c) be the second derivative of 0*c**2 + 8*c**4 + 0*c**3 - 1/14*c**7 + 6*c - 24/5*c**5 + c**6 + 0. Factor j(q).
-3*q**2*(q - 4)**2*(q - 2)
Let h = -362 + 390. Factor 16 - h*c**2 + 10*c**2 + 111*c**4 - 109*c**4 + 14*c - 14*c**3.
2*(c - 8)*(c - 1)*(c + 1)**2
Let j(l) be the first derivative of -l**6/16 - 3*l**5/20 + 9*l**4/4 + 4*l**3 - 24*l**2 - 437. What is a in j(a) = 0?
-4, 0, 2, 4
Let h(y) be the second derivative of 25/8*y**4 + 1/120*y**6 + 0 + 8*y + 1/4*y**5 - 2/3*y**3 + 0*y**2. Let i(v) be the second derivative of h(v). Factor i(s).
3*(s + 5)**2
Factor -2*x**2 - 40 + 504/5*x.
-2*(x - 50)*(5*x - 2)/5
Solve 122/5*k**4 - 24/5*k**2 + 0 + 0*k - 104/5*k**3 - 32/5*k**5 = 0 for k.
-3/16, 0, 2
Suppose -23*v + 2*v = -84. Let t(p) = -p**2 + 4*p + 2. Let i(x) = 2*x**2 - 4*x - 3. Let l(q) = v*i(q) + 6*t(q). Let l(u) = 0. What is u?
-4, 0
Let q(u) be the third derivative of -u**5/20 - 19*u**4/2 - 75*u**3/2 + 483*u**2 - 1. Factor q(x).
-3*(x + 1)*(x + 75)
Let u(t) = 3*t**3 - 5140*t**2 - 661270*t. Let s(v) = v**3 - 2570*v**2 - 330605*v. Let f(n) = 13*s(n) - 6*u(n). Find x such that f(x) = 0.
-257, 0
Let i be (-6)/((-3990)/2983) + 2/(-7). Factor -12*y - 9/5*y**2 + i.
-3*(y + 7)*(3*y - 1)/5
Find w, given that 156/7 - 2/7*w**2 - 46/7*w = 0.
-26, 3
Let z(k) be the second derivative of -2/21*k**3 - 1/140*k**5 + 41*k + 0*k**2 + 0 - 1/21*k**4. Determine h so that z(h) = 0.
-2, 0
Let k(v) be the second derivative of -v**4/78 + 434*v**3/13 - 423801*v**2/13 + 10208*v. Factor k(t).
-2*(t - 651)**2/13
Let k(i) be the first derivative of -3*i**4/4 + 13*i**3 + 27*i**2/2 - 1215*i - 22. Let k(f) = 0. Calculate f.
-5, 9
Suppose 3*o - 211*m + 213*m = 34, -o + 4*m = 26. Factor 3/4*t**4 + 18*t + 27/4 + o*t**3 + 33/2*t**2.
3*(t + 1)**2*(t + 3)**2/4
Let g(f) = 15*f - 120. Let d be g(6). Let a be d/(-9)*(-2)/(-10). Factor -2/3*z**3 - a + 2/3*z**2 + 2/3*z.
-2*(z - 1)**2*(z + 1)/3
Factor 2/3*j - 4/9*j**2 - 2/9*j**3 + 0.
-2*j*(j - 1)*(j + 3)/9
Let t = 41 - 65. Let f be (-255)/t - (-9)/24. Determine l, given that f*l + 7*l**2 + 9*l**2 - 13*l**2 + 6 = 0.
-3, -2/3
Factor 44*f**5 + 198*f**5 - 238*f**5 + 5184*f**3 - 288*f**4.
4*f**3*(f - 36)**2
Let h be (-5 - -6) + 4 + -2. Let -10*x**4 + 3*x**2 + 13*x**h + 8*x**3 + 27*x**4 - 20*x**4 - 21*x = 0. Calculate x.
-1, 0, 1, 7
Let v(l) = -2*l**2 - 39*l - 83. Let s be v(-17). Determine m so that 120*m - 498 - 622*m**2 + 624*m**s + 2298 = 0.
-30
Suppose 2*f = 6, 122 = 5*n + 2*f + 566. Let t = -65 - n. Determine i so that 10*i**4 + 11*i**4 - 10*i**5 - t*i**4 = 0.
-2/5, 0
Let x(y) be the first derivative of -9*y**5/20 - 147*y**4/4 - 441*y**3/4 + 3*y**2/2 + 189*y - 1254. Find p such that x(p) = 0.
-63, -2, -1, 2/3
Let f(y) be the first derivative of y**4/20 - 59*y**3/15 + 88*y**2 - 780*y - 1588. Solve f(r) = 0.
10, 39
Suppose -655 = -6*h - 133. Suppose h*p - 82*p + 12 = 3*i, i - 5*p = 4. Factor -3/4*k**2 + 0*k + 3/4*k**5 - 9/4*k**i + 9/4*k**3 + 0.
3*k**2*(k - 1)**3/4
Suppose 35 + 115 = 30*q. Let j be ((-8)/(96/q))/(6/(-96)). Let -6*c - 2/3*c**2 + j = 0. What is c?
-10, 1
Let p be (-31 - -58) + (-23 - 2). Determine o so that 4/3*o**3 + 0*o**p - 8/3 - 4*o = 0.
-1, 2
Let h be (-60)/270*-46 - (-12)/(-54). Factor h + 7/3*w - 1/3*w**2.
-(w - 10)*(w + 3)/3
Let w(d) be the second derivative of 0 + 16/3*d**3 + 12*d**2 - 1/10*d**5 + 1/2*d**4 - 44*d. Let w(r) = 0. What is r?
-2, -1, 6
Let f = 168657/2 - 84325. Let f*q**3 - 7/4 + 9/4*q**4 + 1/4*q**5 - 1/2*q**2 - 15/4*q = 0. Calculate q.
-7, -1, 1
Let b(d) be the third derivative of -d**6/40 - 27*d**5/100 - d**4/4 - 902*d**2 + 2*d. Find l such that b(l) = 0.
-5, -2/5, 0
Let i(l) be the first derivative of 4*l**3/3 + 1100*l**2 + 302500*l - 1636. Suppose i(p) = 0. Calculate p.
-275
Solve 16/11 + 612/11*m**2 + 632/11*m - 14*m**4 - 158/11*m**3 = 0.
-2, -1, -2/77, 2
Suppose -5*f = -4*q + 4, 5*q + 28 = 7*f - 9*f. Let z be 10/(-80)*(0/(-1) + q). Find j, given that -1/4*j**2 + 1/4*j + z = 0.
-1, 2
Suppose 6*i - 4*i - 2*w - 326 = 0, -812 = -5*i + 2*w. Suppose -62*q - i = -1650. Factor -16/3*y + 0 - q*y**2 - 27*y**3.
-y*(9*y + 4)**2/3
Let d(h) be the first derivative of h**6/720 - h**5/120 + 55*h**3/3 + 10. Let u(n) be the third derivative of d(n). Factor u(g).
g*(g - 2)/2
Determine c, given that -1111*c**2 - 278*c**3 - 192*c - 1186*c**2 + 2773*c**2 - 6*c**4 = 0.
-48, 0, 2/3, 1
Let a(o) = -1 - 7*o - 10*o**2 + 9*o**2 - 3. Let j be a(-6). Suppose 0*s**2 - 9*s + 11*s + j*s**3 + 4*s**2 = 0. Calculate s.
-1, 0
Suppose 96 = -3*g + 7*j, -5*g + 44*j = 58*j - 225. Determine t so that 96*t + 56*t**2 + 2/3*t**4 + 0 + 32/3*t**g = 0.
-6, -4, 0
Suppose 0 = -259*d + 251*d - 8. Let g be 4/180*(d - -7). Determine u so that g - 2/15*u**3 + 2/15*u - 2/15*u**2 = 0.
-1, 1
Let w(r) be the second derivative of r**7/1575 - r**6/225 + r**5/90 - r**4/90 - 59*r**2/2 + 2*r + 7. Let k(o) be the first derivative of w(o). Factor k(q).
2*q*(q - 2)*(q - 1)**2/15
Let k(c) = 114240*c**2 - 8116*c + 120. Let t(z) = z**2 + z + 6. Let s(a) = k(a) + 4*t(a). Factor s(q).
4*(169*q - 6)**2
Let f be (-6)/(-27)*((0 - -20) + -2). Suppose -12*s - 2*s = f*s. Find z such that 2/3*z + 5/3*z**3 + 7/3*z**2 + s = 0.
-1, -2/5, 0
Let c(z) be the third derivative of z**7/140 + 39*z**6/40 - z**5/40 - 39*z**4/8 + 5619*z**2. Factor c(n).
3*n*(n - 1)*(n + 1)*(n + 78)/2
Let g(h) = -22*h + 83 - 56 - 73*h**2 + 72*h**2. Let b be g(-23). Factor -2/9*l + 0 + 0*l**2 + 0*l**b - 2/9*l**5 + 4/9*l**3.
-2*l*(l - 1)**2*(l + 1)**2/9
Suppose -4 = -l + 2*u, -5*l - 39 = -2*u - 51. Let g(i) = i**3 + i**2 - 3*i - 4. Let q be g(l). Factor -2/3*x**4 + 0 + 2/3*x - 2/3*x**3 + 2/3*x**q.
-2*x*(x - 1)*(x + 1)**2/3
Suppose k - 53 = -2*s, 2*k + 2583 = -3*s + 2662. Let p(a) be the first derivative of -1/3*a**3 + s + 1/2*a**4 - 2*a - 5/2*a**2. Factor p(h).
(h - 2)*(h + 1)*(2*h + 1)
Suppose 2*b + b - 8 = -o, 0 = 4*o - 8. Solve 8*h**4 + 253*h + 4*h**5 + 4*h**3 - 96*h**b + 22*h**4 - 6*h**4 - 189*h = 0.
-4, 0, 1
Suppose 28 = 2*k - 36. Suppose -k = -z - 5*u, z = 2*u - 3 + 7. Determine o, given that -z + 14*o + 3*o**2 + 4*o**2 + 2*o - 11*o**2 = 0.
1, 3
Let i(n) = n**4 + n. Let u(l) = -12*l**3 + 2*l - 3*l**3 - 9*l**2 - 3*l**4 + 21*l**3. Let k(t) = 10*i(t) + 5*u(t). Factor k(r).
-5*r*(r - 4)*(r - 1)**2
Let a(f) be the second derivative of -f**5/100 - 17*f**4/60 + 14*f**3/5 - 173*f. Factor a(b).
-b*(b - 4)*(b + 21)/5
Let g(p) = -17*p**2 + 14189*p + 9. Let b(o) = -75*o**2 + 63850*o + 40. Let x(q) = -9*b(q) + 40*g(q). Let x(c) = 0. What is c?
-1418, 0
Let j be ((-6)/27)/(10/(-88275)*5). Let x = j + -392. Factor -1/3*w**3 + 0 + 0*w - x*w**2.
-w**2*(w + 1)/3
Let o(i) be the first derivative of 5*i**3/3 - 2150*i**2 + 924500*i - 3989. Factor o(a).
5*(a - 430)**2
Let t be 12 - ((-36)/84 + 1726/140). Determine q, given that -3/5*q - 3/5*q**3 + 0 - 11/10*q**2 - t*q**4 = 0.
-3, -2, -1, 0
Let n = -1099/13 - -4435/52. Let k(x) be the second derivative of 8*x - 1/10*x**6 - n*x**5 + 0*x**3 - 3/4*x**4 + 0*x**2 + 1/14*x**7 + 0. Factor k(w).
3*w**2*(w - 3)*(w + 1)**2
Let h(s) be the third derivative of 7/20*s**5 + 61/480*s**6 + 3/8*s**4 - 57*s**2 + 0*s + 1/60*s**7 + 0*s**3 + 0 + 1/1344*s**8. Factor h(k).
k*(k + 1)**2*(k + 6)**2/4
Let o(g) be the first derivative of -5*g**3/3 + 2295*g**2 - 1053405*g - 1663. Factor o(v).
-5*(v - 459)**2
Suppose 59168/17 - 688/17*g + 2/17*g**2 = 0. Calculate g.
172
Let r be -7 + 1890/(-180)*2*-1. Let a(x) be the first derivative of -32/3*x**3 + 23 + 0*x - r*x**2 - x**4. Factor a(p).
-4*p*(p + 1)*(p + 7)
Let m(s) be the second derivative of -1/60*s**6 + 5/24*s**4 + 1/4*s**3 + 0*s**2 + 0 + 1/40*s**5 + 33*s. Factor m(b).
-b*(b - 3)*(b + 1)**2/2
Factor 5*t**4 - 4*t**2 + 20*t**3 - 20*t - 15*t**2 - 9*t**2 + 41*t**2 - 18*t**2.
5*t*(t - 1)*(t + 1)*(t + 4)
Let w = -7 + 12. Let 2*m**3 + 26*m**2 - 5*m**4 + 140*m - 16*m**2 - w - m**5 - 141*m = 0. What is m?
-5, -1, 1
Let a(l) = -l**2 - 5*l + 7. Let w be a(-4). Let g = w + -3. Let 5*j + 4*j**5 + 16*j**4 - 6*j + 8*j**3 - 16*j**2 - g*j - 3*j = 0. What is j?
-3, -1, 0, 1
Let n(i) be the third derivative of 65*i**2 + 8/105*i**5 + 0*i**4 - 1/42*i**6 + 0 + 0*i**3 + 0*i + 1/735*i**7. Factor n(b).
2*b**2*(b - 8)*(b - 2)/7
Suppose 2*c - 3 = 2*l - 15, 5*l + c - 12 = 0. Let x be (-54)/72 - 5225/(-140). Solve 688/7*d**2 - 4/7*d**5 - 292/7*d**l - 704/7*d + x + 8*d**4 = 0 for