1
Let k(m) be the first derivative of 2*m**3/39 + 11*m**2/13 - 120*m/13 - 153. Factor k(f).
2*(f - 4)*(f + 15)/13
Find a such that 1101014 + 7927*a - 5*a**2 - 8413744 + 13353*a - 15975070 + 645880 = 0.
2128
Let i(w) be the third derivative of -w**7/105 + w**6/10 + 167*w**5/30 - 44*w**4 - 7744*w**3/3 + 63*w**2 - 2. Factor i(t).
-2*(t - 11)**2*(t + 8)**2
Let p(d) = d**3 - 12*d**2 - 12*d - 13. Let i be p(13). Let q be 9 - 4 - i/(-2). Suppose 2/3*b**3 + 2/3*b**q + 0*b + 0*b**2 + 0 + 4/3*b**4 = 0. Calculate b.
-1, 0
Let n(m) be the third derivative of -m**7/35 - 13*m**6/60 - m**5/5 + 3*m**4 + 40*m**3/3 + 783*m**2. Determine z so that n(z) = 0.
-2, 5/3
Let f(x) be the second derivative of -x**5/10 + 139*x**4/6 + 94*x**3 - 15*x - 1. Find o, given that f(o) = 0.
-2, 0, 141
Let y = -194 + 197. Factor t**3 + 7*t**y - 6 + t**2 - 15*t**3 + 4*t**3 + 3*t + 5*t**2.
-3*(t - 2)*(t - 1)*(t + 1)
Determine a, given that 55*a**3 + 366*a + 54*a**3 - 164*a**3 + 58*a**3 - 504 + 135*a**2 = 0.
-42, -4, 1
Let g(o) be the third derivative of -o**5/30 + o**4/2 - 8*o**3/3 + 311*o**2. Determine u, given that g(u) = 0.
2, 4
Let a(r) = -r**2 + 8*r + 4. Let d be 62/8 - 12/(-48). Let c be a(d). Factor -10*o + 199*o**4 + 0 + 0 + 206*o**c - 315*o**3 - 135*o**5 + 95*o**2.
-5*o*(o - 2)*(3*o - 1)**3
Let j be ((-57)/1539)/((-17)/51). Determine y so that -j*y**2 - 16/9*y - 13/3 = 0.
-13, -3
Suppose -102 - 167 - 187 = -228*l. Let h(i) be the second derivative of 9*i + 0*i**l + 3/20*i**5 + 1/2*i**3 + 0 - 1/2*i**4. Factor h(q).
3*q*(q - 1)**2
Let k(j) be the first derivative of 2*j**5/5 - j**4 - 14*j**3/3 + 20*j**2 - 24*j - 25. Let k(w) = 0. What is w?
-3, 1, 2
Factor 138/7*b + 9/7*b**2 + 529/7.
(3*b + 23)**2/7
Let v(z) be the third derivative of -11/42*z**7 + 19/24*z**6 + 0*z + 5/336*z**8 - 13 + 3*z**2 + 0*z**3 + 0*z**4 - 3/4*z**5. Find x, given that v(x) = 0.
0, 1, 9
Let m(n) = -9*n**2 - 59*n + 107. Let o be m(-8). Factor 1/4*c**5 + 0*c - 1/2*c**2 + 0*c**4 - 3/4*c**o + 0.
c**2*(c - 2)*(c + 1)**2/4
Suppose 72 + 159 = -7*g. Let u = -29 - g. Factor 0*y**2 - u*y**3 - 23*y**2 + 7*y**2.
-4*y**2*(y + 4)
Determine p so that 13 + 49/3*p + 3*p**2 - 1/3*p**3 = 0.
-3, -1, 13
Let w(l) be the third derivative of -l**5/15 - 88*l**4/3 + 712*l**3/3 - 2333*l**2. Determine b, given that w(b) = 0.
-178, 2
Let r(n) = n**3 + 5*n**2 - 3*n - 4. Let x be r(-4). Let 43 + 429 + 58*m + x + m**2 + 345 = 0. Calculate m.
-29
Let y be 152/6 - 18 - 6. Let k(p) be the second derivative of 0 + 4/9*p**3 + 0*p**2 + 26*p + 1/3*p**4 - y*p**5. Factor k(w).
-4*w*(4*w + 1)*(5*w - 2)/3
Solve -32*u + 10*u**3 - 15*u**3 - 20*u**2 + 61*u - 70 + 66*u = 0 for u.
-7, 1, 2
Suppose -5*x - 5*q - 5 = 0, 4*x + 15 = 2*q - 19. Let c be 9*x/(-270) + 1/(-5). Factor -4/9*d**2 + c + 2/9*d.
-2*d*(2*d - 1)/9
Let h(m) be the first derivative of m**7/42 - 2*m**6/15 - 3*m**5/20 + 5*m**4/6 + 4*m**3/3 + 61*m - 5. Let f(n) be the first derivative of h(n). Factor f(q).
q*(q - 4)*(q - 2)*(q + 1)**2
Let o(i) = 34*i + 3. Let n be o(3). Factor n*l - 12 + 6433*l**2 - 6376*l**2 - 6*l**3 - 54.
-3*(l - 11)*(l + 2)*(2*l - 1)
Let o(v) be the third derivative of v**6/60 - 17*v**5/165 + v**4/44 + 8*v**2 - 19. Factor o(m).
2*m*(m - 3)*(11*m - 1)/11
Let q(c) = c**3 - 6*c**2 + 4*c + 1. Let p be ((-1)/(-8))/(2/8)*4. Let v(d) = -2*d**3 + 2 - 1 + d**3. Let k(r) = p*v(r) - 2*q(r). Factor k(j).
-4*j*(j - 2)*(j - 1)
Find g such that -2/5*g**2 + 92/5*g + 294/5 = 0.
-3, 49
Let y(q) be the first derivative of -q**7/2520 - q**6/36 - 8*q**5/15 + 64*q**4/9 + 63*q**3 - 211. Let r(o) be the third derivative of y(o). Factor r(i).
-(i - 2)*(i + 16)**2/3
Let j be 3570/235 - 10 - 5. Let f = j - -219/329. Factor 0 - 8/21*o + 2/21*o**4 - 4/7*o**3 + f*o**2.
2*o*(o - 4)*(o - 1)**2/21
Suppose 4*t**4 - 8*t**2 - 1 - 1 + 6 + 1039*t - 1039*t = 0. What is t?
-1, 1
Let a = -26127 + 182967/7. Factor 507/7 + 3/7*t**2 - a*t.
3*(t - 13)**2/7
Suppose k = -k - 92. Let z = 48 + k. Factor 5 - i**2 + 0*i**z + 3*i**3 - 9*i + 4*i**2 - 2*i**3.
(i - 1)**2*(i + 5)
Suppose 11*f = 6*f + 15. Let p(a) be the first derivative of -a**3 + 19 + 43*a**2 - 81*a**2 + 35*a**2 - f*a. Factor p(j).
-3*(j + 1)**2
Suppose 323*n + 9 = 328*n - h + 4*h, 0 = 5*h - 15. Suppose 0*v**2 + n - 1/4*v**3 + 1/4*v = 0. Calculate v.
-1, 0, 1
Let r(v) be the third derivative of -v**7/490 - v**6/28 - 4*v**5/35 + 45*v**4/28 + 225*v**3/14 + 453*v**2 + 1. Determine f, given that r(f) = 0.
-5, -3, 3
Let i = 132 + -132. Factor -28*h - 2*h**2 + 189 + i*h**2 - 159.
-2*(h - 1)*(h + 15)
Suppose -5*c + 2*n + 22 = 0, 5*n + 13 = 5*c - 12. Let 9758*t**5 - 36*t**4 - 9502*t**5 + c*t**3 + 100*t**4 = 0. What is t?
-1/8, 0
Let n(x) be the second derivative of 1/3*x**4 + 1 - 80/3*x**3 + 24*x + 800*x**2. Solve n(f) = 0.
20
Suppose 376971*u - 376870*u = 303. Let -9/2*m**3 - u*m**2 + 0*m**4 + 0 + 3/2*m**5 + 0*m = 0. Calculate m.
-1, 0, 2
Factor 12 + 48/5*s**3 + 168/5*s**2 + 176/5*s - 4/5*s**4.
-4*(s - 15)*(s + 1)**3/5
Let f = -987038 + 987065. Let -49/2*i**2 + f*i - 12*i**4 - 4 + 8*i**5 - 151/2*i**3 = 0. Calculate i.
-2, -1, 1/4, 4
Let i(k) = 9*k. Let h(m) = -3*m**2 + 420*m - 8112. Let p(c) = -h(c) + 12*i(c). Factor p(r).
3*(r - 52)**2
Let i(z) be the first derivative of z**4 + 5*z**3/3 + 3*z**2 - 5*z - 85. Let q(g) = g**3 + g**2 + g - 1. Let y(n) = i(n) - 5*q(n). Factor y(r).
-r*(r - 1)*(r + 1)
Let p be (31/(-62))/((-84)/8). Let b(a) be the first derivative of -p*a**3 + 0*a**2 + 1/7*a - 11. What is l in b(l) = 0?
-1, 1
Suppose -769*g - 506 = -791*g. Let a(r) be the first derivative of 15*r - 5/3*r**3 - g + 5*r**2. Factor a(s).
-5*(s - 3)*(s + 1)
Let a = 5796 + -5796. Let k be -2*1/2*0. Factor k - 1/4*x + a*x**2 - 1/4*x**5 + 1/2*x**3 + 0*x**4.
-x*(x - 1)**2*(x + 1)**2/4
Let n(s) be the third derivative of -1/210*s**7 - 1/30*s**5 + 5/6*s**4 - 1/24*s**6 + 0 + 105*s**2 + 0*s + 4*s**3. Factor n(u).
-(u - 2)*(u + 2)**2*(u + 3)
Let q = -262792/7 - -37542. Suppose 18/7*f**3 + 0 - 10/7*f**4 + 4/7*f - 2*f**2 + q*f**5 = 0. What is f?
0, 1, 2
Let l(p) = p**3 + 3*p**2 - p. Let g(x) = -8*x**5 + 190*x**4 - 474*x**3 + 200*x**2 + 86*x. Let q(o) = -g(o) - 2*l(o). Let q(w) = 0. What is w?
-1/4, 0, 1, 2, 21
Suppose -2*i - k + 14 = 0, 72*k = -5*i + 75*k - 20. Determine p so that -4/5*p - 6*p**i - 66/5*p**3 - 18/5*p**5 - 58/5*p**4 + 0 = 0.
-1, -2/9, 0
Let v(h) be the third derivative of -h**6/80 - 479*h**5/160 - 1785*h**4/8 + 225*h**3 - 3321*h**2. Determine q, given that v(q) = 0.
-60, 1/4
Let p(o) = 79*o - 397. Let t be p(5). Let n be (((-80)/t)/(-8))/(-3 - 0). Factor 8/3 + n*m**2 + 22/3*m.
(m + 4)*(5*m + 2)/3
Let h = 2217 + -99749/45. Let k(f) be the first derivative of -25/36*f**4 - 9 - 2/27*f**6 + h*f**5 + 1/9*f + 19/27*f**3 - 7/18*f**2. Factor k(u).
-(u - 1)**3*(2*u - 1)**2/9
Suppose -1179*r - 7203 + 1755 = -2995*r. Factor 0 + 0*j + 2/7*j**4 + 0*j**r - 32/7*j**2.
2*j**2*(j - 4)*(j + 4)/7
Let v(f) be the second derivative of 19/4*f**4 - 20 - 60*f**2 - 3/20*f**5 + 11*f**3 + f. What is a in v(a) = 0?
-2, 1, 20
Let w(p) be the first derivative of 97 + 3/20*p**4 + 99/10*p**2 + 34/5*p**3 + 0*p. Let w(g) = 0. What is g?
-33, -1, 0
Suppose 10*o - 8 = 6*o. Find h such that -h**3 - 8*h**2 + 26*h**o - 19*h**2 = 0.
-1, 0
Let l(h) be the second derivative of -2*h**6/105 - 3*h**5/20 + 13*h**4/12 + 4*h**3/7 - 1723*h. Determine p so that l(p) = 0.
-8, -1/4, 0, 3
Suppose 15*b - 155 = 25. Factor -5*k**3 - b*k**2 - 40*k**2 - 30 + 12*k**2 - 65*k.
-5*(k + 1)**2*(k + 6)
Let b(n) be the third derivative of -n**5/20 - 235*n**4/8 - 117*n**3 + 807*n**2. Factor b(r).
-3*(r + 1)*(r + 234)
Suppose -w = -f - 7, -16 = 4*f - 0*f. Let q be 221/408 - 5/120. Solve q*r**w - 1/2*r**2 - 1/6*r**4 + 0 + 1/6*r = 0 for r.
0, 1
Let t(u) = -u**3 + u**2 + 2*u. Let n(y) = 3*y**4 + 147*y**3 + 3*y**2 - 141*y. Let s(k) = -n(k) + 6*t(k). What is p in s(p) = 0?
-51, -1, 0, 1
Suppose 15 = -19*i + 22*i. Solve -8*x - i*x**5 + 3*x**5 - 4*x**4 - 13 + 20*x**2 + 10*x**3 - 3 = 0.
-2, -1, 1, 2
Let u = -4/91 - -18/91. Let z be 352/(-26) + 3766/269. Factor 6/13*q - z*q**2 - 2/13 + u*q**3.
2*(q - 1)**3/13
Let f = -7 - -30. Let j = f + -21. Factor 6*i**2 + 5*i - 7*i - 4*i**j.
2*i*(i - 1)
Let y(n) be the second derivative of n**4/66 - 25*n**3/3 + 71*n - 16. Suppose y(f) = 0. Calculate f.
0, 275
Factor 2850*h**3 - 307*h**5 + 232*h**4 - 777*