r). Factor v(j).
-3*(j - 3)*(j + 1)**2/7
Let q be -8*(-41)/(4059/36). Factor 0 + q*t + 2/11*t**3 + 16/11*t**2.
2*t*(t + 4)**2/11
Let w(v) be the first derivative of -v**5/20 - 2*v**4 - 37*v**3/2 - 40*v**2 + 575*v/4 - 1084. Factor w(q).
-(q - 1)*(q + 5)**2*(q + 23)/4
Let s(d) = -d**3 + 6*d**2 + 4. Suppose 5*n + 7 - 32 = 0. Let a be s(n). Find f, given that -15*f**3 - 9*f**3 + a*f**3 = 0.
0
Let f(x) be the third derivative of -x**8/336 - 4*x**7/35 + x**6/2 + 556*x**5/15 - 552*x**4 + 3456*x**3 + 118*x**2. Factor f(q).
-(q - 4)**3*(q + 18)**2
Let u = 87681/2 + -44881. Let x = u + 1041. Factor -4 + 9/2*c - x*c**2.
-(c - 8)*(c - 1)/2
Solve -8*y - 1/4*y**3 + 15/4*y**2 - 12 = 0.
-1, 4, 12
Let w(o) be the second derivative of 2*o**6/15 + 77*o**5/5 + 554*o**4 + 4608*o**3 + 15552*o**2 + 86*o - 4. Find v such that w(v) = 0.
-36, -3, -2
Suppose 2*s + 0 = 5*b - 6, -s = 2*b - 6. Let u be ((-130)/(-78))/((24/27)/b). Factor -u - 5/4*i**2 + 5*i.
-5*(i - 3)*(i - 1)/4
Let k be -1 - (-7*3 - 0). Let h = 109443 - 218881/2. Factor -40*i**2 + k*i - h.
-5*(4*i - 1)**2/2
Let s(n) be the first derivative of n**3/15 + 17*n**2/5 - 611*n/5 - 1945. Find k such that s(k) = 0.
-47, 13
Let c = -4529/2 - -2269. Let i(p) be the first derivative of 4*p**3 - c*p**2 + 0*p - 6 - 3/4*p**4. Factor i(d).
-3*d*(d - 3)*(d - 1)
Let t(v) = -270*v**2 + 280*v + 2. Let o(a) = -810*a**2 + 842*a + 8. Let n(s) = 3*o(s) - 10*t(s). Solve n(z) = 0.
2/135, 1
Let p(o) = 98*o + 1783. Let m be p(-18). Factor 1/2*a**2 + m*a + 0.
a*(a + 38)/2
Suppose 2*s - s = q, -q + 5*s = 16. Find y, given that 23*y**2 - 3*y**3 - 21*y**5 - 24*y - 32*y**2 + 24*y + 33*y**q = 0.
-3/7, 0, 1
Let t(m) = 227*m**2 - 144178*m + 25977650. Let u(r) = 112*r**2 - 72088*r + 12988824. Let s(k) = -4*t(k) + 9*u(k). Factor s(n).
4*(5*n - 1802)**2
Let r(i) be the first derivative of -16 - 1/3*i**6 - 4/3*i**3 + 2*i**4 - 3*i - 3/10*i**5 + 0*i**2. Let m(y) be the first derivative of r(y). Factor m(w).
-2*w*(w - 1)*(w + 2)*(5*w - 2)
Let p = -30 + 34. Find m such that 173*m**4 - 183*m**p - 6*m**2 + 35*m - 35*m**3 + m**2 + 15 = 0.
-3, -1, -1/2, 1
Let i(c) be the second derivative of -3*c**5/80 + 127*c**4/3 - 114469*c**3/8 - 114921*c**2/4 + 11542*c. Find m such that i(m) = 0.
-2/3, 339
Let o(h) be the first derivative of -h**3/3 - 5*h**2 + 15*h + 12. Let s be o(-11). Let -15*f**2 - 6*f - 4*f**2 - s*f + 4*f**2 = 0. Calculate f.
-2/3, 0
Let k(y) be the second derivative of 27*y**5/20 + 127*y**4/2 + 910*y**3 + 588*y**2 - 10688*y. Suppose k(i) = 0. Calculate i.
-14, -2/9
Let z = 5498/12155 + -98/1105. What is j in 0 + 4/11*j**2 + 1/11*j + z*j**3 = 0?
-1/2, 0
Let g(u) be the third derivative of u**6/480 + u**5/8 + 23*u**4/24 - 13*u**3 - 12*u**2 - 3*u - 22. Factor g(i).
(i - 2)*(i + 6)*(i + 26)/4
Let c(n) be the first derivative of 1/2*n**2 + 0*n - 26 + 13/6*n**3. Factor c(p).
p*(13*p + 2)/2
Let k = -1285473 + 1285477. Factor 9/2*j**2 - 1/2 - 1/2*j + 2*j**k - 11/2*j**3.
(j - 1)**3*(4*j + 1)/2
Let l(w) be the first derivative of -3*w**5/10 - 271*w**4/8 + 229*w**3/3 - 46*w**2 - 1758. Let l(n) = 0. What is n?
-92, 0, 2/3, 1
Let g = 619103 + -619101. Suppose 1023/2*m + 1/2*m**3 - 1089/2 + 65/2*m**g = 0. Calculate m.
-33, 1
Let r(h) be the first derivative of 5*h**6/6 + 6*h**5 - 125*h**4/4 + 30*h**3 + 894. Factor r(y).
5*y**2*(y - 2)*(y - 1)*(y + 9)
Suppose -3*p - 3*b + 25 - 28 = 0, 4*b + 1 = -p. Let t be (-36)/(-108)*(p + 1). Find u such that 3/4*u - u**3 + t + 11/4*u**2 = 0.
-1/4, 0, 3
Factor 366 - 120*c - 2/3*c**2.
-2*(c - 3)*(c + 183)/3
Let i(h) = h**3 - h**2 - 2*h + 10. Let g be i(4). Factor -16*k + 77*k**2 + g*k**4 + 6*k**2 - 25*k**2 - 140*k**3 + 30*k**2.
2*k*(k - 2)*(5*k - 2)**2
Let l(r) = -917*r**3 + 3*r**2 - 15*r - 16. Let f be l(-1). Suppose t - f = -917. Factor 0 + 2/9*x**t - 2/9*x**3 + 4/9*x.
-2*x*(x - 2)*(x + 1)/9
Let k(u) be the third derivative of u**7/315 + 19*u**6/120 + 9*u**5/20 - u**4/72 - 3*u**3/2 + 1462*u**2. Determine b, given that k(b) = 0.
-27, -1, 1/2
Let s = 553/19 + -11003/380. Let q(c) be the second derivative of 0 - s*c**5 - 1/2*c**4 + 0*c**2 + 24*c + 0*c**3. Solve q(n) = 0 for n.
-2, 0
Let a(i) be the third derivative of -i**8/168 - i**7/5 + 47*i**6/60 + 7*i**5/10 - 23*i**4/6 - 2734*i**2. Determine v, given that a(v) = 0.
-23, -1, 0, 1, 2
Let c(f) be the third derivative of 5*f**8/224 + 771*f**7/140 + 909*f**6/80 - 1379*f**5/40 - 153*f**4/8 - 6385*f**2 + 2*f. What is x in c(x) = 0?
-153, -2, -1/5, 0, 1
Let x be 4445/(-2540)*((-78)/21 - -2). Let o(n) be the first derivative of -49*n + 11 - 7*n**2 - 1/3*n**x. Solve o(r) = 0 for r.
-7
Suppose 46*m + 105*m = 26*m + 250. Factor -c + 0 + 1/4*c**m.
c*(c - 4)/4
Suppose -3*c = -g - 19, -g = -2*c + 8 + 3. Factor 44*h**3 - 3 - 4*h**4 + 3 - 16*h**4 - c*h**2.
-4*h**2*(h - 2)*(5*h - 1)
Let r = -18 + 45. Let n be r/36 - (-1 + (-5)/4). Determine a so that -21*a - 10*a**2 - 117 - 45*a**5 + 70*a**n + 112 - 4*a + 15*a**4 = 0.
-1, -1/3, 1
Suppose x = 3*l - 1073, 2*l = 6*x - 3*x + 713. Suppose 0 = 2*s - l + 52. Factor -6*h**3 - 141*h + 0*h**4 + 12 + s*h - 9*h**2 - h**4 + 4*h**4.
3*(h - 2)**2*(h + 1)**2
Factor -8*h**3 - 3*h - 32 + 288*h**2 + h - 8*h + 44*h**3 + 6*h.
4*(h + 8)*(3*h - 1)*(3*h + 1)
Let q(w) be the first derivative of 105 - 51/2*w**2 - w**3 + 0*w. Factor q(u).
-3*u*(u + 17)
Let c(w) be the second derivative of w**6/2340 - w**5/130 + 14*w**3 - 34*w. Let d(b) be the second derivative of c(b). Solve d(j) = 0.
0, 6
Let y(t) be the second derivative of 3*t**5/40 + 18*t**4 - t**3/4 - 108*t**2 + 5*t + 107. Determine l, given that y(l) = 0.
-144, -1, 1
Let q(j) be the first derivative of -9*j + 44/3*j**3 + 3/4*j**2 + 39 - 10*j**4. Factor q(v).
-(4*v - 3)**2*(5*v + 2)/2
Let c = 3789 + -45467/12. Let o(x) be the second derivative of 0*x**3 + 0 - c*x**4 + 0*x**2 + 1/168*x**7 + 13*x + 9/80*x**5 - 1/20*x**6. Factor o(s).
s**2*(s - 4)*(s - 1)**2/4
Let d be 3/((-12)/4 - (-36)/8). Factor -69*z + 273*z - 13*z**2 - 360 - 28*z**3 + 24*z**3 - 3*z**d.
-4*(z - 3)**2*(z + 10)
Let r be (-8)/(-5) + 0/(-2). Let h be (-825786)/(-35290) - (-1)/(-1)*23. Factor h*i**2 + r - 8/5*i.
2*(i - 2)**2/5
Find x, given that -8*x**3 - 105 - 73 - 22 - 14*x**2 + 590*x - 221*x**2 + 33*x**3 = 0.
2/5, 4, 5
Let h(a) = -105*a**3 + 95*a**2 + 3425*a + 19500. Let j(d) = 4*d**3 - d. Let s(g) = h(g) + 25*j(g). Factor s(p).
-5*(p - 39)*(p + 10)**2
Let b(r) be the second derivative of -5*r**7/84 - 2*r**6/3 + 5*r**5/4 + 205*r**4/6 + 25*r**3/4 - 1125*r**2 - 1049*r. What is p in b(p) = 0?
-5, -4, 3
Let y(b) be the first derivative of 3/8*b**4 + 0*b - 66 + 1/12*b**6 + 3/10*b**5 + 1/6*b**3 + 0*b**2. Factor y(u).
u**2*(u + 1)**3/2
Let y(m) = 26*m + 630. Let a be y(-24). Let j be ((-10)/a)/(-1) - (-996)/180. Factor j*p**2 + 64/5 + 4/5*p**3 + 96/5*p.
4*(p + 1)*(p + 4)**2/5
Suppose -c - 13*u + 12*u = -10, u = c. Suppose 5*y + 14 - 34 = 5*a, 5*a + c = 0. Solve 0 + 2/13*i**y - 2/13*i**2 - 12/13*i = 0 for i.
-2, 0, 3
Suppose -4*o + 74 = -j, -o - 70 = -5*o + 3*j. Suppose -2 = -o*d + 18*d. Suppose g**d + g + 0*g + 0*g = 0. What is g?
-1, 0
Let k(d) be the first derivative of -d**6/1080 - d**5/120 - d**3 + 12*d - 70. Let r(c) be the third derivative of k(c). Suppose r(o) = 0. Calculate o.
-3, 0
Let q = -259718 + 259723. Determine d, given that -3/2*d**4 + 3/4*d**q - 228*d + 168*d**2 - 141/4*d**3 + 96 = 0.
-8, 1, 4
Let k(h) be the first derivative of 4/27*h**3 - 101 - 2/9*h**2 + 0*h. Factor k(w).
4*w*(w - 1)/9
Factor -20/11*s**2 + 138/11*s - 2/11*s**3 - 180/11.
-2*(s - 3)*(s - 2)*(s + 15)/11
Let x(u) be the third derivative of -u**8/6048 - 37*u**7/7560 - 7*u**6/540 - 7*u**5/12 - 12*u**2. Let s(l) be the third derivative of x(l). Factor s(k).
-2*(k + 7)*(5*k + 2)/3
Suppose 97 + 50 = 21*k. Let g be (51/(-12) - -3)*-4. Determine h, given that -k - 3*h**2 - 8 - 13*h - g*h = 0.
-5, -1
Let b(g) = g**3 - 20*g**2 - 22*g + 26. Suppose d + 7*d - 168 = 0. Let w be b(d). Factor 75*y**3 + 45*y**4 - 215*y**2 + 103*y**2 + w*y + 147*y**2.
5*y*(y + 1)*(3*y + 1)**2
Let b(w) be the first derivative of 3*w**4 - 3/5*w**5 - 80 - 6*w**2 + 9*w - 2*w**3. Suppose b(z) = 0. What is z?
-1, 1, 3
Let u be ((-36)/20)/(13/(-260)). Let c be (54/u)/(66/16). Factor 0 - 2/11*g**3 - 2/11*g - c*g**2.
-2*g*(g + 1)**2/11
Let d(c) = 9*c**2 - 51*c - 15. Let p be d(6). Let z(t) be the first d