 -w + 2*b, -w - 4*b - r = 4*w. Factor w*q + 2*q**2 + 0*q**2 + 2*q + 0*q - 2*q**3.
-2*q*(q - 2)*(q + 1)
Let r(m) be the third derivative of m**8/112 + 23*m**7/210 - 13*m**6/120 - 13*m**5/20 + 5*m**4/12 + 8*m**3/3 - 7*m**2 - 79*m. Determine w so that r(w) = 0.
-8, -1, -2/3, 1
Let m(z) be the third derivative of -z**8/2184 + 4*z**7/1365 + z**6/260 - 3*z**5/65 + 493*z**2 + z - 2. Factor m(t).
-2*t**2*(t - 3)**2*(t + 2)/13
Factor -1/2*j**3 + 39/2*j + 10 + 9*j**2.
-(j - 20)*(j + 1)**2/2
Suppose 2*n = 5*n + 15, 4*n = -5*q - 20. Suppose -2*f - 3*u = 7 + 1, 2*f + 4*u + 12 = q. Factor -7*s**2 + 0*s - 4 + 2*s**2 - 4*s + 4*s**f.
-(s + 2)**2
Factor 2/9*u**2 + 0 - u**3 + 0*u + 4/9*u**4.
u**2*(u - 2)*(4*u - 1)/9
Let s be -16 + 28 - 9*1. Suppose 23*f + s = 3. Factor 2/15*i**3 + 4/3*i + f - 14/15*i**2.
2*i*(i - 5)*(i - 2)/15
Let m be (193 + -190)/(-1 + 1 + 1). Factor 0 + 1/2*a**m + 0*a + 1/2*a**4 - 1/2*a**2 - 1/2*a**5.
-a**2*(a - 1)**2*(a + 1)/2
Determine u so that -44/9*u**3 + 16/9*u**4 - 20 - 446/9*u**2 + 278/3*u = 0.
-5, 1/4, 3/2, 6
Let k(d) be the first derivative of d**5/5 - 2*d**4/3 + d**3/3 + d**2/3 - 2036. Factor k(c).
c*(c - 2)*(c - 1)*(3*c + 1)/3
Suppose 0 = 44*r - 45*r + 14. Suppose -5 = -5*f + 10. Determine w, given that r*w - w + f*w + 12 + 4*w**2 = 0.
-3, -1
Let t(b) be the second derivative of b**6/60 - 3*b**5/40 - b**4/8 + 7*b**3/12 + 3*b**2/2 + 945*b. Find y such that t(y) = 0.
-1, 2, 3
Let f be ((-63760)/(-1848) - 4/(-6)) + -42 + 25456/602. Determine x so that 58/11*x**2 + f*x + 2/11*x**3 - 450/11 = 0.
-15, 1
Let z be (-24)/(-90)*(5 + (-3 - -3))/1. Let h(g) be the third derivative of 0 - 1/2*g**4 + z*g**3 + 0*g + 16*g**2 + 1/15*g**5. Let h(o) = 0. Calculate o.
1, 2
Suppose 0 = -7*b + 9 + 12. Suppose i - 13 = 2*s, 4*s = b*i - 16 - 15. Determine a so that -74*a**4 + 44*a**4 - a**i + 60*a**4 + 6*a**5 + 25*a**3 = 0.
-5, -1, 0
Let d be -29 + 9064/308 - (36/(-14) - 2). Solve 81/7*g**d + 48/7 - 216/7*g**3 + 24/7*g**2 - 81/7*g**4 + 144/7*g = 0.
-2/3, 1, 2
Let g(o) be the third derivative of -2*o**7/525 - 11*o**6/50 - 2*o**5/5 + 32*o**4/15 + 5*o**2 + 73. Solve g(j) = 0.
-32, -2, 0, 1
Let h(k) = -16*k - 29. Let r be h(-2). Let z(n) be the third derivative of 0 + 1/2*n**4 + 0*n**r + 0*n + 9*n**2 + 1/20*n**5. Determine v, given that z(v) = 0.
-4, 0
Let w(a) be the third derivative of 0*a**3 + 0*a**4 + 0*a + 0 - 1/60*a**6 + 1/30*a**5 + 69*a**2. Factor w(u).
-2*u**2*(u - 1)
Let x = -2/5683 - -51157/28415. Let y(k) = 12*k - 9. Let c be y(1). Factor -x*z**3 + 32/5*z + 12/5 + c*z**2.
-(z - 3)*(3*z + 2)**2/5
Determine n, given that 366/5 - 2/5*n**2 - 116/5*n = 0.
-61, 3
Suppose 8*d - 10*d = -19520. Let k be 2/(-23) + (-6 - d/(-1150)). Determine b, given that -2/5*b - 2/5*b**2 + k = 0.
-3, 2
Let p = -1/258743 - -6209837/1293715. Suppose p*g**2 + 246/5*g + 12 = 0. What is g?
-10, -1/4
Let d(k) be the third derivative of k**6/240 + k**5/40 - k**4/8 - 2*k**3/3 - 10*k**2 - 11. Factor d(x).
(x - 2)*(x + 1)*(x + 4)/2
Factor -53582633/7 - 426387/7*b - 1/7*b**3 - 1131/7*b**2.
-(b + 377)**3/7
Factor -20*y**2 + 1794 - 4422 - 2398 + 975*y - 644.
-5*(y - 42)*(4*y - 27)
Suppose 39*o = 9 + 69. Factor -2*r**o - 44*r + 40 + 11*r**2 - 5*r**2.
4*(r - 10)*(r - 1)
Factor -5*f**3 - 57279*f + 53964*f + 3320*f**2 + 9 - 16 + 7.
-5*f*(f - 663)*(f - 1)
Let w(i) be the second derivative of i**4/12 - 4*i**3/3 + i**2 + 21*i. Let h be w(8). Determine k, given that -4*k + 115*k**2 - 12 - 106*k**h + 0*k - k**4 = 0.
-3, -1, 2
Let b = -296 - -321. Suppose 25*x**2 + 2091 - 9*x**4 + 25*x - 6*x**4 - 2101 - b*x**3 = 0. What is x?
-2, -1, 1/3, 1
Let j be (-35 - (-5616)/195) + 17. Determine s, given that -243/5*s - j*s**2 + 0 - 3/5*s**3 = 0.
-9, 0
Let z(o) = -67*o**2 + 615*o - 171. Let l(c) = 89*c**2 - 820*c + 227. Let h(t) = -7*l(t) - 9*z(t). Factor h(r).
-5*(r - 10)*(4*r - 1)
Let p = -95 + 100. Suppose -2*q + 24 = -z, -5*q + 2*z + 0*z + 58 = 0. Determine w so that 129 + 109*w**2 - 49*w**2 + q*w**3 + 31 - 200*w - p*w**4 = 0.
-4, 2
Let t(h) be the first derivative of 6/5*h - 2/15*h**3 - 14 + 2/5*h**2. Factor t(d).
-2*(d - 3)*(d + 1)/5
Let i = 13177/336 + -549/14. Let h(r) be the second derivative of -1/24*r**3 + 1/160*r**5 + 0*r**2 - 1/32*r**4 + 0 + 1/80*r**6 - 21*r + i*r**7. Factor h(w).
w*(w - 1)*(w + 1)**2*(w + 2)/8
Let k(g) = -265*g**2 - 5287*g + 261. Let m be k(-20). What is t in 5/2*t**3 - m - 1/2*t**4 - 9/2*t**2 + 7/2*t = 0?
1, 2
Let o = -3/40469 - -7361/40469. Factor -1/11*k**3 - 8/11 + 4/11*k + o*k**2.
-(k - 2)**2*(k + 2)/11
Suppose 0 = -7*l + 657 - 349. Let 8*i + 9*i**2 + 4*i**3 + 19*i**2 + 0*i - 4*i**2 + 32 - l*i**2 = 0. What is i?
-1, 2, 4
Factor 0*p**2 + 0 + 0*p + 1/7*p**5 + 382/7*p**4 + 381/7*p**3.
p**3*(p + 1)*(p + 381)/7
Suppose 2*b + 12 = -4*p - 2*b, b = 4. Let v be (3/p)/((-88)/154). Factor 33/8*z**4 + 0 - 9/8*z**5 - v*z - 45/8*z**3 + 27/8*z**2.
-3*z*(z - 1)**3*(3*z - 2)/8
Let j be 6 - 2 - (-3 - 2). Let t(o) = 6*o - 9. Let b be t(j). Factor 31*y**3 - 5*y**5 - 66*y**3 - 5 + b*y**3 + 10*y**2 - 5*y - 5*y**4.
-5*(y - 1)**2*(y + 1)**3
Let f be (-20)/350*-5 + 4/35. Suppose 9 = 3*q, -3*w + 17 = 2*q + 5. Determine l, given that 8/3*l - 14/15 + f*l**w = 0.
-7, 1/3
Let n = -13 - -18. Suppose 5*p + 177*b = 172*b + 155, 4*p - 2*b = 172. Determine k so that 81/2*k**n - 9/2*k - 81*k**4 - p*k**2 + 0 - 108*k**3 = 0.
-1/3, 0, 3
Let l(y) = 11*y - 164. Let q be l(37). Let s = 243 - q. Suppose 7/8*f**2 - 3/8*f + 1/8*f**4 + s - 5/8*f**3 = 0. What is f?
0, 1, 3
Let i(f) be the second derivative of f**4/60 + 253*f**3/15 + 101*f**2/2 + 4*f - 83. Factor i(p).
(p + 1)*(p + 505)/5
Suppose -u + 3 = k - 12, 4*k = 5*u - 84. Suppose 2*y - 5*a - u = 0, 5*y + a + 4 - 17 = 0. Solve 39/2*f**2 + 3/2 - 90*f**y + 15*f + 54*f**4 = 0 for f.
-1/6, 1
Suppose 2*s + 5*u = 9970, 2043*s - 2038*s - 3*u = 25018. Factor -100*a + s + 1/2*a**2.
(a - 100)**2/2
Let o be (-14)/21*(-3)/(-2) - (-9760)/1952. Suppose -34/3*w + 34/3*w**2 - 14/3*w**3 + 2/3*w**4 + o = 0. What is w?
1, 2, 3
Let q = -282 + 282. Let p be ((-1)/(-4) + q)*56/105. Determine g, given that 0 + p*g**3 + 2/15*g**2 + 0*g = 0.
-1, 0
Let k(u) = -15*u**2 - 3045*u + 15930. Let v(d) = -7*d**2 - 1354*d + 7080. Let t(c) = -9*k(c) + 20*v(c). Solve t(y) = 0.
6, 59
Suppose 2*v = 2*d - 6, 2*v - 15*d + 12*d = -12. Let b(j) be the first derivative of 1/5*j**3 + v + 0*j - 1/25*j**5 - 1/10*j**4 + 0*j**2. Solve b(t) = 0.
-3, 0, 1
Let n(p) = p**2 - 20*p + 101. Let d be n(11). Find h, given that -32*h**d + 13*h - 9*h + 24*h**2 + 0 + 6 + 9*h = 0.
-3/8, 2
Factor -12*r + 260 + 5*r**2 - 116*r - 203*r + 66*r.
5*(r - 52)*(r - 1)
Let i(n) be the third derivative of 2*n**7/735 - 67*n**6/105 - 9*n**5/7 - 298*n**2 - 1. Let i(f) = 0. What is f?
-1, 0, 135
Let l(a) = a - 10. Let i be (-26)/(-3 - (-1)/1). Let v be l(i). Factor -v*m - 21*m - 8 - 12*m**3 + m**2 - 27*m**2 - 2*m**4.
-2*(m + 1)**2*(m + 2)**2
Let s(t) = -54*t**2 + 156*t - 2. Let i(w) = w**3 + 40*w**2 - 156*w + 3. Let k(x) = -2*i(x) - 3*s(x). Solve k(y) = 0.
0, 2, 39
Let b(y) be the first derivative of 47 + 40*y + 95*y**2 - 55/3*y**3 - 25/4*y**4. What is z in b(z) = 0?
-4, -1/5, 2
Let u(o) be the second derivative of -3*o**5/20 + 19*o**4/2 + 82*o**3 + 252*o**2 + 13*o - 141. Factor u(r).
-3*(r - 42)*(r + 2)**2
Let m(k) be the second derivative of 285*k**4/4 + k**3 + 22*k + 2. Factor m(z).
3*z*(285*z + 2)
Let y(v) be the first derivative of v**7/70 + v**6/10 - 11*v**5/20 + 3*v**4/4 - 4*v**2 + 153. Let g(f) be the second derivative of y(f). Factor g(h).
3*h*(h - 1)**2*(h + 6)
Suppose 2*l - 24 - 26 = 0. Determine r so that -r**2 - 4*r**2 - 10*r + l*r + 20*r = 0.
0, 7
Let i(c) be the second derivative of -3*c**5/20 - 2769*c**4/2 - 5111574*c**3 - 9435965604*c**2 - 3344*c. Find t such that i(t) = 0.
-1846
Let m(x) = -x + 22. Let h be m(0). Suppose 2*g - 3*j = 89, -106 = -3*g - 0*j - j. Factor -g*r**2 + 19*r**2 + 8 + 12*r + h*r**2.
4*(r + 1)*(r + 2)
Let i(f) be the third derivative of 4/15*f**4 - 69*f**2 + 0*f + 0 - 17/15*f**3 + 1/150*f**5. Find l such that i(l) = 0.
-17, 1
Let d be (539/56 + -10)/((-2)/16). Determine g so that 71*g**3 + 81*g + 12*g - 20*g**d + 119*g**2 + 18 + 7*g**4 = 0.
-3, -1, -2/7
Let t(u) be the second derivative of -3*u**5/140 + 41*u**4/14 - 233*u**3/14 - 474*u**2/7 + 6405*u. Let t(a) = 0. Calculate a.
-1, 4, 79
Factor 5