)). Let w(r) be the second derivative of -7/12*r**4 + 0 + 1/3*r**d - 1/5*r**5 + 0*r**2 - 10*r. Factor w(k).
-k*(k + 2)*(4*k - 1)
Determine s, given that -466/9*s - 2/9*s**2 - 464/9 = 0.
-232, -1
Let o be (-2*5)/2 - (-11431)/1988. Determine q, given that o*q**2 - 1/4*q**4 - 1/4*q**3 + 5/4*q + 1/2 = 0.
-1, 2
Let p(n) be the first derivative of 2*n**3/33 - 3486*n**2/11 + 6076098*n/11 - 6426. Factor p(x).
2*(x - 1743)**2/11
Suppose -66*i - 976 + 1636 = 0. Factor -i + 6*a - 1/2*a**2.
-(a - 10)*(a - 2)/2
Let h be (-542)/(-2710)*(1 + -1). Factor 4/7*o**3 + 0*o + h - 16/7*o**2.
4*o**2*(o - 4)/7
Let 0 + 12/5*n + 19683/5*n**3 - 972/5*n**2 = 0. Calculate n.
0, 2/81
Let b = 71142 - 284565/4. Let b*i**2 - 1/4 + 1/4*i - 1/2*i**4 - 1/4*i**3 = 0. What is i?
-1, 1/2, 1
Let k(l) = -l**2 + 2. Let j(t) = -t**3 + 9*t**2 - 17*t + 10. Suppose 5*u - 2*c + 3*c = 19, 5*c = 4*u + 8. Let v(a) = u*k(a) - 3*j(a). Factor v(d).
3*(d - 8)*(d - 1)**2
Let j(m) be the third derivative of -m**6/540 - 263*m**5/270 + 133*m**4/18 - 464*m**2. Factor j(s).
-2*s*(s - 3)*(s + 266)/9
Let y(r) be the first derivative of -16/15*r**5 - 8/3*r**2 - 260 + 2/9*r**6 - 32/3*r + 1/3*r**4 + 40/9*r**3. Factor y(p).
4*(p - 2)**3*(p + 1)**2/3
Let i(l) = 4*l**3 - 2013*l**2 - 7450*l - 7456. Let y(m) = -2*m**3 + 1023*m**2 + 3726*m + 3728. Let d(q) = 3*i(q) + 5*y(q). Factor d(k).
2*(k - 466)*(k + 2)**2
Let p(y) = -4 + 405*y - 12 - 345*y + 13*y**3 - 62*y**2 + 0*y**3. Let x(w) = -14*w**3 + 62*w**2 - 60*w + 16. Let a(v) = 4*p(v) + 5*x(v). Factor a(j).
-2*(j - 2)*(j - 1)*(9*j - 4)
Solve 484*s**2 - 53*s**4 + 412*s + 338*s**2 - 83*s**4 + 408*s**3 + 134*s**4 = 0 for s.
-1, 0, 206
Suppose 2*k - 17*x + 12 = -21*x, -9 = -5*k + 3*x. Let h(l) be the first derivative of k*l + 19 + 0*l**2 + 1/30*l**4 + 2/45*l**3. Solve h(b) = 0.
-1, 0
Let h(d) be the second derivative of d**5/20 - 20*d**4/3 - 83*d**3/2 - 1467*d. Let h(w) = 0. What is w?
-3, 0, 83
Suppose -3*m = 4*o - 2, 5*m = -165*o + 168*o + 13. Let b(z) be the first derivative of 2/27*z**3 + 0*z**m - 12 + 0*z. Factor b(c).
2*c**2/9
Let a(m) be the third derivative of -m**7/420 + 141*m**6/80 + 283*m**5/40 + 425*m**4/48 - m**2 - 20*m + 54. Factor a(w).
-w*(w - 425)*(w + 1)**2/2
Let z(c) be the second derivative of -3 + 3*c + 13/60*c**4 - 2/5*c**3 + 2/5*c**2 + 1/150*c**6 - 3/50*c**5. Suppose z(q) = 0. Calculate q.
1, 2
Let v(j) be the second derivative of j**4/54 - 5*j**3/27 + 275*j. What is d in v(d) = 0?
0, 5
Let o(p) be the second derivative of 0 + 565/3*p**3 - 88*p - 160*p**2 - 35/12*p**4. Find d, given that o(d) = 0.
2/7, 32
Let p(d) be the third derivative of -d**6/1440 - 19*d**5/240 - 361*d**4/96 - 2*d**3 - 24*d**2 + 2. Let k(r) be the first derivative of p(r). Factor k(h).
-(h + 19)**2/4
Suppose 4 - 820/9*k**2 + 34/3*k**3 - 886/9*k = 0. Calculate k.
-1, 2/51, 9
Factor 26/3 + 2/3*v**2 + 28/3*v.
2*(v + 1)*(v + 13)/3
Let i be (-36)/78 - 14/((-20384)/9772). Find n, given that 6*n + i*n**2 - 1/4 = 0.
-1, 1/25
Let r(w) be the first derivative of 2/3*w**3 - 1/14*w**4 - 42 - 15/7*w**2 + 18/7*w. Let r(f) = 0. Calculate f.
1, 3
Let u(y) be the first derivative of -50*y - 5/3*y**3 + 55/2*y**2 - 103. Factor u(i).
-5*(i - 10)*(i - 1)
Let m(v) = -5*v**3 - 30*v**2 + 18*v - 7. Let q(g) = 2*g**3 + 10*g**2 - 6*g + 2. Let r = 1 - -6. Suppose -10 = 2*f - 14. Let d(z) = f*m(z) + r*q(z). Factor d(o).
2*o*(o + 3)*(2*o - 1)
Let x(b) be the third derivative of -56/5*b**5 + 27*b**2 + 31/8*b**4 - 32/5*b**6 - 1/2*b**3 + 0 + 0*b. Let x(w) = 0. Calculate w.
-1, 1/16
Factor 489542 + 10696*u + 486725 - 980547 + 10*u**2.
2*(u + 1070)*(5*u - 2)
Let i = -929 - -931. Let x(w) = -23*w - 18*w**2 - 7*w**3 - 6 + w**3 + w**3. Let q(o) = -6*o**3 - 19*o**2 - 23*o - 6. Let g(d) = i*q(d) - 3*x(d). Factor g(k).
(k + 2)*(k + 3)*(3*k + 1)
Let h(d) be the first derivative of -d**3/24 + 347*d**2/8 - 120409*d/8 + 646. Factor h(q).
-(q - 347)**2/8
Let a be 3 - (-42)/(-15) - 130/900. Let v(g) be the second derivative of 0 - 1/36*g**4 + 0*g**2 + 13*g - a*g**3. What is i in v(i) = 0?
-1, 0
Suppose 48*z**4 + 9*z**3 - 48*z**2 + z**5 - 51*z - 5*z**5 + 28*z**3 + 17*z**3 + z**5 = 0. Calculate z.
-1, 0, 1, 17
Factor -1/4*o**2 + 365/4*o + 0.
-o*(o - 365)/4
Suppose 5*y + 854 + 21 = 5*c, 25 = 5*c. Let j be y/(-425) + -8*(-2)/(-90). Suppose j*z**3 - 4/9 - 2/3*z + 0*z**2 = 0. What is z?
-1, 2
Let b be (8/24)/(8/(-48)). Let i be (-2)/((-12)/39) + (-7 - b). Factor -27/2*u**5 + 0*u + 0 + 0*u**2 - i*u**3 + 9*u**4.
-3*u**3*(3*u - 1)**2/2
Suppose 0 - 32 = -4*k. Let d = k - 5. Factor -3*j**4 - j**2 - 11*j**d + 5*j**2 + 11*j**4 - 2*j**5 + j**3.
-2*j**2*(j - 2)*(j - 1)**2
Let r(y) be the third derivative of -y**6/40 - 719*y**5/20 - 1435*y**4/8 - 717*y**3/2 + 3347*y**2. Solve r(j) = 0 for j.
-717, -1
Let y(x) be the second derivative of -2*x**6/15 - 4*x**5/5 + 30*x**4 - 216*x**3 + 702*x**2 - 754*x + 1. Factor y(i).
-4*(i - 3)**3*(i + 13)
Let f be (-15)/(-6)*(172 + -174) + (-148)/(-8). Find t, given that -33/2*t - 3/2*t**4 + 15 + 33/2*t**3 - f*t**2 = 0.
-1, 1, 10
Let z = 59 + -53. Suppose z*h = 11*h - 10. Factor -7*s - 15*s**h - 6*s + 12*s**2 + s.
-3*s*(s + 4)
Let f be 5472/30*(-60)/8. Let b = f - -9602/7. Find o such that -40/7*o + 22/7*o**3 + b*o**2 - 8/7 = 0.
-2, -2/11, 1
Let s be ((-63)/126 + 2/(-4))*0. Let l be s - (-564)/(-84) - -7. Factor 2/7*y**3 - l*y + 10/7*y**2 - 10/7.
2*(y - 1)*(y + 1)*(y + 5)/7
Let g = 370 - 386. Let a be g + 18 - (-68)/(-126)*3. Factor -8/21*z**2 - a*z - 2/21*z**5 + 2/7*z**3 + 4/21*z**4 + 0.
-2*z*(z - 2)**2*(z + 1)**2/21
Suppose 6 = y + 2*y. Suppose 0 = -y*x + 6 + 24. Find w, given that 8*w**2 + x*w - 11*w**2 + w - w**2 - 12 = 0.
1, 3
What is p in 22/3*p**4 - 16/3*p + 24*p**2 + 28*p**3 + 0 = 0?
-2, 0, 2/11
Let l(c) be the second derivative of c**4/6 + 620*c**3/3 - 621*c**2 - 2303*c. Suppose l(j) = 0. Calculate j.
-621, 1
Factor -11/5*h**2 + 0 + 3/5*h**4 + 1/5*h**5 - 6/5*h - 3/5*h**3.
h*(h - 2)*(h + 1)**2*(h + 3)/5
Suppose 0 = q - 79 + 76. Find h, given that -1096 + q*h**2 + 24*h + 1096 = 0.
-8, 0
Solve 152/13 + 232/13*d + 82/13*d**2 + 2/13*d**3 = 0 for d.
-38, -2, -1
Solve -10*v**4 - 19*v - 2*v**5 - 4*v**4 - 63*v - 2*v**2 + 16 + 110*v - 26*v**3 = 0.
-4, -2, -1, 1
Let t(l) be the third derivative of l**6/720 + 95*l**5/72 + 7021*l**4/18 - 14161*l**3/9 - 39*l**2 - 3. Determine r, given that t(r) = 0.
-238, 1
Let x(o) be the third derivative of o**6/300 + 79*o**5/30 + 3234*o**4/5 - 13068*o**3/5 + 5*o**2 - 237*o. Factor x(h).
2*(h - 1)*(h + 198)**2/5
Suppose 5*x + 55 = t, 0*x - 4*x = -t + 60. Let p be t/(10 + -2) - 5. Determine f, given that 0 + 3/2*f**3 + 9/4*f**4 + 0*f + 1/4*f**2 + f**p = 0.
-1, -1/4, 0
Let o(f) be the second derivative of f**4/12 + 167*f**3/24 - 21*f**2/4 - 2336*f. Factor o(b).
(b + 42)*(4*b - 1)/4
Let k(m) be the second derivative of 0 + 0*m**2 + 34/3*m**4 - m - 1/5*m**5 - 578/3*m**3. Solve k(y) = 0.
0, 17
Let x(t) = -12*t + 29. Let n be x(2). Determine b so that -95*b + 5*b**5 - 144*b**3 + 24*b**n - 13*b - 33*b**5 + 216*b**2 + 40*b**4 = 0.
0, 1, 3
Suppose -9*f + 5*k - 53 = -11*f, k = f + 5. Solve -6/11*l**f + 2/11*l**3 - 8/11*l + 24/11*l**2 + 0 = 0.
-2, 0, 1/3, 2
Let z(j) be the second derivative of j**7/147 - j**6/15 + j**5/35 + 2*j**4/3 - 8*j**3/7 + 7*j + 16. Let z(r) = 0. Calculate r.
-2, 0, 1, 2, 6
Determine o, given that 3*o**3 + 4*o**2 - 2*o**3 + 54*o + 2*o**3 + 31*o**2 - 2*o**2 = 0.
-9, -2, 0
Let a(w) be the first derivative of -w**9/15120 + w**8/8400 + w**7/2100 - w**3 - 4*w - 97. Let k(j) be the third derivative of a(j). Factor k(y).
-y**3*(y - 2)*(y + 1)/5
Suppose -2 = -b, -16*b = -4*j - 20*b + 16. Factor 28*u**4 + 2*u**5 + 2*u**4 + 522*u**3 + 36*u**4 + 12288*u + 8192 + 4864*u**j + 310*u**3.
2*(u + 1)*(u + 8)**4
Let b be 4 - 16*1/(-20)*(-80)/18. Let m(s) be the second derivative of 0 + 1/72*s**4 - b*s**3 - 8*s + 16/3*s**2. Factor m(j).
(j - 8)**2/6
Let g(d) be the second derivative of -1/114*d**4 + 0 + 55/57*d**3 - 211*d + 0*d**2. Solve g(p) = 0 for p.
0, 55
Factor 252/19 + 2/19*s**2 + 254/19*s.
2*(s + 1)*(s + 126)/19
Let c = -540860 + 2163443/4. Factor -33/4 + 9*k - c*k**2.
-3*(k - 11)*(k - 1)/4
Suppose 10*q + 13 = -c + 15*q, 5*c + 2*q - 43 = 0. Suppose 0 = 3*o - 2 - c. Suppose -3/8*a**o + 3/4*a - 3/8*a**5 - 9/8*a**2 + 9/8*a**4 + 0 = 0. What is a?
-1, 0, 1, 2
Let q(h) be the