hat a(q) = 0.
-1, 1
Let d(a) = -a**3 - 7*a**2 - 23*a - 112. Let b be d(-6). Let k(w) = 6*w + 62. Let n be k(b). Find s, given that 24 + 8*s + 2/3*s**n = 0.
-6
Let r = 47 - 57. Let s be r/15*(46 + 2)*-1. Factor 640*j - 4*j**5 - 88*j**4 - 240*j**3 + 99*j**2 - 140*j + s*j**4 - 299*j**2.
-4*j*(j - 1)*(j + 5)**3
Let c(a) be the first derivative of 10/3*a + 12 - 10/9*a**3 - 1/6*a**4 + 1/3*a**2. Find x, given that c(x) = 0.
-5, -1, 1
Let g(f) be the first derivative of f**3/9 + 255*f**2/2 - 3499. Let g(k) = 0. What is k?
-765, 0
Let t be (-73875)/156 - 3/(-12) - -5. Let p = -468 - t. What is s in 4/13*s**4 + p*s**3 - 2/13*s**5 - 16/13*s**2 - 4/13 + 14/13*s = 0?
-2, 1
Suppose 3*u - 74 = 2*i, -4*i - 92 = -4*u - 8*i. Factor -21*s + 3*s**2 + 4 + 20 - u*s + 27*s.
3*(s - 4)*(s - 2)
Let w be (4/(-2)*1)/((-204)/1122). Suppose -23*b + w*b - b**2 - 182 - 16*b - 14 = 0. What is b?
-14
Factor -119/5*l - 1/10*l**2 + 239/10.
-(l - 1)*(l + 239)/10
Let a = 11080/16611 - 2/5537. Let x(u) be the first derivative of 18 - 1/2*u**4 + 4/9*u**3 + 0*u**2 - a*u**5 + 0*u. Factor x(g).
-2*g**2*(g + 1)*(5*g - 2)/3
Factor 2/5*f**4 - 532/5*f**3 - 1612/5*f - 1608/5*f**2 - 538/5.
2*(f - 269)*(f + 1)**3/5
Let j(a) be the third derivative of a**9/756 - a**8/420 - a**7/210 + a**6/90 - a**3/3 + 51*a**2 - a. Let o(g) be the first derivative of j(g). Factor o(n).
4*n**2*(n - 1)**2*(n + 1)
Factor 661*k**2 - 36*k**3 + 41*k**3 + 24500*k + 39*k**2.
5*k*(k + 70)**2
Factor -15145469*v + 15145209*v + 3*v**3 - v**3 - 126*v**2.
2*v*(v - 65)*(v + 2)
Let d(x) = x**2 - 18*x - 61. Let g be d(21). Solve -10*o + 19*o**g + 142 - o - 7*o - 143 = 0.
-1/19, 1
Let o = 12072 - 84502/7. Let -450/7 - o*w**2 - 60/7*w = 0. What is w?
-15
Let t = 103 + -53. Let b = t + -53. Let p(i) = -60*i**2 + 445*i - 995. Let h(j) = -5*j**2 + 37*j - 83. Let y(k) = b*p(k) + 35*h(k). Factor y(s).
5*(s - 4)**2
Let a(f) = -3*f**2 + 142*f - 128. Let r(i) = -i**2 - 12*i - 2. Let w(t) = a(t) - 7*r(t). Solve w(p) = 0 for p.
-57, 1/2
Solve 215/3 - 1/3*x**2 + 38/3*x = 0 for x.
-5, 43
Let p = 119973/5 - 23994. Solve -12/5*y**2 + 6/5 - p*y**3 + 7/5*y + 2/5*y**4 = 0.
-2, -1/2, 1, 3
Let k(w) be the second derivative of w**5/2 - 17*w**4/6 + 19*w**3/3 - 7*w**2 + 3*w + 226. Factor k(c).
2*(c - 1)**2*(5*c - 7)
Let i(p) be the first derivative of -p**3/6 - 75*p**2/4 + 117*p - 351. Factor i(u).
-(u - 3)*(u + 78)/2
Let c(w) be the first derivative of -w**3 - 5280*w**2 - 9292800*w - 4715. Determine i, given that c(i) = 0.
-1760
Let z be ((-9)/2)/((325/26 - 13)*(-228)/(-38)). Factor -z*w**3 + 6*w - 6 + 3/2*w**2.
-3*(w - 2)*(w - 1)*(w + 2)/2
Let j(h) be the first derivative of -h**5/15 + 32*h**4/3 + 175*h**3/3 + 66*h**2 + 679. Factor j(n).
-n*(n - 132)*(n + 1)*(n + 3)/3
Let q(r) be the second derivative of r**4/12 - 211*r**3/6 - 106*r**2 - 138*r + 2. Let q(v) = 0. What is v?
-1, 212
Let r be ((-60)/40)/(0 - (-6)/(-8)). Factor 8 + 15*j**2 - 2*j**r + 8 - 11*j**2 - 12*j.
2*(j - 4)*(j - 2)
Let c(a) = 54*a**3 - 117*a**2 + 12. Let p(q) = -q**4 + 4*q**3 - q**2 - 4. Let u(h) = c(h) + 3*p(h). Factor u(g).
-3*g**2*(g - 20)*(g - 2)
Let l(j) be the third derivative of -1/120*j**5 + 131*j**2 + 0 - 5/24*j**4 + 0*j - 7/4*j**3. Solve l(o) = 0 for o.
-7, -3
Let z(o) be the third derivative of 0*o**5 + 0*o + 0 - 1/280*o**6 - 1/490*o**7 + 0*o**3 + 0*o**4 - 4*o**2. Factor z(r).
-3*r**3*(r + 1)/7
Let o(g) be the third derivative of -g**5/80 + 3*g**4/2 - 23*g**3/2 + 6071*g**2. Find j such that o(j) = 0.
2, 46
Let a = -496/15 - -167/5. Let m(g) be the first derivative of -1/9*g**3 + 1/6*g**2 + 5 - 1/12*g**4 + a*g. What is u in m(u) = 0?
-1, 1
Suppose -4*y - 46 + 11 = -3*d, d - 2*y - 15 = 0. Suppose -d*p = -16*p + 66. Determine w, given that 0*w + 0*w**2 + 3*w**2 + p*w - 2*w**3 + w**2 = 0.
-1, 0, 3
What is z in -53429*z**2 - 100 - 37719*z**2 - 59871*z**2 + 49895*z**2 - 6360*z = 0?
-5/159
Let b(o) be the third derivative of o**5/140 + 149*o**4/28 + 2*o**2 - 1707*o - 1. Determine z so that b(z) = 0.
-298, 0
Let -54*t**2 - 696*t**4 + 6*t**3 + 84 + 352*t**4 + 26*t + 346*t**4 = 0. What is t?
-7, -1, 2, 3
Let p(y) = 5*y**3 - 75*y**2 + 200*y - 130. Let d(s) be the first derivative of s**2/2 - s + 19. Let h(j) = 35*d(j) + p(j). Find g, given that h(g) = 0.
1, 3, 11
Suppose 441*n - 39 = 428*n. Let l(i) = 15*i - 42. Let a be l(n). Solve 9/4*x**4 + 21/4*x**2 - 39/4*x**a - 9/2 + 51/4*x = 0 for x.
-1, 1/3, 2, 3
Let k = -71977 - -71979. Let 944/7*p**k + 212/7*p**4 + 20/7*p**5 + 752/7*p**3 - 256/7 + 128/7*p = 0. What is p?
-4, -2, -1, 2/5
Let g(l) be the second derivative of -l**5/80 + 7*l**4/16 - 13*l**3/8 - 35*l**2 + 46*l + 1. Let m(u) be the first derivative of g(u). Factor m(h).
-3*(h - 13)*(h - 1)/4
Suppose -121 = 5*z + 2*j + 1555, -659 = 2*z - 3*j. Let r be (-8016)/z*1/(6/4). Find n such that 64/3*n - 2/3*n**4 - r*n**2 + 16/3*n**3 - 32/3 = 0.
2
Factor -345 - 1/6*w**2 + 1037/6*w.
-(w - 1035)*(w - 2)/6
Let y(d) = 2*d**3 - 328*d**2 + 331*d - 811. Let l be y(163). Let 76/3*a**3 - 112/3*a - 32/3 - 8*a**2 - 4*a**5 + 8/3*a**l = 0. Calculate a.
-2, -1, -1/3, 2
Suppose -29*s + 84 = -213 - 58 + 123. Factor -1/7*z**3 + s*z - 11/7*z**2 - 60/7.
-(z - 2)**2*(z + 15)/7
Let h(l) be the second derivative of -l**4/12 - 17*l**3/2 + 140*l**2 + 4952*l. Find x, given that h(x) = 0.
-56, 5
Factor -195*z + 517*z**2 - 185 - 499 - 1066 - 522*z**2.
-5*(z + 14)*(z + 25)
Factor -1/2*k**2 + 101*k - 201/2.
-(k - 201)*(k - 1)/2
Factor 176/17 - 2/17*r**3 - 268/17*r + 94/17*r**2.
-2*(r - 44)*(r - 2)*(r - 1)/17
Let f(w) be the second derivative of -2*w**6/15 + w**5/3 - w**4/6 + 28*w**2 - 29*w - 2. Let p(i) be the first derivative of f(i). Factor p(r).
-4*r*(r - 1)*(4*r - 1)
Let n be -3*(-6)/(-27)*(12 - 6). Let v(k) = 2*k**3 + k**2 + k + 2. Let u(y) = 11*y**3 - 11*y**2 - 2*y + 80. Let q(j) = n*v(j) + u(j). Factor q(p).
3*(p - 4)*(p - 3)*(p + 2)
Factor 0 + 1/2*n**3 - 47/4*n - 93/4*n**2.
n*(n - 47)*(2*n + 1)/4
Let b(z) be the second derivative of -9*z + 1/3*z**2 + 1/18*z**4 + 2/9*z**3 - 5. Find c such that b(c) = 0.
-1
Let 171/2*x**3 + 8320*x - 6144 - 7/4*x**4 - 1416*x**2 = 0. What is x?
6/7, 16
Let r(q) be the first derivative of 0*q + 265 + 0*q**2 + 5/3*q**3 + 1/6*q**6 - 9/4*q**4 + 3/5*q**5. Factor r(x).
x**2*(x - 1)**2*(x + 5)
Suppose 5*b = 4*w + 50, -3*w = -1623*b + 1629*b - 60. Factor 147/5*n**5 + w + 96/5*n**3 + 231/5*n**4 + 12/5*n**2 + 0*n.
3*n**2*(n + 1)*(7*n + 2)**2/5
Find h such that 24/7*h**2 + 4*h**3 + 0*h**4 - 24/7 - 2/7*h**5 - 26/7*h = 0.
-3, -1, 1, 4
Let a = 426276/1435 - -156/287. Factor -81/5*d**4 + 432*d**2 + 972/5*d**3 + a*d + 336/5.
-3*(d - 14)*(3*d + 2)**3/5
Let a(d) be the second derivative of -4/3*d**3 - d**2 + 0 + 171*d - 7/24*d**4. Factor a(g).
-(g + 2)*(7*g + 2)/2
Let n be (-5)/35*10*(6538/(-70) - -23). Solve -128/7*w**5 - 1472/7*w**3 - 1440/7*w**2 - n*w**4 - 648/7*w - 108/7 = 0.
-3/2, -1/2
Let n(i) be the first derivative of i**4/14 + 608*i**3/7 + 207936*i**2/7 + 1869. Determine z, given that n(z) = 0.
-456, 0
Let u(b) be the first derivative of -b**5/25 - b**4/4 + 37*b**3/5 - 47*b**2/2 - 70*b + 2300. Factor u(o).
-(o - 5)**2*(o + 1)*(o + 14)/5
Let c be 2279/(-6) + -2 - 67/(-134). Let x = -381 - c. Let 2/3*h + 0 + x*h**3 + h**2 = 0. Calculate h.
-2, -1, 0
Let n be (40/16)/(2 + 2298/(-12)). Let f = n + 389/758. Find u such that 0 - 3*u - f*u**3 + 5/2*u**2 = 0.
0, 2, 3
Suppose -895*l = 218*l - 4452. Factor -2/3*n**l + 10/3*n**3 + 72 + 6*n**2 - 54*n.
-2*(n - 3)**3*(n + 4)/3
Suppose -30*z - 6 = -31*z. Let r(i) be the first derivative of z*i - 2/3*i**3 - 4 - 2*i**2. Suppose r(c) = 0. What is c?
-3, 1
Let b(u) = 10*u**3 - 74*u**2 - 256*u. Let w(a) = -2*a**3 + 15*a**2 + 51*a. Let n be 1 + 2 + -5 + 4*2. Let f(o) = n*b(o) + 28*w(o). Factor f(v).
4*v*(v - 9)*(v + 3)
Let b(c) = -c + 2. Let n be b(0). Suppose 34*x - 23*x - 385 = 0. Factor -28*w + 3*w**3 + x*w + 56*w + 42*w**n + 84*w.
3*w*(w + 7)**2
Suppose 5399*f = 5110*f. Let -2/7*k**3 + 4/7*k**4 + f*k**2 + 0*k - 2/7*k**5 + 0 = 0. What is k?
0, 1
Suppose -3*f - 12 = 4*i, 3 = 19*i - 20*i. Let r(j) be the third derivative of -1/45*j**5 + 0 + f*j - 7*j**2 + 7/36*j**4 + 4/9*j**3. Solve r(s) = 0 for s.
-1/2, 4
Factor -2/9*b**2 + 220/3*b - 6050.
-2*(b - 165)**2/9
Let v(o) be the third derivative of 8*o**2 + 0*o**4 + 0*o**3 + 1/120*o**5 + 1/1260*o**7 + 1/1