ve of s**6/180 + 163*s**5/45 + 325*s**4/36 + 4*s**2 + 2*s + 73. Factor y(p).
2*p*(p + 1)*(p + 325)/3
Let v(g) be the second derivative of -g**4/3 - 58*g**3/3 - 360*g**2 + 2*g + 619. Factor v(t).
-4*(t + 9)*(t + 20)
Let c(a) be the first derivative of -a**4 + 96*a**3 + 296*a**2 + 164. Factor c(g).
-4*g*(g - 74)*(g + 2)
Let g(q) be the third derivative of -q**5/12 + 335*q**4/8 - 500*q**3/3 - 411*q**2. Suppose g(z) = 0. What is z?
1, 200
Let b = -51 + -1. Let f = b + 55. Suppose 4*t**2 + 9*t**3 - 4*t**4 - 4*t - 22*t**f + 17*t**3 = 0. What is t?
-1, 0, 1
Suppose -5*i = -3*f + 107, -25 = -f + i + 10. Factor 52/3 + 16*a**2 + f*a - 2/3*a**3.
-2*(a - 26)*(a + 1)**2/3
Let x be (-20)/((-84)/6*1/2). Let u be (-14)/(-147)*18*10/15. Find k such that u + 16/7*k**2 + 4/7*k**3 + x*k = 0.
-2, -1
Let r(s) be the first derivative of -s**3/15 - 57*s**2/10 + 244*s/5 + 2876. Factor r(q).
-(q - 4)*(q + 61)/5
Let l(w) be the second derivative of w**6/120 + 7*w**5/80 - 17*w**4/48 + 3*w**3/8 + 1063*w. Let l(f) = 0. Calculate f.
-9, 0, 1
Let p(i) be the third derivative of -i**5/140 + 19*i**4/28 - 297*i**3/14 - i**2 - 972*i. Determine t, given that p(t) = 0.
11, 27
Let x be (2 - 4)*((-3)/(-13) + 1775/(-650)). Solve 0 + 3/2*z**2 + 3*z**3 + 0*z + 21/8*z**x - 57/8*z**4 = 0 for z.
-2/7, 0, 1, 2
Let s(c) be the third derivative of -c**6/60 - c**5/15 + 5*c**4/3 - 8*c**3 + 525*c**2. Factor s(k).
-2*(k - 2)**2*(k + 6)
Suppose 11*l - 2779 - 3260 = 0. Let a = 552 - l. Suppose 2/3*k**a - 4/3*k**2 + 0*k + 0 = 0. Calculate k.
0, 2
Let i(k) be the third derivative of -2 - 1/240*k**7 + 0*k - k**2 + 0*k**3 + 0*k**4 + 1/120*k**5 - 1/80*k**6. Suppose i(t) = 0. What is t?
-2, 0, 2/7
Solve 463*v + 1/2*v**2 + 925/2 = 0.
-925, -1
Let o(s) = s**2 - 8*s + 3. Suppose 8*a - 6*a - 16 = 0. Let u be o(a). Factor m + 137*m**4 + m**3 + m**2 + 0*m**u - 2*m**3 - 138*m**4.
-m*(m - 1)*(m + 1)**2
Let c be (-1)/(116/20 + -6). Determine d so that 4*d - 2*d**5 - 49*d + 6*d**2 - 24 - d**c + 18*d**4 + 0*d**5 + 48*d**3 = 0.
-1, 1, 8
Let v(f) be the second derivative of 3*f**4/2 + 17*f**3 + 16*f**2 + 568*f. Determine i so that v(i) = 0.
-16/3, -1/3
Let u(t) be the third derivative of 0 - 17*t**2 + 11/24*t**4 + 0*t + 121/6*t**3 + 1/240*t**5. Find k, given that u(k) = 0.
-22
Let g be 6*(-1 + 16)/45. Factor -g*u**2 + 2/5*u**3 - 26/5*u - 14/5.
2*(u - 7)*(u + 1)**2/5
Let q(r) = -6*r**2 - 9*r + 78. Let t(a) be the first derivative of a**3 + 2*a**2 - 40*a + 16. Let w(i) = 5*q(i) + 9*t(i). Factor w(n).
-3*(n - 2)*(n + 5)
Solve -44402 - 1/2*a**2 + 298*a = 0.
298
Let q(v) = -11*v**4 + v**3 - 13*v**2 + 5*v - 10. Let t(d) = -5*d**4 + 2*d**3 - 6*d**2 + 2*d - 4. Let b(p) = 2*q(p) - 5*t(p). Factor b(c).
c**2*(c - 2)*(3*c - 2)
Let w be (-8)/(-128) + 229551/784 + 0 + (-10)/(-1). Suppose -16/7 + 1409938/7*b**4 - 92916/7*b**2 + w*b + 1314886/7*b**3 = 0. What is b?
-1, 2/89
Let s(i) = -15*i**2 - 3166*i + 2080. Let w(g) = -135*g**2 - 28480*g + 18720. Let l(y) = -35*s(y) + 4*w(y). Let l(f) = 0. Calculate f.
-208, 2/3
Let a(p) be the first derivative of -p**9/1008 + p**8/70 - p**7/40 - 2*p**3/3 - 3*p**2 - 72. Let l(o) be the third derivative of a(o). Factor l(d).
-3*d**3*(d - 7)*(d - 1)
Suppose 2*a - 2*d + 3*d = 62, -2*a - 3*d = -62. Factor 95*l + 632 + a*l**2 + 74*l**2 - 5*l**4 - 95*l**3 - 732.
-5*(l - 1)**2*(l + 1)*(l + 20)
Let w(s) be the second derivative of -s**7/147 + 41*s**6/105 - 111*s**5/35 + 214*s**4/21 - 40*s**3/3 + 2553*s - 2. Factor w(j).
-2*j*(j - 35)*(j - 2)**3/7
Let c(s) be the first derivative of -10*s**3/9 + 106*s**2 + 256*s/3 - 144. Find v such that c(v) = 0.
-2/5, 64
Let f = -159 - -163. Solve 168*p**5 + 16*p + 162*p**5 + 60*p**2 - 15*p**f - 320*p**5 - 50*p**3 + 24*p = 0 for p.
-2, -1/2, 0, 2
Let j(c) be the first derivative of -c**8/336 - 5*c**7/336 - c**6/72 - 44*c**3/3 - 60. Let t(u) be the third derivative of j(u). What is z in t(z) = 0?
-2, -1/2, 0
Let u(a) = a**2 - 117*a + 12. Let w(t) = t**2 - 120*t + 8. Let h(n) = -2*u(n) + 3*w(n). Suppose h(z) = 0. What is z?
0, 126
Factor 1071/5*u + 3/5*u**2 + 0.
3*u*(u + 357)/5
Let l(y) = 14404*y - 43210. Let w be l(3). Determine m so that 4/5*m + 1/5*m**w - 4/5 - 1/5*m**3 = 0.
-2, 1, 2
Let b(i) be the third derivative of 40/3*i**3 - 1/24*i**6 - 5/4*i**4 - 3/4*i**5 + 16 + 0*i + 3*i**2. Factor b(m).
-5*(m - 1)*(m + 2)*(m + 8)
Let w be (336/120)/(385/150). Suppose -6/11 - w*k**3 + 10/11*k + 4/11*k**2 + 2/11*k**4 + 2/11*k**5 = 0. What is k?
-3, -1, 1
Let q(w) be the first derivative of -w**4/28 + 17*w**3/14 + 27*w**2/7 + 6*w - 135. Let o(k) be the first derivative of q(k). Determine v so that o(v) = 0.
-1, 18
Let f be (2/(-11))/(2208/(-24288)). Factor -2/15*p**f + 22/15*p - 4/3.
-2*(p - 10)*(p - 1)/15
Let f = -97999 - -1862157/19. Factor f*t + 72/19 - 10/19*t**2.
-2*(t - 18)*(5*t + 2)/19
Let r be (-7)/(21/6)*(-14 - (2 - 15)). Factor 4/5 - 1/5*p**r - 3/5*p.
-(p - 1)*(p + 4)/5
Let p(c) be the first derivative of 7*c**6/30 - c**5/4 - 3*c**4/4 + 5*c**3/6 + c**2 - 114*c + 128. Let f(y) be the first derivative of p(y). Factor f(w).
(w - 1)**2*(w + 1)*(7*w + 2)
Let -37/4*j + 5/2 + 51/4*j**2 - 31/4*j**3 + 7/4*j**4 = 0. What is j?
1, 10/7
Suppose -12*b = -383 + 107. Let v = b - 67/3. What is z in 1/3*z**3 + 5/3*z - v - 4/3*z**2 = 0?
1, 2
Suppose -5 = -4*n - 1, -3*b = 3*n - 12. Let u(a) be the first derivative of a**b + 0*a**3 + 30*a - 7 + 26*a - 29*a - 9*a**2. Factor u(r).
3*(r - 3)**2
Let c(a) be the first derivative of -2*a**2 + 5/4*a**4 - 1/6*a**6 - 20/3*a**3 + 4/5*a**5 - 208 + 16*a. Let c(d) = 0. Calculate d.
-2, -1, 1, 2, 4
Let d(r) = 5*r**2 - 44*r - 98. Let x(l) = 73 + 2160*l**2 + 122 + 90*l - 2170*l**2. Let q(i) = -5*d(i) - 2*x(i). Factor q(o).
-5*(o - 10)*(o + 2)
Find c such that 0 - 3*c**4 + 27/8*c + 33/4*c**3 - 9*c**2 + 3/8*c**5 = 0.
0, 1, 3
Let z(f) be the first derivative of f**8/840 + f**7/30 - f**6/180 - 7*f**5/30 - 7*f**3/3 + f**2/2 - 7. Let v(a) be the third derivative of z(a). Factor v(h).
2*h*(h - 1)*(h + 1)*(h + 14)
Let 640*l**3 - 41*l**2 - 4*l - 633*l**3 - 4*l**4 + 2*l**4 + 37*l**2 = 0. Calculate l.
-1/2, 0, 2
Let f(h) = -19*h**3 - 5*h**2 - 2*h. Let l be 4*(2 + (-91)/28). Let v(z) = 20*z**3 + 5*z**2 + 5*z. Let j(d) = l*f(d) - 4*v(d). Factor j(c).
5*c*(c + 1)*(3*c - 2)
Let x(o) = -o**4 - 21*o**3 + 101*o**2 + 2477*o. Let g(z) = z**4 + 22*z**3 - 99*z**2 - 2478*z. Let n(r) = -2*g(r) - 3*x(r). Let n(k) = 0. What is k?
-15, 0, 11
Let y(j) be the third derivative of -j**7/1680 + j**6/240 + 9*j**5/160 + 19*j**4/96 + j**3/3 - 338*j**2 - 1. Suppose y(b) = 0. What is b?
-2, -1, 8
Let x = -473 - -480. Suppose -318 = -x*k - 304. Factor -k*m**2 + 8/5 - 8/5*m + 6/5*m**3.
2*(m - 2)*(m + 1)*(3*m - 2)/5
Let w(b) be the third derivative of 25/12*b**4 + 0*b - 1/60*b**6 + 1/105*b**7 - 13/30*b**5 + 1 - 4*b**3 - 44*b**2. Factor w(x).
2*(x - 3)*(x - 1)**2*(x + 4)
Determine b so that -1894/9*b**2 - 228 + 2/9*b**4 - 82/9*b**3 + 1342/3*b = 0.
-18, 1, 57
Let f(k) be the third derivative of -625/27*k**3 + 0*k - 1/270*k**5 + 86*k**2 + 0 - 25/54*k**4. Factor f(l).
-2*(l + 25)**2/9
Let l(f) = 4*f**2 - 506*f - 15876. Suppose 418*d = 427*d - 18. Let b(q) = -8*q**2 + 507*q + 15876. Let o(m) = d*b(m) + 3*l(m). Solve o(n) = 0 for n.
-63
Determine f so that -56 - 1760/7*f + 18/7*f**2 = 0.
-2/9, 98
Let u(z) be the first derivative of z**5/25 - 21*z**4/10 - 139*z**3/15 + 18*z**2 - 4359. Let u(p) = 0. Calculate p.
-4, 0, 1, 45
Let u(s) = -s**4 - s**3 - 4*s**2 + s. Let r(q) = 3*q**3 + 5*q**2 - 3*q. Let f(m) = 3*r(m) + 3*u(m). Factor f(c).
-3*c*(c - 2)*(c - 1)*(c + 1)
Let m(y) be the second derivative of -3*y**5/40 + 59*y**4/8 - 176*y**3 - 3840*y**2 - 1005*y. Factor m(d).
-3*(d - 32)**2*(d + 5)/2
Suppose d + 6*t = 9*t + 73, d + 3*t = 97. Let b = -165/2 + d. Factor b*a**2 + 5*a - 5/2*a**3 + 0.
-5*a*(a - 2)*(a + 1)/2
Let a(c) = 7*c**4 + 4*c**3 - 9*c**2 + 3*c - 3. Let z(n) = -23*n**4 - 14*n**3 + 29*n**2 - 10*n + 10. Let g(v) = 10*a(v) + 3*z(v). What is i in g(i) = 0?
-1, 0, 3
Let z(c) be the third derivative of c**5/180 - 17*c**4/18 + 67*c**3/18 - 441*c**2. Factor z(k).
(k - 67)*(k - 1)/3
Let i(b) = 429*b + 79796. Let r be i(-186). What is x in 2/3*x**r + 64/3*x + 62/3 = 0?
-31, -1
Suppose 24 = 2*i - 0*i. Let b be -9*(32/i - 3). Determine c so that -2*c**2 + c**4 + b*c**3 - 3*c**3 + c**2 = 0.
-1, 0, 1
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