k**3 + 61*k**3 - 134160*k**2 = 0.
-258, -1, 0
Let g(m) be the third derivative of m**7/420 + m**6/10 + 27*m**5/20 + 43*m**3/3 + m**2 + 17. Let i(c) be the first derivative of g(c). Factor i(s).
2*s*(s + 9)**2
Let n(h) = -h**3 + 3*h**2 - h + 160. Let f be n(0). Let d be (f/(-192))/(15/(-4)). Determine z so that -8/9*z - 8/9 - d*z**2 = 0.
-2
Let k be (-6)/(-8) + 3/60*-373. Let v = k + 92/5. Factor v*r**5 + 1/2*r**2 + 0*r - 1/2*r**4 - 1/2*r**3 + 0.
r**2*(r - 1)**2*(r + 1)/2
Let b(g) = -49*g**3 + g**2 + 19*g**3 + 31*g**3. Let v(o) = -3*o**4 + 7*o**2. Let x(t) = -5*b(t) + v(t). Let x(l) = 0. Calculate l.
-2, 0, 1/3
Let v = 6429/1133 + 163/1133. Let -2/11*l**2 + 36/11*l - v = 0. What is l?
2, 16
Let x(d) be the first derivative of 2*d**5/35 + 3*d**4/2 + 4*d**3/7 - 172*d**2 + 336*d - 1345. Let x(p) = 0. Calculate p.
-14, 1, 6
Solve -288 - 30914*o - 3*o**3 - 60*o**2 + 61951*o - 30761*o = 0 for o.
-24, 2
Let x(c) = -11*c**2 + 211*c - 208. Let t(g) = -18*g**2 + 805*g - 76*g + 964*g - 72*g**2 - 4*g - 1665. Let r(q) = 4*t(q) - 33*x(q). Let r(z) = 0. Calculate z.
1, 68
Let h = 169/815 - -109/7335. Factor -2/9*t + h*t**2 - 4/9.
2*(t - 2)*(t + 1)/9
Let t(v) be the second derivative of v**4/18 + 64*v**3/3 + 3072*v**2 - 3*v + 96. Let t(j) = 0. What is j?
-96
Let n be (-1021)/2*(8 + (-260)/35). Let a = 292 + n. Factor 0*k - 2/7*k**2 + 0 - 2/7*k**3 + 2/7*k**5 + a*k**4.
2*k**2*(k - 1)*(k + 1)**2/7
Let u(d) be the second derivative of -25/78*d**4 + 1/3*d**3 + 1/195*d**6 + 0*d**2 + 11/130*d**5 + 49 - 2*d. Find a such that u(a) = 0.
-13, 0, 1
Let w(u) be the third derivative of -u**6/40 - 17*u**5/20 - 10*u**4 - 50*u**3 + 408*u**2 - 1. Let w(f) = 0. Calculate f.
-10, -5, -2
Let c(w) be the second derivative of w**8/420 + w**7/42 + 5*w**3/2 + 16*w + 1. Let t(h) be the second derivative of c(h). Suppose t(m) = 0. What is m?
-5, 0
Let u(q) be the third derivative of -8/3*q**3 + 0*q - 1/2*q**4 + 142*q**2 + 0 - 1/30*q**5. Factor u(o).
-2*(o + 2)*(o + 4)
Let o = 235 - 231. Let 230*j**3 + 8*j**4 - 20 + o*j**2 - 956*j - 319*j**2 + 1116*j - 63*j**4 = 0. Calculate j.
2/11, 1, 2
Let l(b) = 420*b**2 - 222375*b - 63460. Let g(h) = -35*h**2 + 18531*h + 5288. Let x(o) = -35*g(o) - 3*l(o). Factor x(n).
-5*(n - 530)*(7*n + 2)
Suppose -5 = 16*r - 37. Factor -42*k**2 + 132*k + 12*k + 242 + 54*k + r*k**3.
2*(k - 11)**2*(k + 1)
Suppose 312*o - 292*o - 9 = 71. Factor -3/5*u + 3/5*u**3 + 0 + 3/5*u**o - 3/5*u**2.
3*u*(u - 1)*(u + 1)**2/5
Let j(v) be the second derivative of -19*v - 1/20*v**5 + 2*v**3 + 0 - 1/12*v**4 + 0*v**2. Factor j(x).
-x*(x - 3)*(x + 4)
Let d(s) be the second derivative of s**7/42 + 8*s**6/15 + 5*s**5/4 - 7*s**4/2 - 2499*s. Factor d(t).
t**2*(t - 1)*(t + 3)*(t + 14)
Suppose 0 = 6*o - 379 + 19. Factor -128*d**3 - 4*d**5 + 8*d**2 - 24*d**4 - 6 - 24*d + o*d + 22 + 96*d**3.
-4*(d - 1)*(d + 1)**3*(d + 4)
Suppose 0 = -5*g + 5*s - 15, g + 3*s - 22 = -5. Factor 3*a - 584*a**2 + 587*a**g - 3*a**4 + 0*a**4 - 3*a**3.
-3*a*(a - 1)*(a + 1)**2
Suppose 4*m - 44 = 3*p, 0 = -2*m + 3*p - 82 + 122. Let a be 4/(-14) - 2/(-7). Suppose 0*c + 8/15*c**4 - 2/15*c**m + a + 2/5*c**3 = 0. What is c?
-1, 0, 1/4
Let v(t) be the first derivative of -2*t**3/9 + 47*t**2/3 - 60*t - 226. Factor v(i).
-2*(i - 45)*(i - 2)/3
Factor 9468*s**2 + 1458 + 115*s**4 - 450*s**3 - 7128*s - 17*s**4 - 1398*s**3.
2*(s - 9)**2*(7*s - 3)**2
Factor 1/4*p**2 + 7/4*p + 0.
p*(p + 7)/4
Let p(h) be the first derivative of -h**6/42 - 4*h**5/35 + 2*h**4/7 + 2*h**3/3 - h**2/2 - 10*h/7 + 1265. What is z in p(z) = 0?
-5, -1, 1, 2
Factor 1/3*b**2 + 40/3 + 14/3*b.
(b + 4)*(b + 10)/3
Let w(c) be the second derivative of -c**7/3780 - c**6/405 + 43*c**3/6 + 79*c. Let z(q) be the second derivative of w(q). Factor z(r).
-2*r**2*(r + 4)/9
Let a(g) be the second derivative of g**5/5 - 53*g**4/3 + 474*g**3 - 5670*g**2 - 4878*g. Factor a(c).
4*(c - 35)*(c - 9)**2
Find f, given that 645/2*f + 387/2*f**2 + 150 + 39/2*f**3 - 3/2*f**4 = 0.
-5, -1, 20
Let h(s) = -10*s**2 - 30*s - 44. Let l(k) be the second derivative of -k**4/2 - 10*k**3/3 - 29*k**2/2 + k - 5. Let i(v) = 5*h(v) - 8*l(v). Factor i(u).
-2*(u - 6)*(u + 1)
Suppose -2*q + 4*n = -180, -4*q + 4*n + 324 = 8*n. Factor 784 - 6*g**2 + 233*g + 66*g**2 + 355*g + 2*g**3 - q*g.
2*(g + 2)*(g + 14)**2
Let g(v) be the first derivative of -1/2*v**4 + 51 + 4/3*v**3 + 5*v**2 - 12*v. Factor g(c).
-2*(c - 3)*(c - 1)*(c + 2)
Suppose 75 = -122*n + 123*n. Factor 20*m**3 + 8 + 87*m - 10 - 27*m - 18 + n*m**2.
5*(m + 2)**2*(4*m - 1)
Let v(n) = -2*n**2 - n + 1. Let l(r) = -11*r**2 + 60*r - 23. Let f(p) = l(p) + 2*v(p). Let u(o) = 15*o**2 - 59*o + 18. Let j(w) = -4*f(w) - 3*u(w). Factor j(b).
5*(b - 3)*(3*b - 2)
Let h(b) be the third derivative of -1/420*b**6 - 6 - 19/210*b**5 + 5/21*b**4 - 2*b**2 + 0*b**3 + 0*b. Factor h(m).
-2*m*(m - 1)*(m + 20)/7
Let q = -25429 - -177574/7. Let u = q + 865/14. Factor -u*g**2 + 3/2 - g.
-(g - 1)*(g + 3)/2
Let s be (-35)/(-14)*(-84)/(-875)*(-4 + 9). Determine c, given that -9/5*c - s*c**2 - 4/5 - 1/5*c**3 = 0.
-4, -1
Let f(m) = -m**2 - 52*m - 64. Let l be f(-29). Let z = -1205/2 + l. Factor 1/2*i**2 - i + z*i**3 + 0.
i*(i - 1)*(i + 2)/2
Let d(r) = -5*r + 67. Let s be d(13). Solve -80*b**s - 45*b**3 + 10 - 65*b + 133*b - 93*b = 0 for b.
-1, 2/9
Let c be 0*(77/22)/(-7). Suppose 45*f - 95*f = c. Factor -o + f + 1/2*o**2.
o*(o - 2)/2
Let r(y) = -3*y - 18 + 4*y + 2*y - y - 12. Let t be r(16). Factor 1/4*x - 1/4*x**t + 0.
-x*(x - 1)/4
Factor 0 + 2/5*y**2 + 54*y.
2*y*(y + 135)/5
Suppose -17*c - 20*c = -15*i - 39*c + 33, 2*c = -4*i. Suppose -3/2*t**4 + 9/2*t**2 + 0*t**3 - i*t + 0 = 0. What is t?
-2, 0, 1
Let t(h) = 18*h**2 - 80*h - 42. Suppose 3*r - 6 = -b, 32*b + 30 = 37*b + 5*r. Let m(w) = -2*w**2 + 9*w + 5. Let a(z) = b*t(z) + 52*m(z). Solve a(s) = 0.
1, 2
Let v = -729 + 669. Let m be 10/(-25) - 69/v. Factor 3/4*i**2 + 0 - m*i.
3*i*(i - 1)/4
Suppose -13 = -5*