11*o(t). Factor c(h).
5*(h + 2)*(15*h - 2)**2
Let b(w) be the second derivative of 305*w - 1/150*w**5 + 0 - 121/45*w**3 + 0*w**2 + 11/45*w**4. Determine h, given that b(h) = 0.
0, 11
Let h(v) = 3*v**5 + 7*v**4 + 15*v**3 + 7*v**2 + 2*v. Let r(q) = 17*q**5 + 37*q**4 + 78*q**3 + 36*q**2 + 11*q. Let f(w) = -33*h(w) + 6*r(w). Factor f(d).
3*d**2*(d - 5)*(d + 1)**2
Let g(v) = 5*v**3 + 91*v**2 + 202*v - 778. Let s(c) = -c**3 - 2*c**2 + c - 1. Let t(z) = -g(z) - 2*s(z). Factor t(q).
-3*(q - 2)*(q + 5)*(q + 26)
Suppose 62*r**3 + 66*r**4 + 693 - 693 - 66*r**2 - 3*r**5 + 3*r**5 - 64*r + 2*r**5 = 0. Calculate r.
-32, -1, 0, 1
Suppose f - 5*s = -0*f + 4, 5*s = -2*f - 22. Let m(c) = -3*c**2 - 18*c + 2. Let y be m(f). Factor 2*l**2 - l + 62 - 60 - 3*l**y.
-(l - 1)*(l + 2)
Let m(a) be the second derivative of -4/5*a**5 + 64*a + 8/3*a**3 - 1 + 1/5*a**6 - a**4 + 3*a**2. Determine j, given that m(j) = 0.
-1, -1/3, 1, 3
Let z be 163*1/(-4)*4. Let y = 1143/7 + z. Determine f, given that 32/7 + 18/7*f**2 - 48/7*f - y*f**3 = 0.
1, 4
Let t = 1/119803 + 2635661/599015. Factor -52/5 + t*a + 2/5*a**2.
2*(a - 2)*(a + 13)/5
Let x = 4569 - 4565. Let n(z) be the first derivative of 0*z + 1/6*z**6 + 2/3*z**3 + 0*z**5 + 0*z**2 + 7 - 3/4*z**x. Find q, given that n(q) = 0.
-2, 0, 1
Let d(b) be the first derivative of 28*b**5 - 139*b**4 + 520*b**3/3 + 56*b**2 - 96*b + 4459. Suppose d(i) = 0. What is i?
-3/7, 2/5, 2
Let c(r) = -r**2 + 6*r. Let t(d) = -7*d**2 - 103*d - 30. Let z(s) = -3*c(s) + t(s). Factor z(a).
-(a + 30)*(4*a + 1)
Let h be ((-24)/(-44))/((-165)/(-605)). Factor 13/2*s + 0*s**h - 1/2*s**3 - 6.
-(s - 3)*(s - 1)*(s + 4)/2
Let u be (-8)/(-164) - 104006/(-33005). Find w, given that 26/5*w**3 + 2/5*w**2 + 14/5*w**4 + 2/5*w**5 - u - 28/5*w = 0.
-4, -2, -1, 1
Suppose -417 = -33*x - 351. Let z(u) be the second derivative of 16/7*u**4 - 5*u + 0 - 8/35*u**5 + 256/7*u**x - 256/21*u**3 + 1/105*u**6. Factor z(w).
2*(w - 4)**4/7
Determine w, given that -10416*w - 4/5*w**4 + 716/5*w**2 + 168/5*w**3 - 76880 = 0.
-10, 31
Find x such that 1225*x**4 - 1680*x - 10056*x**2 + 26794*x**2 - 15*x**5 - 27918*x**2 + 6400 - 1860*x**3 = 0.
-2, -1, 2/3, 4, 80
Let x(t) be the first derivative of t**3/3 - 171*t**2 + 341*t - 3968. Determine k so that x(k) = 0.
1, 341
Let s(o) be the first derivative of 1/21*o**6 + 10/21*o**3 - 2/7*o**5 - 123 - 1/14*o**4 + 0*o + 0*o**2. What is y in s(y) = 0?
-1, 0, 1, 5
Suppose 11 = 4*l - 9, 4*l = -3*i - 130. Let x be (35/126)/(i/(-30)). Factor 1/2 + x*a**2 - 2/3*a.
(a - 3)*(a - 1)/6
Suppose -3*y + 6 + 0 = 0. Suppose 156 = 72*g + 6*g. Factor -3*a**g + 4*a**2 + 2*a**4 - 2*a + y*a**3 + 0*a**2 - 3*a**2.
2*a*(a - 1)*(a + 1)**2
Let k = -351 - -356. Suppose -k*j - 5 = 28*d - 27*d, -d = -4*j + 5. Factor -10/9*m**4 + j + 0*m + 2/9*m**2 + 8/9*m**3.
-2*m**2*(m - 1)*(5*m + 1)/9
Let l(c) be the first derivative of c**7/168 + 17*c**6/24 + 26*c**5 - 845*c**4/6 - 7*c**3/3 - 167. Let v(y) be the third derivative of l(y). Factor v(t).
5*(t - 1)*(t + 26)**2
Let k(y) be the second derivative of 39*y + 0*y**4 - 1/40*y**5 + 1/40*y**6 + 0*y**2 - 1/168*y**7 + 0*y**3 + 0. Let k(m) = 0. What is m?
0, 1, 2
Solve -7949*y + 4*y**2 - 2756*y + 1489*y = 0 for y.
0, 2304
Let 50/7*f**4 + 0 + 2*f**3 - 362/7*f**2 + 300/7*f - 2/7*f**5 = 0. What is f?
-3, 0, 1, 2, 25
Let f(k) = 2*k**2 + k - 8. Let s be f(2). Let 9*u - 3 - u**2 - u**3 + u - 3*u - s*u = 0. Calculate u.
-3, 1
Suppose j - 177 = -3*h, -h + 53 = 4*j - 17. Let g = h + -53. Factor -11*n**4 - 2*n**2 + n**2 - 62*n + 9*n**3 + 4*n**g + 61*n.
n*(n - 1)**3*(4*n + 1)
Let r(g) be the second derivative of 42 - 7/27*g**4 - 1/90*g**5 + 0*g**3 - g + 0*g**2. Find p, given that r(p) = 0.
-14, 0
Let t be 52/8*(-1 + 3). Suppose 0 = t*q - 67 + 2. Factor 18/11*n**3 + 0*n**4 + 0 - 12/11*n**2 + 0*n - 6/11*n**q.
-6*n**2*(n - 1)**2*(n + 2)/11
Let v(t) be the first derivative of 9*t**4/28 + 71*t**3/7 - 270*t**2/7 + 156*t/7 + 181. Solve v(f) = 0.
-26, 1/3, 2
Let n(j) = -j**3 + 5*j**2 - j + 9. Suppose 4*u = 12 + 8. Let q be n(u). Solve -4*y**q + 2*y - 13*y**5 + 22*y**5 - 11*y**5 + 4*y**2 = 0.
-1, 0, 1
Let n(b) = 23*b - 13. Let p be n(1). Suppose -10*d = -5*d - p. Factor -1/2 - 3/2*s - 3/2*s**d - 1/2*s**3.
-(s + 1)**3/2
Let v(h) be the third derivative of -131*h**2 + 215/24*h**4 + 1/12*h**5 + 0*h + 1 + 0*h**3. Factor v(n).
5*n*(n + 43)
Let v(z) be the second derivative of z**5/150 + z**4/60 - 2*z**3/15 - 43*z**2/2 - 27*z + 1. Let r(h) be the first derivative of v(h). Factor r(x).
2*(x - 1)*(x + 2)/5
Let d(i) be the first derivative of -i**3 - 9075*i**2/7 - 5184*i/7 - 3462. Let d(z) = 0. What is z?
-864, -2/7
Find n, given that -4240*n - 4/3*n**2 - 3370800 = 0.
-1590
Find m such that 4*m**2 + 0 - 2/15*m**3 - 54/5*m = 0.
0, 3, 27
Let n(z) be the third derivative of 174*z**2 + z**4 + 0 - 7/60*z**6 + 0*z + 7/15*z**5 - 1/70*z**7 + 0*z**3. What is q in n(q) = 0?
-6, -2/3, 0, 2
Let q(o) be the first derivative of -o**4/8 - 11*o**3/6 - 35*o**2/4 - 25*o/2 - 1979. Factor q(l).
-(l + 1)*(l + 5)**2/2
Let f(h) = 5*h - 132. Let k(p) = 2*p + 2. Let b(y) = f(y) - 6*k(y). Let j be b(-21). Determine u, given that -1/3 - u**2 + u + 1/3*u**j = 0.
1
Let x(f) be the second derivative of -f**5/5 + 55*f**4/3 - 522*f**3 + 1458*f**2 - 7*f - 18. Factor x(p).
-4*(p - 27)**2*(p - 1)
Let o(q) be the first derivative of -q**3/3 - 121*q**2/2 + 246*q + 5647. Determine p so that o(p) = 0.
-123, 2
Let h be 7/1554*3*(-27)/(-12). Let b = h + 7/74. Solve -1/4*t**4 + 1/4*t**2 + 0*t**3 - 1/8*t**5 + 0 + b*t = 0.
-1, 0, 1
Let r = -667380 + 667381. Factor -2/7*k**2 - 13/7*k + r.
-(k + 7)*(2*k - 1)/7
Let t = -493552 + 8390386/17. What is o in 0 - t*o**3 + 4/17*o**2 + 6/17*o = 0?
-1, 0, 3
Let 331*q + 281*q + 400 + 65*q**3 + 135*q - 167*q + 300*q**2 + 5*q**4 = 0. Calculate q.
-5, -4, -2
Let m(q) = q**3 + 11*q**2 + 9*q - 4. Let n be m(-10). Let j = -319 + 321. Factor 5*w**4 + 10*w**2 + n*w**4 + j*w**4 - 15*w**3 - 8*w**4.
5*w**2*(w - 2)*(w - 1)
Let q(m) be the first derivative of -1/2*m**4 - 2/3*m**3 + 2/5*m**5 + 0*m + m**2 + 70. Factor q(s).
2*s*(s - 1)**2*(s + 1)
Let b = 228 - 220. Solve 12 - b*x**3 + 519*x - 12*x**4 - 1103*x + 64*x**2 + 528*x = 0 for x.
-3, 1/3, 1
Let c = -2019 - -398. Let p = -1603 - c. Factor -2/5*f**5 - p*f**3 - 108/5*f + 0 - 22/5*f**4 - 162/5*f**2.
-2*f*(f + 2)*(f + 3)**3/5
Let x(f) be the first derivative of -1/18*f**6 + 124 - 8/15*f**5 - 8/3*f**3 - 11/6*f**4 + 0*f - 3/2*f**2. Factor x(m).
-m*(m + 1)**2*(m + 3)**2/3
Let j(p) be the third derivative of p**7/735 + p**6/84 - 5*p**4/21 - 16*p**3/21 - 2*p**2 + 450*p. Solve j(d) = 0.
-4, -2, -1, 2
What is r in 1/2*r**2 - 407/2*r + 0 = 0?
0, 407
Suppose -10*z = -17*z - 147. Let u be z/(-6)*(-12)/(-14). Let u*a + 12*a**2 - 18*a - 2 - 3*a**3 + 6 + 2 = 0. What is a?
1, 2
Suppose 3*c = 12 + 6. Let z be c + -2 - (9 + -14). Factor i**2 - 25 - z*i - 55 - 6*i**2 - 31*i.
-5*(i + 4)**2
Let m(s) = 7*s**2 + 1005*s - 2. Let j(a) = 3*a**2 - a - 1. Let u(d) = 6*j(d) - 3*m(d). Factor u(r).
-3*r*(r + 1007)
Let x be -482*(-4)/(-8) - -8. Let r = x + 236. Let -4/3*d**2 + 2/3*d**4 + 0*d**r + 0*d + 2/3 = 0. Calculate d.
-1, 1
Let c = 22 + -20. Suppose 5*j + 7*q = 4*q + 31, 5*j + c*q = 34. What is h in h**4 + 3*h**4 + 0*h**4 - j*h**3 = 0?
0, 2
Factor -3*x**4 - 448*x**3 + 2*x**4 + 439*x**3 + 0*x**4.
-x**3*(x + 9)
Let x(d) be the first derivative of -d**5/30 - 17*d**4/6 - 11*d**3 - 3*d**2/2 + 50*d - 56. Let z(a) be the second derivative of x(a). Factor z(n).
-2*(n + 1)*(n + 33)
Let z be (-4 + 240/70)*21/(-90). Factor 28/15 + z*n**2 - 2*n.
2*(n - 14)*(n - 1)/15
Let c(u) be the first derivative of 0*u**2 + 10 - 1/8*u**3 - u - 1/80*u**5 + 1/12*u**4. Let x(i) be the first derivative of c(i). Factor x(p).
-p*(p - 3)*(p - 1)/4
Factor -22/3*f**2 - 30*f - 68/3.
-2*(f + 1)*(11*f + 34)/3
Suppose 70 + 45 = 13*d + 89. Let t(z) be the third derivative of 2/3*z**3 + 9*z**d + 0 + 1/15*z**5 + 0*z + 1/3*z**4. What is i in t(i) = 0?
-1
Let n be ((-1)/3)/(2/(-1902)). Let a = n - 317. Factor 7/4*g**5 + 0*g**3 + 0 + 1/2*g**4 + a*g**2 + 0*g.
g**4*(7*g + 2)/4
Let b be (-2)/7*(-280)/4. Find s, given that 16*s**2 - 109*s**3 + 16*s**2 - 23*s**3 + b*s**3 - 8*s**4 + 28*s**5 = 0.
-2, 0, 2/7, 2
Let r(u) be the first derivative of -u**4/7 - 184*u**3/3 - 7406*u**2 + 1870. Factor r(j).
-4*j*(j + 16