et h(s) be the first derivative of -11 + 15/16*s**4 + 5/2*s - 15/8*s**2 - 5/6*s**3. Factor h(v).
5*(v - 1)*(v + 1)*(3*v - 2)/4
Suppose 2*p - 4*g = 14, g = -3*p - 0*p + 7. Determine m, given that 0*m**3 + m**3 + 4*m**p + 1 - 6*m**3 - 3*m + 3*m**2 = 0.
1
Let c be (360/(-35))/(-4) - (-13 - -15). Let -c*s**2 + 16/7*s - 16/7 = 0. Calculate s.
2
Let c(t) be the first derivative of -130*t**6/9 - 73*t**5/3 + 20*t**4/3 + 215*t**3/9 + 5*t**2 - 240. Solve c(j) = 0 for j.
-1, -2/13, 0, 3/4
Let v(o) be the first derivative of 1/20*o**5 - 1/6*o**4 + 1/6*o**3 + 4*o - 4 + 0*o**2. Let r(l) be the first derivative of v(l). Let r(h) = 0. What is h?
0, 1
Let r(n) be the first derivative of 4 + 0*n**2 - 2/27*n**3 + 8/9*n. Solve r(g) = 0.
-2, 2
Let p = 42902 + -42900. Factor -1/5*s**p + 8/5*s + 9/5.
-(s - 9)*(s + 1)/5
Solve 289/2 + 17*o + 1/2*o**2 = 0 for o.
-17
Let a(j) be the second derivative of 3*j**2 + 1/12*j**3 + 1/240*j**6 - 1/48*j**4 + 2*j - 1/120*j**5 + 0. Let k(d) be the first derivative of a(d). Factor k(z).
(z - 1)**2*(z + 1)/2
Let g be (-4)/(-5 + 1) + 7. Let p(r) be the third derivative of 2/27*r**3 + 0*r - g*r**2 + 0 + 8/135*r**5 - 7/540*r**6 - 11/108*r**4. Factor p(f).
-2*(f - 1)**2*(7*f - 2)/9
Let g(w) be the first derivative of w**6/72 - w**5/3 + 10*w**4/3 + 2*w**3 + 8. Let c(s) be the third derivative of g(s). Determine l, given that c(l) = 0.
4
Let a(t) = 4*t - 10. Let b be a(3). Factor 2 + b + n**2 - 2*n + 0*n - 7.
(n - 3)*(n + 1)
Let s be -3 - (-17 - (-1)/(1/2)). Let j be (4/(-5))/(s/30) + 2. Factor -1/3*m + j + m**4 + 1/3*m**3 - m**2.
m*(m - 1)*(m + 1)*(3*m + 1)/3
Let q(s) be the first derivative of -s**6/540 - s**5/135 - s**4/108 + s**2 - 12. Let t(r) be the second derivative of q(r). Suppose t(v) = 0. What is v?
-1, 0
Let k(b) be the second derivative of 33/10*b**5 + b**3 - 19/3*b**4 + 2*b**2 + 0 - 19*b. Suppose k(f) = 0. Calculate f.
-2/11, 1/3, 1
Let i = 1421 + -1418. Factor 2/19*y**4 - 2/19*y**5 + 0 + 0*y + 2/19*y**i - 2/19*y**2.
-2*y**2*(y - 1)**2*(y + 1)/19
Let q(o) be the third derivative of -o**6/30 - 3*o**5/5 + 2*o**2 - 105. Find p, given that q(p) = 0.
-9, 0
Let k(c) be the second derivative of c**4/60 + c**3/5 + 9*c**2/10 + 143*c. Factor k(d).
(d + 3)**2/5
Suppose 0 = 7*f - 6 - 106. Let o be (35/(-42)*-2)/(f/6). Solve 1/2*g**5 - 3/8*g**3 + 0 - o*g**2 - 1/8*g + 5/8*g**4 = 0.
-1, -1/4, 0, 1
Let p(l) be the third derivative of -l**6/96 - l**5/48 + 5*l**4/16 + 889*l**2. Solve p(x) = 0.
-3, 0, 2
Let t be (-32)/(-56) - (-85)/(-210). Factor 1/6*m + t*m**3 + 0 - 1/3*m**2.
m*(m - 1)**2/6
Let j = 4926 - 4923. Suppose 2*u - 2 = 6. Determine v so that 2/3*v**j + 10/9*v**2 - 8/9*v**u - 2/3*v - 2/9 = 0.
-1, -1/4, 1
Suppose 9*c = 8*c + 4. Let 28*b**5 - 27*b**5 - b**c + 4*b**4 + 2*b**3 = 0. What is b?
-2, -1, 0
Find p such that 2/17*p**3 + 0 + 54/17*p - 56/17*p**2 = 0.
0, 1, 27
Suppose 18*h = 22*h + 4. Let x be -4*(h + -4)/30. Factor x*f**2 + 2/3 + 4/3*f.
2*(f + 1)**2/3
Suppose 13*h - 6 = 10*h. What is j in -8*j**2 + 7*j**2 - 6*j**3 - 2*j**h = 0?
-1/2, 0
Let s(n) = n**3 + 31*n**2 - 269*n - 114. Let u be s(-38). Suppose -5/2*k**4 - 7/2*k**2 - 9/2*k**3 + u - k - 1/2*k**5 = 0. Calculate k.
-2, -1, 0
Let d be (-210)/49*((-360)/(-25))/(-6). Factor d + 2/7*q**2 + 24/7*q.
2*(q + 6)**2/7
Let q(r) be the third derivative of -r**5/150 - r**4/12 + 14*r**3/15 + 21*r**2. Factor q(l).
-2*(l - 2)*(l + 7)/5
Suppose -2*v + 2 = -0. Suppose 5 = 2*z - v. Factor 3 - 3 - 6*h**3 - 3*h**2 + 0*h**2 - z*h**4.
-3*h**2*(h + 1)**2
Let n(b) be the first derivative of 5*b**6/6 - 5*b**5 - 35*b**4/4 + 25*b**3/3 + 15*b**2 - 126. Solve n(u) = 0.
-1, 0, 1, 6
Let y(o) = -2*o**2 - 9*o + 60. Let j be y(-8). Let c = 3/316 + 933/1580. Factor c*s**5 + 6/5*s**2 + 0 + 0*s**3 - 3/5*s - 6/5*s**j.
3*s*(s - 1)**3*(s + 1)/5
Suppose -3*k - 5*z + 935 = 0, 8*k - 11*k + 947 = -z. Let y be -1*18/k*(-6 - 1). Find n, given that y*n**3 - 2/5*n + 6/5*n**2 - 4/5 - 2/5*n**4 = 0.
-1, 1, 2
Let t(c) be the second derivative of 3*c**5/28 + c**4/7 - 5*c**3/14 - 6*c**2/7 + 147*c. Factor t(z).
3*(z - 1)*(z + 1)*(5*z + 4)/7
Factor 24/7 + 2/7*g**2 - 26/7*g.
2*(g - 12)*(g - 1)/7
Let u(y) be the third derivative of y**8/168 + y**7/35 + y**6/30 - y**5/15 - y**4/4 - y**3/3 + 43*y**2. Suppose u(i) = 0. Calculate i.
-1, 1
Let n be 224/392 + (-4)/7. Factor 0 + 16/7*p**2 + 4/7*p**3 + n*p.
4*p**2*(p + 4)/7
Let y = 17976 + -17972. Let 4/3*t + 2/3*t**2 - 2*t**3 + 2/3*t**5 + 0 - 2/3*t**y = 0. What is t?
-1, 0, 1, 2
Let a = 38978 - 350788/9. Find t such that a*t**2 - 4/3 + 38/9*t = 0.
-3, 2/7
Suppose 3*m + 87 = 4*i - 17, m - 19 = -i. Factor -9*s**2 - 9*s - 2 - 9*s**2 + i*s**2.
(s - 2)*(5*s + 1)
Let q(h) = 11*h - 5. Let c be q(-5). Let d be (c/40)/((-42)/8). Determine y, given that 2/7*y**4 - 2/7*y**2 + 2/7*y**3 - d*y + 0 = 0.
-1, 0, 1
Let w be (-5)/(-3)*(-5 + 1080/25). Let v = -63 + w. Factor -v*u**3 - 2/9*u**2 + 0 - 2/3*u**4 + 0*u - 2/9*u**5.
-2*u**2*(u + 1)**3/9
Determine d, given that -16/3 - 2/3*d**2 - 2/3*d**3 + 20/3*d = 0.
-4, 1, 2
Let x(i) = -9*i + 3 + 10 + 138*i**2 - 133*i**2. Let w(v) = 6*v**2 - 8*v + 12. Let j(z) = 3*w(z) - 4*x(z). Factor j(u).
-2*(u - 4)*(u - 2)
Let p(g) be the third derivative of -g**6/540 - 2*g**5/135 + g**4/9 - g**2 - 27. Let p(c) = 0. Calculate c.
-6, 0, 2
Let u(h) = h**2 - 13*h + 24. Let b be u(11). Suppose -5 - c**3 - b + 11 - 3*c**2 = 0. Calculate c.
-2, 1
Let y(f) be the third derivative of -5/504*f**8 + 0*f + 0*f**3 + 0 + 0*f**4 - 8/315*f**7 - 1/180*f**6 + 10*f**2 + 1/45*f**5. Let y(l) = 0. What is l?
-1, 0, 2/5
Let k = -209 - -106. Let m = k + 153. Factor -23*g + 7*g + m + 2*g**2 - 18.
2*(g - 4)**2
Let d be (-38)/(-13) - 80/(-1040). Find a such that 35/4*a**2 - 5/4*a**d + 45/4 - 75/4*a = 0.
1, 3
Let s(d) be the first derivative of 14 + 0*d - 2/15*d**3 + 1/5*d**2. Factor s(q).
-2*q*(q - 1)/5
Let a(p) be the first derivative of -3*p**5/20 - 3*p**4/16 + 5*p**3/2 - 3*p**2 + 226. Find g, given that a(g) = 0.
-4, 0, 1, 2
Solve -90*m**2 + 24/7 + 96/7*m = 0.
-2/15, 2/7
Let f be 6 + (-7 - (-13 + 8)). Let j(c) be the first derivative of 0*c**2 - 5 + 3/4*c**f + 0*c - 3*c**3. Factor j(z).
3*z**2*(z - 3)
Let s be (-2)/5 - (-141)/15. Suppose -o + s = -3*t, -2*o + 12 = -0*t - 4*t. Solve o*z**2 + 14*z**4 + 0*z + 2*z**3 + 49/2*z**5 + 0 = 0 for z.
-2/7, 0
Let o = -9/53 + 257/265. Factor 2/5*u**3 + o - 2/5*u - 4/5*u**2.
2*(u - 2)*(u - 1)*(u + 1)/5
Suppose -7*b = -38 - 18. Suppose -31*o**5 - 2*o**4 + 5*o**3 + 10*o**2 - b*o**4 + 26*o**5 = 0. Calculate o.
-2, -1, 0, 1
Determine z, given that 3/4*z**4 + 1/4*z**5 - 1/2*z + 0 + 1/4*z**3 - 3/4*z**2 = 0.
-2, -1, 0, 1
Let -51/2*w + 0 + 3/4*w**4 + 27/2*w**3 + 45/4*w**2 = 0. What is w?
-17, -2, 0, 1
Let q(t) = 7*t**3 + 18*t**2 - 57*t + 36. Let r(g) = -29*g**3 - 71*g**2 + 229*g - 147. Let f(m) = -9*q(m) - 2*r(m). Find a such that f(a) = 0.
-6, 1
Suppose 7/3*w**3 - 1/6*w**4 - 7/3*w - 8*w**2 + 49/6 = 0. Calculate w.
-1, 1, 7
Let o = -93 - -93. Let n be ((-15)/10)/((-6)/16) + o. Find l, given that 0*l**3 + 3/2*l**2 + 0 - 3/2*l**n + 0*l = 0.
-1, 0, 1
Let l(f) be the first derivative of 3*f**4/20 - 7*f**3/5 + 9*f**2/2 - 27*f/5 - 161. Factor l(x).
3*(x - 3)**2*(x - 1)/5
Let b(n) be the second derivative of 9*n**5/140 + n**4/14 - n**3/2 + 3*n**2/7 - 127*n. Determine w so that b(w) = 0.
-2, 1/3, 1
Let i(q) be the second derivative of 1/6*q**3 + 42*q + 1/36*q**4 + 0 + 1/3*q**2. Factor i(r).
(r + 1)*(r + 2)/3
Factor 1/4*z**2 + 0 - 1/2*z.
z*(z - 2)/4
Let o(k) = -20*k**2 - 15*k + 19. Let r(p) = -3*p**2 - 1. Let j(n) = 3*o(n) - 21*r(n). Determine y so that j(y) = 0.
2, 13
Let r(z) be the third derivative of z**8/2352 - z**7/490 - z**6/140 + z**5/15 - z**4/7 + 2*z**2 - 10*z. Factor r(k).
k*(k - 2)**3*(k + 3)/7
Let n(y) be the first derivative of 10/3*y**3 + 3/2*y**4 - 4*y**2 + 1/3*y**6 - 22 + 0*y - 2*y**5. Determine b, given that n(b) = 0.
-1, 0, 1, 4
Let q(d) be the second derivative of 0 + 8/3*d**3 + 11/10*d**4 + 1/75*d**6 + 1/5*d**5 + 16/5*d**2 + 29*d. What is p in q(p) = 0?
-4, -1
Let g be (301/35 - 4/(-10))*12/96. Let u be (1 - 11/(-8)) + 1. Factor g*a**2 + 1/8*a**3 + u*a + 27/8.
(a + 3)**3/8
Let x(b) be the second derivative of -b**6/540 + b**5/90 - 4*b**3/27 + 9*b**2 + 28*b. Let t(i) be the first derivative of x(i). Let t(j) = 0. Calculate j.
-1, 2
Solve -13*x**2 - 78 + 90