 f(d) = d**3 - 12*d**2 + 35*d + 4. Let j = -1445 - -1450. Let b be f(j). Determine z so that 14/3*z**5 + 0 - 2*z**b + 0*z**2 + 0*z + 0*z**3 = 0.
0, 3/7
Let b(h) be the third derivative of h**7/420 - 17*h**6/240 + 17*h**5/30 - 25*h**4/12 + 4*h**3 + 975*h**2. Factor b(n).
(n - 12)*(n - 2)**2*(n - 1)/2
Let d = 124 + -92. Suppose -120 = -d*q + 27*q. Determine j so that -q*j + 0*j**2 - 5*j**2 + 8*j**2 + 48 = 0.
4
Let q(p) be the first derivative of -p**6/12 - 13*p**5/20 + 57*p**4/16 + 109*p**3/12 + 5*p**2/8 - 9*p - 3751. Determine d so that q(d) = 0.
-9, -1, 1/2, 4
Let k = -79 - -81. Factor 1 + 3*w**2 - 3*w + w**3 - 30 + 2*w**2 - w**k + 11.
(w - 2)*(w + 3)**2
Let w(h) = -10*h**2 + 41*h + 4. Let c be w(4). Suppose -6 - 10 = -c*p. Factor 3/2*l**p - 3/2*l**4 - 3/4*l + 0 + 0*l**3 + 3/4*l**5.
3*l*(l - 1)**3*(l + 1)/4
Let k = 213 + -211. What is x in 8*x**3 + 16*x**k - 12*x**3 - 2*x + 6*x - 11*x**4 - 5*x**4 = 0?
-1, -1/4, 0, 1
Let i(f) be the third derivative of f**8/40320 - f**7/720 - f**6/45 - 63*f**5/20 - 186*f**2. Let d(j) be the third derivative of i(j). Factor d(m).
(m - 16)*(m + 2)/2
Let p be (-8*7/294)/((-6)/9). Factor -2/7*h**2 - 6/7 - p*h**3 + 10/7*h.
-2*(h - 1)**2*(h + 3)/7
Factor -2/7*i**3 - 2*i - 2*i**2 + 30/7.
-2*(i - 1)*(i + 3)*(i + 5)/7
Let o(d) = -147*d**2 + 87*d - 6. Let p(y) = -2 - 1564*y + 1563*y + 0. Let v(t) = o(t) + 3*p(t). Suppose v(s) = 0. What is s?
2/7
Let h be (-23)/(-46)*3528/(-26). Let u = h + 68. Let -10/13*b**2 + 0*b**3 + 0*b + u*b**4 + 8/13 = 0. What is b?
-2, -1, 1, 2
Let u be 10/4 + -2 - 317/(-951). Let o(m) be the first derivative of -3*m**5 + 0*m + u*m**6 + 5/4*m**4 - 23 - 5*m**2 + 5*m**3. Factor o(w).
5*w*(w - 2)*(w - 1)**2*(w + 1)
Let o(w) be the first derivative of 4*w**6/3 + 12*w**5/5 - 23*w**4 - 272*w**3/3 - 120*w**2 - 64*w - 221. Suppose o(a) = 0. What is a?
-2, -1, -1/2, 4
Let j(o) be the second derivative of o**6/15 - 13*o**5/10 + 29*o**4/6 + 133*o**3/3 - 294*o**2 - 70*o. What is f in j(f) = 0?
-3, 2, 7
Let p(s) = -11*s**3 - s**2 - 2*s - 2. Let b be p(-1). Let t be 1352/(b/8 - 1). Factor -15*q**3 + 24*q**2 + 12*q - 5408 + t.
-3*q*(q - 2)*(5*q + 2)
Let u = 1589417/5 - 317879. Factor 294/5 - 14/5*f - u*f**2 - 2/5*f**3.
-2*(f - 3)*(f + 7)**2/5
Let q(d) be the third derivative of d**8/1440 + d**7/315 - d**6/270 - 29*d**4/12 + 27*d**2. Let f(l) be the second derivative of q(l). Factor f(y).
2*y*(y + 2)*(7*y - 2)/3
Factor 3*j - 16*j - 10*j**3 + 25 + 15*j**3 - 10 - 3*j**2 - 4*j**3.
(j - 5)*(j - 1)*(j + 3)
Let b(f) = 146*f - 29635. Let m be b(203). Find v, given that 0 - 2/3*v**m + 12*v - 14/3*v**2 = 0.
-9, 0, 2
What is j in -397*j**3 - j**2 - 5*j**5 - 105*j**4 - 163*j**3 + 4307*j + 97*j**2 + 6000 + 264*j**2 + 893*j = 0?
-10, -2, 3
Let h = 2084/1095 - 273/146. Let i(z) be the second derivative of h*z**4 + 1/5*z**3 + 0 - 30*z - 4/5*z**2. Let i(k) = 0. What is k?
-4, 1
Let a(d) be the second derivative of d**4/12 + 11*d**3/3 + 97*d**2 - 15*d + 2. Let m(s) = 3*s + 1. Let t(j) = -2*a(j) - 4*m(j). Solve t(v) = 0 for v.
-14
Let z = 9 + -2. Let m(c) be the second derivative of -1/45*c**6 + 0 + 13/120*c**5 + z*c - 11/72*c**4 + 1/18*c**3 + 0*c**2. Solve m(k) = 0.
0, 1/4, 1, 2
Let t(x) be the first derivative of x**8/336 - x**6/72 + 55*x**3/3 + 31. Let v(d) be the third derivative of t(d). Factor v(s).
5*s**2*(s - 1)*(s + 1)
Let l = -15 + 23. Suppose -29 = -l*m - 5. Factor 0*g**m + 5*g - 3*g**3 - 14 - 2*g**3 - 10*g**2 + 24.
-5*(g - 1)*(g + 1)*(g + 2)
Suppose 3*m - 8*m = -10. Suppose -5*t**m + t**2 + t**2 - 2*t**2 + 230*t - 2645 = 0. What is t?
23
Let t(b) be the third derivative of -b**5/105 + 5*b**4/14 - 1543*b**2. Find i such that t(i) = 0.
0, 15
Let c = -163 + 166. Let g(i) be the second derivative of -i + 4/9*i**4 + 0 - 1/6*i**5 - 1/9*i**c - 2/3*i**2. Let g(j) = 0. What is j?
-2/5, 1
Let b(q) be the first derivative of 273/2*q**2 + 1/4*q**4 - 676*q - 10*q**3 + 242. Factor b(g).
(g - 13)**2*(g - 4)
Let p be 93/36 + (-56)/24. Let t(w) be the third derivative of 1/30*w**5 - p*w**4 + 0*w**3 + 35*w**2 + 0*w + 0. Solve t(y) = 0 for y.
0, 3
Suppose 28 = 4*n - 90*j + 87*j, 2*j = 2*n - 16. Factor 1/3*a**3 - 9*a + 14/3 + n*a**2.
(a - 1)**2*(a + 14)/3
Let w(t) be the first derivative of -2*t**3/51 + 284*t**2/17 - 1128*t/17 - 3516. Suppose w(i) = 0. What is i?
2, 282
Let b(s) be the first derivative of -2/9*s**3 - 179 + 12*s + 17/3*s**2. Let b(a) = 0. Calculate a.
-1, 18
Suppose -2*x + 2*p = -10 - 6, -4*x + 2*p + 24 = 0. Factor x*n + 10*n**5 + 2*n**4 - 11*n**5 - 8*n**2 + 3*n**3 + 0*n + 0*n**5.
-n*(n - 2)*(n - 1)**2*(n + 2)
Factor -f**2 + 60*f - 82*f - 128 + 47 - 146*f - 86.
-(f + 1)*(f + 167)
Let k(n) = -14*n + 60. Let z be k(4). Let z*w**3 - 2*w**2 - 191 - 2*w**4 + 191 = 0. What is w?
0, 1
Suppose 24 = 5*f + 4. Let u(h) = 13 + 7 - 28 + 40*h - f*h**2 - 83. Let m(z) = -z**2 + 10*z - 23. Let p(i) = 18*m(i) - 4*u(i). Let p(x) = 0. What is x?
5
Suppose 4*m = -2*n + 2*m - 22, -25 = 5*m. Let l be 1 + (-2 - n) - 1848/(-216). Suppose -8*q - 28/9*q**4 - 56/3*q**2 + 0 - 2/9*q**5 - l*q**3 = 0. Calculate q.
-6, -1, 0
Suppose -5*z - 5 = 0, -4*j - 1 + 10 = 3*z. Let m be j + (-120)/(-88) + -4. Factor 26/11*v**2 + 0 + m*v.
2*v*(13*v + 2)/11
Let g(w) be the first derivative of 5*w**6/6 + 154*w**5 + 375*w**4/2 - 2320*w**3/3 - 3835*w**2/2 - 1530*w + 7987. Factor g(s).
5*(s - 2)*(s + 1)**3*(s + 153)
Suppose -3*o + 43 - 49 = 0. Let m be o/(-7) - (-36)/(-567). Determine b so that m + 2/9*b**2 - 4/9*b = 0.
1
Suppose 0 = 39*s - 56*s + 119. Suppose 5*o + 14 = s*o - 5*a, 10 = 4*o - a. Suppose 7*x - 49/2 - 1/2*x**o = 0. What is x?
7
Suppose 147/4*p - 75/4*p**2 - 73/4 + 1/4*p**3 = 0. What is p?
1, 73
Find y such that 0 - 3/7*y**5 - 1062/7*y**3 + 204*y**2 + 108/7*y**4 + 2601/7*y = 0.
-1, 0, 3, 17
Let r(n) = 14*n - 188. Let a be r(14). Factor 42 - 99*j - a + 261*j - 3*j**2 + 70 + 61.
-3*(j - 55)*(j + 1)
Let r(n) be the third derivative of n**6/120 + 23*n**5/180 - 35*n**4/72 + n**3/2 - n**2 - 2345. Find j, given that r(j) = 0.
-9, 1/3, 1
Let i(y) be the third derivative of 2 + 0*y**5 - 2/105*y**7 + 0*y**4 + 69*y**2 + 0*y - 7/30*y**6 + 0*y**3. Factor i(r).
-4*r**3*(r + 7)
Let o(z) be the first derivative of -z**3/7 - 732*z**2/7 - 1461*z/7 + 1415. Factor o(f).
-3*(f + 1)*(f + 487)/7
Let q = -19930/26103 - -2/1243. Let j = q - -76/63. Factor -2/9*c**2 + 0 + j*c.
-2*c*(c - 2)/9
Let z be 23/(-138) + (-62)/(-12) + -3. Suppose -63 + 171*q**3 - 215*q**2 - 206*q**z - 4*q - 3 - 41*q**2 + 373*q - 12*q**4 = 0. What is q?
1/4, 1, 2, 11
Factor -57/7*q - 3/7*q**2 - 144/7.
-3*(q + 3)*(q + 16)/7
Let j(v) be the second derivative of -1/144*v**6 - 1/24*v**5 + 5/16*v**4 + 0 - 2*v + 0*v**2 - 13/6*v**3. Let g(b) be the second derivative of j(b). Factor g(a).
-5*(a - 1)*(a + 3)/2
Let t(o) be the first derivative of -o**6/60 - o**5/20 + o**4/24 + o**3/6 + 38*o + 45. Let v(w) be the first derivative of t(w). Find c such that v(c) = 0.
-2, -1, 0, 1
Let z be (1 + 4/5)/(2898/805). Solve -1/10*k**3 + 7/10 + 13/10*k + z*k**2 = 0.
-1, 7
Let g be (-22)/(-4752)*-45*-8. Factor -1/3*u**3 + 1/3*u + g*u**2 - 5/3.
-(u - 5)*(u - 1)*(u + 1)/3
Suppose 4*o + 3*w = 7, o = -o + 2*w + 14. Let u be (o/(-10))/(172/(-1935)). Suppose 1/2*a**3 - 7/2 + 15/2*a - u*a**2 = 0. What is a?
1, 7
Let c be 24/(-64) + (22790/(-48))/(-43). Determine k so that c + 1/6*k**2 - 8/3*k = 0.
8
Find u, given that 49*u**4 - 21*u**4 - 38*u**4 + 74*u**3 - 38*u**2 - 24*u**4 - 2*u**5 = 0.
-19, 0, 1
Solve 61*o**4 + 65*o**3 + 297*o**2 - 40*o**4 - 2*o**5 + 153*o**2 + 360*o - 51*o**4 - 3*o**5 = 0.
-6, -3, -1, 0, 4
Let w(b) = -b**3 - 190*b**2 - 174*b - 33058. Let f be w(-190). Factor 64/5*p - 22/5 + 16/5*p**3 - 12*p**f + 2/5*p**4.
2*(p - 1)**3*(p + 11)/5
Let j(d) be the second derivative of 111*d - 1/48*d**4 + 1/160*d**5 + 0*d**2 + 0*d**3 + 0. Find g such that j(g) = 0.
0, 2
Let t(s) be the first derivative of 3/2*s**4 - 236 + 1/42*s**6 + 0*s - 64/21*s**3 + 16/7*s**2 - 11/35*s**5. Solve t(i) = 0 for i.
0, 1, 2, 4
Let m be 3*(-10)/(-315) + 200/105. Factor -4*l + 5*l**2 - 23*l**2 + 6*l**2 + 11*l**m.
-l*(l + 4)
Let r(t) = 48*t + 2. Let v be r(0). Let m(s) be the first derivative of 0*s**3 - 2*s**5 + 0*s - 5/4*s**4 + 0*s**v + 5 - 5/6*s**6. Factor m(n).
-5*n**3*(n + 1)**2
Let a(m) = 4*m**5 - 2*m**4 - 4*m**3 - 13*m**2 - 12*m. Let z(n) = -7*n**5 