3
Find s such that -1026*s**2 + 4942 + 0*s**4 - 3*s**4 - 168*s**3 - 3913 + 168*s = 0.
-49, -7, -1, 1
Let z(i) be the third derivative of i**5/40 + 19*i**4/16 + 12*i**3 + 918*i**2. Factor z(p).
3*(p + 3)*(p + 16)/2
Let x(w) be the third derivative of -5*w**8/112 + w**7/42 + 113*w**6/24 + 179*w**5/12 + 175*w**4/12 + 34*w**2 + 2*w + 2. Solve x(v) = 0 for v.
-5, -1, -2/3, 0, 7
Let h(l) be the second derivative of l**7/336 - l**6/6 + 213*l**5/160 - 51*l**4/16 - 537*l. Factor h(o).
o**2*(o - 34)*(o - 3)**2/8
Suppose -22*l = 212797 - 212841. Factor 2/9*q**5 - 18 + 14/9*q**4 - 30*q - 12*q**l + 4/3*q**3.
2*(q - 3)*(q + 1)*(q + 3)**3/9
Let m(y) be the first derivative of 6*y**2 + 0*y - 91 - 1/6*y**3. Solve m(q) = 0 for q.
0, 24
Let d = -3 + 25. Suppose 0 = -4*z + 76 + 24. Solve z*i**3 + d - 2 - 14*i**4 - 5*i**5 - 20*i - 25*i**2 + 19*i**4 = 0.
-2, -1, 1, 2
Let b(r) be the second derivative of -1/27*r**4 - 2 - 2/45*r**5 - 1/54*r**6 + 0*r**3 - 2*r - 1/378*r**7 + 0*r**2. Factor b(x).
-x**2*(x + 1)*(x + 2)**2/9
Let x = 109 - 43. Let o be x/(-24)*(1/1 + -89). Solve -8788 - o*r**2 - 2028*r + 86*r**2 - 4*r**3 - 4*r**3 + 4*r**3 = 0 for r.
-13
Factor 64309*o**2 + 42*o**4 - 38*o**4 + 4704 + 1400*o - 64801*o**2.
4*(o - 7)**2*(o + 2)*(o + 12)
Let y(h) = 7*h**2 - 2*h - 1. Let w(p) = -20*p**2 + 425*p - 839. Let x(i) = -w(i) - 3*y(i). Suppose x(j) = 0. What is j?
-421, 2
Let i(j) be the third derivative of -j**5/15 - 113*j**4/3 - 25538*j**3/3 + 746*j**2 - 1. Factor i(h).
-4*(h + 113)**2
Let i(c) = -c**2 + 6774*c - 282741. Let s be i(42). Solve 33/2*f**2 - 3/2*f**s + 27/2 - 57/2*f = 0.
1, 9
Let v(z) = 6*z**2 - 50 + 79*z - 76 + 26*z. Let f be 21/28*-12 - -13. Let m(s) = -s**2 - 15*s + 18. Let d(o) = f*v(o) + 27*m(o). Find b such that d(b) = 0.
2, 3
Solve -6/5*r**3 - 84 + 20*r**2 + 566/5*r = 0.
-5, 2/3, 21
Suppose -10*r + 12 = 2*r. Let t be 222/(-259)*-1*1/r. Factor 0 - 2/7*i**3 - t*i**2 + 0*i.
-2*i**2*(i + 3)/7
Solve -540/7*x**3 - 2/7*x**5 - 370/7*x + 0 + 88/7*x**4 + 824/7*x**2 = 0 for x.
0, 1, 5, 37
Let l(x) be the second derivative of x**4/4 - 69*x**3 + 1215*x**2/2 + 2*x - 140. Factor l(t).
3*(t - 135)*(t - 3)
Let g be ((-10)/315)/(276/1242) - -3*(-5)/(-21). Find q, given that 8/7*q + 12/7 - g*q**2 = 0.
-1, 3
Suppose 0 = 10*r - 196 + 176. Let b(y) be the third derivative of 10*y**r + 0*y + 0 - 1/32*y**4 + 1/240*y**5 + 0*y**3. Factor b(f).
f*(f - 3)/4
Let w(h) be the second derivative of -h**7/2100 - h**6/15 - 4*h**5 - h**4/3 - h**3/6 + 3*h - 1. Let p(u) be the third derivative of w(u). Factor p(q).
-6*(q + 20)**2/5
Let o = -457 - -458. Let k be o/((-4)/(-16)) + 88/(-26). Suppose -8/13*p**3 + 10/13*p - k*p**4 + 4/13 - 2/13*p**5 + 4/13*p**2 = 0. Calculate p.
-2, -1, 1
Let i be ((-14)/35)/(2/(-10)). Let g(t) = t**2 + t - 4. Let d be g(i). Determine k, given that -4 + 10 + 3*k**2 + 0*k**d + 4*k - 5*k**2 = 0.
-1, 3
Let f(k) be the first derivative of 3*k**5/20 + 105*k**4/16 - 79*k**3/4 - 537*k**2/8 + 333*k/2 - 665. What is l in f(l) = 0?
-37, -2, 1, 3
Let a(z) be the third derivative of -z**5/390 + 61*z**4/13 - 44652*z**3/13 - 8*z**2 + 21*z. Factor a(m).
-2*(m - 366)**2/13
Let l(m) = m**3 + m**2 - 10*m - 40. Let q be l(-3). Let k(x) = -2*x**3 - 57*x**2 - 26*x + 59. Let d be k(q). Factor 2/21 + 2/21*r - 2/21*r**2 - 2/21*r**d.
-2*(r - 1)*(r + 1)**2/21
Let x(l) = -254*l + 3306. Let m be x(13). Let a(b) be the second derivative of 0 - b + 0*b**2 + 1/3*b**3 + 1/10*b**5 - 1/3*b**m. Factor a(v).
2*v*(v - 1)**2
Let p(i) be the second derivative of 29/18*i**3 - 1/36*i**4 + 122*i + 0*i**2 + 1. Factor p(d).
-d*(d - 29)/3
Factor 1074 - 106*a**3 - 183*a**2 - 45*a**2 + 2*a**4 + 424*a - 194.
2*(a - 55)*(a - 2)*(a + 2)**2
Factor 1004*m + 4*m**2 - 1614 + 207 - 437 - 2620 - 284*m.
4*(m - 6)*(m + 186)
Let n(v) be the second derivative of v**7/24 + v**6/15 - 31*v**5/40 + 17*v**4/12 - 17*v**3/24 - v**2/2 - v + 8. Suppose n(q) = 0. Calculate q.
-4, -1/7, 1
Let t(b) be the second derivative of b**5/10 - 2*b**4/3 - 259*b**3/3 - 494*b**2 - 9*b - 145. Determine q, given that t(q) = 0.
-13, -2, 19
Suppose 24 = s + 7*s. Factor 4*c**5 + 0*c + 6*c - 11*c**s + 7*c**3 - 4*c - 2*c**5.
2*c*(c - 1)**2*(c + 1)**2
Let y(g) = 16*g + 274. Let u be y(-17). Factor -14*f**3 + 16*f - 25*f**3 + 159*f - 3*f**4 - 28*f - 105*f**u.
-3*f*(f - 1)*(f + 7)**2
Let b = -1162 - -5950. Determine w so that w**3 + b*w - 4788*w + 11*w**2 = 0.
-11, 0
Factor 3608/9 + 4/9*s - 3608/9*s**2 - 4/9*s**3.
-4*(s - 1)*(s + 1)*(s + 902)/9
Let q(z) be the first derivative of z**3/2 - 327*z**2/4 + 477*z + 1028. Factor q(j).
3*(j - 106)*(j - 3)/2
Let m(n) be the third derivative of n**6/180 - 5*n**5/12 + 2*n**4 - 9*n**3/2 - 22*n**2. Let z(j) be the first derivative of m(j). Suppose z(g) = 0. Calculate g.
1, 24
Suppose -o - o = 2*k - 4, 4*k = -3*o + 11. Suppose -k*u + 39 = 29. Find f, given that -4/7*f**4 + 0 - 8/7*f**3 - 4/7*f**u + 0*f = 0.
-1, 0
Let i(y) = 2*y**2 + 662*y + 686. Let l(x) = -7*x**2 - 2633*x - 2743. Let w(b) = -9*i(b) - 2*l(b). Solve w(n) = 0.
-172, -1
Let g(b) be the first derivative of -3/2*b**2 - 1/2*b**5 + 19 - b**4 + 0*b + 19/6*b**3. Factor g(h).
-h*(h - 1)*(h + 3)*(5*h - 2)/2
Suppose 2*h = 8, -2*h = -f + 3*h - 19. Let a be (f + 3/(-4))/(2/16). Solve -2*s**4 - 4*s**3 - 14*s**2 - 8*s**3 + 6*s**2 - a*s**4 = 0 for s.
-2, -1, 0
Factor 16/5 + 9/5*m**2 + 1/5*m**3 + 24/5*m.
(m + 1)*(m + 4)**2/5
Suppose -84*d - 52*d + 423 = 5*d. What is j in 2/9*j**5 - 104/9*j - 2/3*j**d - 8/9*j**4 + 68/9*j**2 + 16/3 = 0?
-3, 1, 2
Factor -58 + 69*g**3 - 50 - 4*g**4 + 87*g**3 - 188*g - 336*g**2 + 516*g - 36*g**3.
-4*(g - 27)*(g - 1)**3
Let a(p) = 21 + 3*p**2 + 8*p - 17 - 2*p**2. Let m be a(-9). Factor -j + 0*j - 4*j**3 + 8 + m*j.
-4*(j - 2)*(j + 1)**2
Let k(t) = -30*t**4 - 147*t**3 + 235*t**2 - 17*t. Let l(w) = -9*w**4 - 42*w**3 + 67*w**2 - 5*w. Let n(f) = 5*k(f) - 17*l(f). Suppose n(y) = 0. What is y?
0, 3, 4
Let b be 36/(-30)*20/(-12). Solve 2*q**b - 1 - 264*q + 268*q + 1 = 0 for q.
-2, 0
Let r be (-235)/141*(3 + (-9 - -3)). Let k(m) be the first derivative of 17 + 64/3*m**3 + 8*m**2 + 36/5*m**r + 0*m + 21*m**4. Suppose k(g) = 0. What is g?
-1, -2/3, 0
Suppose 1957*q**2 + 5334 + 5331*q + 1959*q**2 - 3919*q**2 = 0. Calculate q.
-1, 1778
Let u(w) = 5*w**4 + 18*w**3 - 36*w**2 - 64*w + 206. Let r(g) = g**4 + 2. Let v be 12/15 + (-7)/(-35) - 15. Let n(d) = v*r(d) + 2*u(d). Factor n(j).
-4*(j - 4)**2*(j - 3)*(j + 2)
Let b be 3 - -8 - ((7 - 3) + -1). Let j be (-225)/(-30) - (-3 + b). Factor 5/2*d + 0*d**2 + 0 - j*d**3.
-5*d*(d - 1)*(d + 1)/2
Let c = 246197/9 + -27355. Factor -8/3 + c*d**2 + 22/9*d.
2*(d - 1)*(d + 12)/9
Suppose -104*w + 75*w = -67*w + 152. Let c(f) be the second derivative of 0 + 2/3*f**3 - 1/12*f**w + 0*f**2 - 28*f. Factor c(y).
-y*(y - 4)
Let i = 19517/20 + -4843/5. Factor -15/2*n**2 + 0 - i*n - 1/4*n**3.
-n*(n + 1)*(n + 29)/4
Let t = -471/442 + -15641/3094. Let g = 87/13 + t. Factor g*s**2 - 4/7*s - 8/7.
4*(s - 2)*(s + 1)/7
Suppose -36*f = -41*f - 4135. Let c = -825 - f. Factor 0 - 18/5*i + 3/5*i**3 - 3*i**c.
3*i*(i - 6)*(i + 1)/5
Let c(n) be the third derivative of -n**6/10 + 134*n**5/15 + 277*n**4/6 + 280*n**3/3 - 8*n**2 + 144*n. Factor c(x).
-4*(x + 1)**2*(3*x - 140)
Let p = -239 + 233. Let b be p/13 - 384/(-156). Find w, given that b*w + 1/4*w**2 + 4 = 0.
-4
Let n be 5/(-7)*(-108)/(-180)*-7. Find j such that 0 + 2/3*j**n + 72*j**2 + 1944*j = 0.
-54, 0
Let p be (15/18)/(-5) - 2465/(-102). Let i be (10/(-3))/(p/(-144)). Factor -i*o + 6*o**2 + 50/3.
2*(3*o - 5)**2/3
Let p(u) be the third derivative of u**5/255 - 7*u**4/204 + 8*u**2 + 80*u. Factor p(l).
2*l*(2*l - 7)/17
Let x(j) = 2*j**3 - 46*j**2 + 38*j + 134. Let s be x(22). Let f = 2/151 - -1496/1057. Solve -f*y**2 + 0 - s*y = 0.
-7/5, 0
Determine i, given that 16*i**5 + 2827*i + 5908*i**2 - 800 - 1916*i**2 + 302*i**3 + 438*i**3 - 276*i**4 - 667*i = 0.
-2, -1, 1/4, 10
Let b(u) be the second derivative of -3*u**7/28 + 547*u**6/4 - 1868683*u**5/40 - 628369*u**4/24 + 86716*u**3 - 51984*u**2 - 6677*u. Solve b(c) = 0 for c.
-1, 1/3, 456
Solve 3/4*h**2 - 6*h - 15 = 0 for h.
-2, 10
Suppose 36*p - 11 - 11 = 19*p + 29. Determine m so that -4/5*m**2 + 36/5 - 36/5*m + 4/5*m**p = 0.
-3, 1, 3
Let i be -3 - (-8 + -1 + 8)*15. Let t(b) be the first derivative of 2/3*b**6 - 6/5*b**5 + 2*b**2 + 2*b