e j.
-1, 5
Let v(u) be the third derivative of 1/180*u**5 - 1/36*u**4 + 0 + 11*u**2 + 0*u + 0*u**3. Determine m so that v(m) = 0.
0, 2
Suppose -8*c = -99 - 45. Let s be (-3)/15*(-30)/c. Solve -s*w**2 + 1/3*w + 2/3 = 0.
-1, 2
Let f(y) be the first derivative of 5*y**3/3 + 60*y**2 + 720*y + 41. Factor f(o).
5*(o + 12)**2
Suppose -3*h = 9*y - 14*y + 25, -20 = 2*h - 4*y. Let b(j) be the second derivative of h + 40*j**2 + 20/3*j**3 - 4*j + 5/12*j**4. Factor b(a).
5*(a + 4)**2
Let m(w) be the first derivative of -w**3/3 - 8*w**2 + 472. Determine r, given that m(r) = 0.
-16, 0
Let m(k) be the third derivative of 1/160*k**6 - 3/8*k**3 + 31*k**2 - 1/16*k**5 + 0*k + 0 + 7/32*k**4. Find s such that m(s) = 0.
1, 3
Suppose -6 = -8*l + 34. Let c(w) be the third derivative of 0 + 0*w - 1/9*w**3 + w**2 + 1/180*w**l + 1/72*w**4. What is j in c(j) = 0?
-2, 1
Let h = 278137/15171 + -2/15171. Factor -h*a + 5/3*a**2 + 50/3.
5*(a - 10)*(a - 1)/3
Let z(c) be the second derivative of -c**7/84 + c**6/60 + c**5/40 - c**4/24 + c - 31. Factor z(j).
-j**2*(j - 1)**2*(j + 1)/2
Let q(h) = h**2 + 4*h - 2. Let v be -3 + 2 + -1 - 3. Let p be q(v). Find k such that 5/3*k**5 + 50/3*k**4 + 0 + 45*k + 60*k**p + 90*k**2 = 0.
-3, -1, 0
Let s(y) be the third derivative of -y**6/480 + y**5/40 - 11*y**4/96 + y**3/4 - 178*y**2. Factor s(i).
-(i - 3)*(i - 2)*(i - 1)/4
Let w be -127*(-2 + 1) + (-21)/(-7). Let u = -908/7 + w. Factor 2/7 - u*n**4 + 4/7*n - 4/7*n**3 + 0*n**2.
-2*(n - 1)*(n + 1)**3/7
Let -86*t**4 - 17*t**2 - 3172*t**5 + 3190*t**5 - 23*t**2 + 124*t**3 - 16*t = 0. Calculate t.
-2/9, 0, 1, 2
Let w(b) be the third derivative of -5/336*b**8 + 12*b**2 + 1/6*b**5 + 0 + 0*b**6 + 5/24*b**4 - 1/21*b**7 + 0*b**3 + 0*b. Suppose w(m) = 0. Calculate m.
-1, 0, 1
Let v(b) be the third derivative of 0 + 1/3*b**6 + 0*b + 35*b**2 + 10*b**3 + 55/6*b**4 + 35/12*b**5. Factor v(a).
5*(a + 2)**2*(8*a + 3)
Let -6*s**3 - 20*s**4 - 2*s - 72*s**2 + 6*s**5 - 25*s**3 + 13*s**3 + 12 - 66*s**3 = 0. What is s?
-1, 1/3, 6
Suppose 5*k + 3*k + 4*k = 0. Let d(o) be the second derivative of 0*o**5 + 0 - o + k*o**2 + 0*o**3 - 1/60*o**4 + 1/150*o**6. Let d(f) = 0. What is f?
-1, 0, 1
Let q(a) be the third derivative of -1/12*a**4 + 0*a**3 - 16*a**2 + 0 - 1/60*a**5 + 0*a. Factor q(v).
-v*(v + 2)
Suppose 15 - 6 = 3*l. Let y be (-30)/12 + l + (-3)/(-2). Factor 2/3 + 2*p**y - 2*p - 2/3*p**3.
-2*(p - 1)**3/3
Suppose 5 - 14 = r. Let i(h) = h**3 + 8*h**2 - 7*h + 18. Let g be i(r). Factor -6/5*k**4 + 4/5*k**2 + g + 2/5*k**3 + 0*k.
-2*k**2*(k - 1)*(3*k + 2)/5
Let w(t) be the second derivative of t**5/120 - t**4/24 + t**3/12 - 19*t**2/2 + 21*t. Let b(k) be the first derivative of w(k). Suppose b(o) = 0. What is o?
1
Let s(d) be the first derivative of -2*d**3/15 - 6*d**2/5 - 16*d/5 - 62. Suppose s(k) = 0. What is k?
-4, -2
Let i = 1/5408 - -10807/48672. Let u = 86 - 772/9. Determine t, given that 4/9*t - i - u*t**2 = 0.
1
Let k(r) be the first derivative of 4/5*r**5 + 4*r - 2/3*r**6 + 7 - 2*r**2 - 8/3*r**3 + 2*r**4. Factor k(x).
-4*(x - 1)**3*(x + 1)**2
Let x(y) = 2*y**2 + 5*y + 6. Let h be x(-4). Let a be (4/(-7))/(h/(-63)). Factor 12*n**a + 6 - 6*n**4 + 5*n**4 + 16*n - n**4.
-2*(n - 3)*(n + 1)**3
Let r(h) = -84*h**2 + 144*h + 40. Let l(m) = -56*m**2 + 96*m + 27. Suppose -w - 3*i = -4*i + 10, 4*w + 5*i - 5 = 0. Let k(p) = w*r(p) + 8*l(p). Factor k(s).
-4*(s - 2)*(7*s + 2)
Let b(t) be the second derivative of t**4/24 + 35*t**3/6 + 1225*t**2/4 - 2*t + 34. What is c in b(c) = 0?
-35
Suppose 6 + 5 + 19*u - 8*u**2 - 2*u**3 - 15*u - 3 - 2*u**3 = 0. Calculate u.
-2, -1, 1
Factor l**2 + 3844 - 44*l - 58*l - 22*l.
(l - 62)**2
Let i(p) be the third derivative of -p**7/1890 - 17*p**6/2160 - p**5/90 + 11*p**4/8 + 24*p**2. Let c(q) be the second derivative of i(q). Solve c(m) = 0.
-4, -1/4
Let u be (-5 - -1)/((-2)/46). Factor 6*d**4 + 92*d + 9*d**5 - u*d.
3*d**4*(3*d + 2)
Suppose 27*u - 164 = -55*u. Solve 2/5*m**5 + 6/5*m**3 + 2/5*m**u + 0*m + 0 + 6/5*m**4 = 0.
-1, 0
Factor 32/7*z**2 + 0 + 2*z + 22/7*z**3 + 4/7*z**4.
2*z*(z + 1)**2*(2*z + 7)/7
Let j(y) = -5*y - 6. Suppose 4*h - 26 = -46. Let l be j(h). Determine g so that -32*g - 4 + l*g**2 - 2 + 22 - 4*g**3 + g**2 = 0.
1, 2
Suppose -5 - 20 = 5*k. Let w(r) = -3 + 5*r + 0 + 7*r + 3*r**2. Let o(l) = 2*l**2 + 11*l - 3. Let y(c) = k*w(c) + 6*o(c). Determine x, given that y(x) = 0.
1
Let o(y) be the second derivative of y**5/20 - y**4/12 + y**3/6 + 3*y**2/2 + y. Let r be o(0). What is w in 3*w - 2*w**2 + 2 + 2*w**3 - 2*w - r*w = 0?
-1, 1
Let b be 1 - (6/(-9))/((-18)/27). Factor 0*m + b + 4/3*m**3 + 4/3*m**4 + 0*m**2.
4*m**3*(m + 1)/3
Let r(w) be the third derivative of -7*w**2 - 1/24*w**6 - 1/12*w**4 + 0*w + 0 + 7/60*w**5 + 0*w**3. Factor r(v).
-v*(v - 1)*(5*v - 2)
Let g(u) = -120*u**3 - 55*u**2 + 45*u + 65. Let o(a) = 11*a**3 + 5*a**2 - 4*a - 6. Let d(y) = -6*g(y) - 65*o(y). Solve d(q) = 0 for q.
-2, 0, 1
Let i(x) be the second derivative of x**8/840 + x**7/420 - x**6/180 - x**5/60 + x**3/3 - 15*x. Let d(b) be the second derivative of i(b). Factor d(g).
2*g*(g - 1)*(g + 1)**2
Let f be -2*(-9 - (-71)/8). Let b(d) be the third derivative of 0 - 7*d**2 + 0*d**3 + f*d**4 + 0*d + 1/20*d**5. Factor b(k).
3*k*(k + 2)
Find v such that 0 + 0*v + 23/2*v**3 - 12*v**2 + 1/2*v**4 = 0.
-24, 0, 1
Let r(i) be the third derivative of -i**6/1620 + i**5/540 - 5*i**3/3 + 10*i**2. Let w(j) be the first derivative of r(j). Suppose w(v) = 0. What is v?
0, 1
Factor -87*k**2 + 30*k**3 + 19*k**2 - 2326 + 2*k**4 + 2326.
2*k**2*(k - 2)*(k + 17)
Factor -328 + 2*v**2 + 19*v**2 + 454 - 447*v.
3*(v - 21)*(7*v - 2)
Let z be 6/(-8)*(-16)/(-32)*16/(-3). Factor 5/6*b + 5/6 - 5/3*b**z.
-5*(b - 1)*(2*b + 1)/6
Let i(s) be the third derivative of 0 + 1/20*s**4 + 1/200*s**6 + 0*s + 27*s**2 + 3/100*s**5 + 0*s**3. Factor i(a).
3*a*(a + 1)*(a + 2)/5
Let k = 553 - 551. Let r(h) be the first derivative of 1/2*h**4 + 0*h**2 + 4/3*h**3 - 24/5*h**5 + k + 0*h + 3*h**6. Solve r(c) = 0 for c.
-1/3, 0, 2/3, 1
Let f = 19070 + -19070. Factor 0 + 9/4*s**2 + 3/2*s + f*s**3 - 3/4*s**4.
-3*s*(s - 2)*(s + 1)**2/4
Suppose -5*f = -u - 15, 3*u - 4 + 13 = 3*f. Let 5/4*l**2 + 3/4*l - 3/4*l**f - l**4 - 1/4 = 0. What is l?
-1, 1/4, 1
Suppose -71*g = -113*g. Let -2/7*s**2 + 0*s - 2/7*s**3 + g = 0. What is s?
-1, 0
Let z(u) be the first derivative of -u**3/3 - u**2/2 + 2*u + 112. Factor z(a).
-(a - 1)*(a + 2)
Let q(d) be the second derivative of 8*d + 0 + 8/3*d**3 + 1/6*d**4 + 16*d**2. Solve q(m) = 0.
-4
Let v(y) = -y**3 - 65*y**2 + 201*y - 201. Let j be v(-68). Factor 4/3*q**j - 4/3 - 4/3*q + q**2 + 1/3*q**4.
(q - 1)*(q + 1)*(q + 2)**2/3
Suppose 0 = -3*u + 5*h - 4, -19 + 21 = 2*u - h. Factor -4 - 29/2*x**3 + 9/2*x**4 + 3*x**u + 18*x.
(x - 2)**2*(x + 1)*(9*x - 2)/2
Find w, given that -440*w**4 - 642*w**5 - 2234*w**3 - 221*w**2 - 3072*w - 512 - 3651*w**2 + 266*w**3 + 606*w**5 = 0.
-4, -2, -2/9
Let t(h) be the first derivative of 1/9*h**5 - 7 - 5/18*h**2 - 1/54*h**6 + 1/9*h + 10/27*h**3 - 5/18*h**4. Factor t(v).
-(v - 1)**5/9
Let z = -5 - 29. Let n = -32 - z. Find m such that -32 + 2*m**2 + m**2 + 44 - 17*m + n*m = 0.
1, 4
Let w(v) be the first derivative of 10/3*v**2 + 25/6*v**3 + 22 - 5/2*v + 5/6*v**4. Factor w(p).
5*(p + 1)*(p + 3)*(4*p - 1)/6
Let q(b) be the first derivative of -3/16*b**4 + 0*b**2 + 15 + 0*b - 1/2*b**3. Factor q(l).
-3*l**2*(l + 2)/4
Suppose 4 = 3*l + 28. Let q be (92/(-33))/(l/12) - 4. Solve -q + 2/11*b**2 + 0*b = 0.
-1, 1
Let u(g) be the first derivative of 0*g + 1/2*g**3 - 3/16*g**4 + 1 + 0*g**2. Factor u(s).
-3*s**2*(s - 2)/4
Factor -1/5*c**2 - 2304/5 - 96/5*c.
-(c + 48)**2/5
Let y = 18 + -18. Let r(l) be the third derivative of 0*l + 2*l**2 + 0 - 1/6*l**4 - 3/10*l**5 - 7/60*l**6 + y*l**3. Solve r(q) = 0 for q.
-1, -2/7, 0
Let c(x) be the third derivative of x**7/105 + 2*x**6/15 - 43*x**5/30 + 29*x**4/6 - 8*x**3 - 165*x**2. Factor c(d).
2*(d - 2)*(d - 1)**2*(d + 12)
Let b(q) be the third derivative of -q**7/735 - q**6/140 + q**5/21 + 168*q**2. Determine x so that b(x) = 0.
-5, 0, 2
Let p = -1264 - -1266. Factor 4 + 26/3*o + 10/3*o**p.
2*(o + 2)*(5*o + 3)/3
Determine q so that -180*q + 112*q**2 + 110 + 9*q - 50*q - q**3 = 0.
1, 110
Let v(q) be the second derivative of -q**4/72 + 29*q**3/9 - 115*q**2/12 + 92*q - 1. Factor v(g).
-(g 