Let r(y) = 125*i(y) + 6*o(y). Solve r(f) = 0.
-12, -1, 3
Suppose -3*l + 11*k = -77, 0 = -4*l - 18993*k + 18998*k + 35. Determine a so that 5/2*a**3 - 1/4*a**4 + l + 0*a - 9/4*a**2 = 0.
0, 1, 9
Suppose -843 = 2*r + 2*y - 149, 5*r + 1725 = 5*y. Let p = r + 348. Factor 0 - 3/4*z - 3/2*z**p - 3/4*z**3.
-3*z*(z + 1)**2/4
Let k(j) be the third derivative of j**5/330 + 4*j**4 - 9*j**2 - 2*j - 17. Find h, given that k(h) = 0.
-528, 0
Let l(f) be the third derivative of -1/52*f**4 - 26*f**2 + 0 - 2*f + 1/780*f**6 + 2/39*f**3 + 0*f**5. Suppose l(g) = 0. Calculate g.
-2, 1
Let m(j) = 0*j + 12*j**2 - 11*j**2 - j + 1. Suppose -256 = -20*i + 44. Let r(k) = -95*k**2 - 90*k + 5. Let l(h) = i*m(h) - r(h). Solve l(z) = 0.
-1/2, -2/11
Let g(o) be the second derivative of -o**8/6720 - o**7/420 - o**6/80 - 16*o**4/3 + 5*o + 6. Let u(l) be the third derivative of g(l). Factor u(n).
-n*(n + 3)**2
Suppose 10*w + 9 = 7*w + 6*w. Let u(s) be the first derivative of -4*s**w - 16/3*s**2 - 10/3*s - 2/15*s**5 - 4/3*s**4 - 22. Factor u(m).
-2*(m + 1)**3*(m + 5)/3
Let r(k) be the third derivative of -k**7/560 + k**6/24 + k**5/20 - 5*k**4/2 - 251*k**3/6 - 5*k**2 - 3. Let t(a) be the first derivative of r(a). Factor t(o).
-3*(o - 10)*(o - 2)*(o + 2)/2
Let d(z) be the first derivative of -16*z**5/5 + 13*z**4 + 52*z**3/3 - 8*z**2 + 4112. Factor d(f).
-4*f*(f - 4)*(f + 1)*(4*f - 1)
Let o = -1772 - -1774. Let z(b) be the first derivative of -42*b**o - 92/3*b**3 + 2 + 8*b. Find l, given that z(l) = 0.
-1, 2/23
Let y(t) be the first derivative of t**6/840 + t**5/210 + t**4/168 + 18*t**2 - 110. Let q(r) be the second derivative of y(r). Solve q(c) = 0.
-1, 0
Determine a so that 0 - 126/5*a + 87/5*a**2 + 3/5*a**4 + 36/5*a**3 = 0.
-7, -6, 0, 1
Let 184*z - 6461*z**2 + 4*z**5 - 992*z**3 - 3*z**5 + 15*z**5 + 324*z**4 + 6929*z**2 = 0. What is z?
-23, -1/4, 0, 1, 2
Factor -1394842 - 6816*w - 2*w**2 - 3*w**2 - 1335763 - 938*w + 364*w.
-5*(w + 739)**2
Let f = -11 + 12. Let v = -80 - -77. Let z(q) = q - 1. Let c(l) = l**2 + 21*l + 78. Let m(o) = f*c(o) + v*z(o). Solve m(k) = 0.
-9
Let m be (-60)/(-84)*(-903)/(-258). Find a, given that -40*a - m*a**2 - 75/2 = 0.
-15, -1
Let l(r) = -13*r**3 + 218*r**2 + 216*r + 10. Let t(d) = 6*d**3 - 108*d**2 - 108*d - 4. Let v(q) = -2*l(q) - 5*t(q). Factor v(y).
-4*y*(y - 27)*(y + 1)
Let v(a) be the first derivative of a**5/20 + 21*a**4/16 - 23*a**3/4 + 71*a**2/8 - 6*a - 1600. Factor v(k).
(k - 1)**3*(k + 24)/4
Let j(v) be the second derivative of -v**6/30 - 44*v**5/5 - 29*v**4/2 + 88*v**3/3 + 175*v**2/2 + 487*v - 3. Determine t, given that j(t) = 0.
-175, -1, 1
Let v(t) be the first derivative of 2*t**3/3 - 32*t**2 - 370*t - 3277. What is o in v(o) = 0?
-5, 37
Let b be (-427)/(-183) + 2642/3. Let v = b - 3531/4. Factor 0 + 5/4*w - v*w**2.
-w*(w - 5)/4
Factor 0 + 0*y + 17/12*y**3 + 1/12*y**4 + 35/6*y**2.
y**2*(y + 7)*(y + 10)/12
Suppose 75*g = 79*g + a + 6, 18 = -6*g - 3*a. Let i(r) be the second derivative of 13*r - 27/4*r**2 + 2*r**3 + 1/8*r**4 + g. Factor i(h).
3*(h - 1)*(h + 9)/2
Find c, given that 0 - 27/4*c**2 - 9/2*c**3 + 21/2*c + 3/4*c**4 = 0.
-2, 0, 1, 7
Let m(k) = 15*k**2 + 411*k + 10000. Let b(i) = 8*i**2 + 206*i + 5000. Let f(d) = 11*b(d) - 6*m(d). Factor f(r).
-2*(r + 50)**2
Let b be ((-3)/(-6))/((-49)/868). Let o = b - -145/14. Factor 3/2*f**2 - o*f - 1/2*f**3 + 1/2.
-(f - 1)**3/2
Let g(y) = 15*y**2 - 2854*y + 8. Let i(h) = 10*h**2 - 1910*h + 5. Let t(q) = 5*g(q) - 8*i(q). Factor t(c).
-5*c*(c - 202)
Determine p so that -112 + 42*p**3 - 760/3*p + 84*p**2 - 10/3*p**4 = 0.
-3, -2/5, 2, 14
Let y(j) be the first derivative of -2*j**5/5 + 21*j**4/2 - 112*j**3/3 + 36*j**2 + 6268. Find c such that y(c) = 0.
0, 1, 2, 18
Let y(c) be the second derivative of 4*c**6/3 + 31*c**5/4 - 5*c**4 - 155*c**3/6 + 10*c**2 - 133*c. Let y(k) = 0. What is k?
-4, -1, 1/8, 1
Suppose -3*b = -3 + 6, 1 = -2*a - 5*b. Let -2 - 10 + 23 + 18*y - 3*y**a - 11 = 0. Calculate y.
0, 6
Let p(r) be the second derivative of r**5/360 + 5*r**4/144 + r**3/9 + 29*r**2/2 + 62*r. Let j(i) be the first derivative of p(i). Factor j(k).
(k + 1)*(k + 4)/6
Suppose -b = -8*f + 5*f + 7, 21 = 3*b + 5*f. Factor -346*n**2 + 2*n**3 + 4 - 2*n + 113*n**2 + 115*n**b + 114*n**2.
2*(n - 2)*(n - 1)*(n + 1)
Suppose -24*c + 1807 = -11*c. Factor -69*l + 5*l**2 - c*l + 298*l.
5*l*(l + 18)
Let i(l) be the first derivative of -l**6/6 + 7*l**5/5 + 57*l**4/4 + 15*l**3 - 54*l**2 + 479. Suppose i(f) = 0. Calculate f.
-3, 0, 1, 12
Let i(g) = -2*g**2 - 30*g + 41. Let o be i(-22). Let b = -267 - o. Find a such that -5/8*a**2 + b - 1/2*a - 1/8*a**3 = 0.
-4, -1, 0
Let x(c) be the third derivative of 4*c**2 + 0 + 1/10*c**5 + 4/105*c**7 + 13/120*c**6 + 1/336*c**8 + 0*c**3 + 0*c + 0*c**4. Suppose x(g) = 0. What is g?
-6, -1, 0
Solve 248*r**2 - 250*r**2 - 61 - 49 - 32*r = 0.
-11, -5
Let g(r) = 6*r**5 + 2*r**4 - 12*r**3 + 10*r**2 + 14*r - 6. Let k(o) = 7*o**5 + 3*o**4 - 10*o**3 + 11*o**2 + 15*o - 5. Let z(f) = 3*g(f) - 2*k(f). Factor z(s).
4*(s - 1)**3*(s + 1)*(s + 2)
Let b = 18 - 16. Factor 38*o**3 - 2*o**2 - 4*o**5 + 2*o**4 - 36*o**3 + b*o**5.
-2*o**2*(o - 1)**2*(o + 1)
Solve 45*n**5 + 192*n**3 + 241*n**3 - 40*n**2 + 65*n**4 + 211*n**3 - 714*n**3 = 0.
-2, -4/9, 0, 1
Let l(r) be the third derivative of -10*r**3 + 0*r + 0 - 4/3*r**4 - 1/15*r**5 + 143*r**2. Factor l(a).
-4*(a + 3)*(a + 5)
Let p be (-59)/236 - (2550/(-8))/3. Let 634*f**5 + 48*f - 624*f**5 + p*f**2 + 0*f**3 + 54*f**4 + 8 + 110*f**3 = 0. Calculate f.
-2, -1, -2/5
Let r(h) be the third derivative of -1/420*h**7 + 0*h**4 + 0*h**3 + 2*h**2 + 0*h - 27 - 7/480*h**6 + 1/192*h**8 + 1/120*h**5. What is w in r(w) = 0?
-1, 0, 2/7, 1
Let v(f) be the third derivative of 11*f**2 - 19/240*f**5 + 5 + 7/480*f**6 + 0*f + 1/6*f**3 + 1/12*f**4. Factor v(n).
(n - 2)*(n - 1)*(7*n + 2)/4
Factor -41/6*i**3 - 1/6*i**4 + 47/6*i**2 + 71/2*i + 21.
-(i - 3)*(i + 1)**2*(i + 42)/6
Let s(i) be the first derivative of 5*i**4/16 + i**3/4 - i**2/4 + 1282. Let s(z) = 0. What is z?
-1, 0, 2/5
Let u(z) = z**2 + 9*z - 4. Let l be u(-6). Let h(o) = -7*o - 150. Let b be h(l). Factor 4/3*x**3 + 4/3*x - 2*x**2 - 1/3 - 1/3*x**b.
-(x - 1)**4/3
Let b = -3983719/3663 - -9788/9. Let p = b + 3667/4884. Find z, given that -3*z**3 + p*z**4 - 9/4 + 3*z + 3/2*z**2 = 0.
-1, 1, 3
Let i(n) be the first derivative of -20/3*n**3 + 5/6*n**6 + 0*n**2 - 5*n**4 + 0*n + n**5 + 80. Factor i(c).
5*c**2*(c - 2)*(c + 1)*(c + 2)
Let k(v) = 84*v + 254. Let d be k(-3). Let w(t) be the first derivative of -2 - d*t**3 + 3/2*t**2 + 3/4*t**4 + 0*t. Factor w(r).
3*r*(r - 1)**2
Let g(a) be the second derivative of 14*a**2 + 0 + 5/3*a**3 + 8*a - 11/24*a**4 + 1/60*a**5. Let z(v) be the first derivative of g(v). Factor z(t).
(t - 10)*(t - 1)
Let j(t) = t**3 + 10*t**2 - t - 8. Let h be j(-10). Suppose -h*k - 5*s = -45, 2*k - s - 2*s = 5. Let -55*b**3 - 22*b - k*b**2 + 22*b = 0. Calculate b.
-2/11, 0
Let g(m) = 3*m**3 - 4*m**2 + 4*m + 3. Let d be g(3). Factor 5*j**4 - 24 - 70*j - 10*j**3 - d*j**2 + 8 - 9.
5*(j - 5)*(j + 1)**3
Let g(p) = -p**3 - 64*p**2 + 347*p + 140. Let q be g(-69). Factor 1/2*w**3 + 2*w**q + 5/2*w + 1.
(w + 1)**2*(w + 2)/2
Let n = 82183/4746 - -27/1582. Solve n*b - 2/3*b**2 - 338/3 = 0 for b.
13
Find p such that 2/11*p**3 - 94/11*p - 48/11 - 4*p**2 = 0.
-1, 24
Let t(z) = 12*z**2 + 116*z - 688. Let y(u) = u**2 + u - 6. Let k(q) = -t(q) + 8*y(q). Determine g so that k(g) = 0.
-32, 5
Suppose 23*b = 9*b. Let s(a) be the third derivative of -1/6*a**3 + b*a - 5/48*a**4 + 0 - 26*a**2 + 1/140*a**7 + 1/48*a**6 - 1/120*a**5. Factor s(g).
(g - 1)*(g + 1)**2*(3*g + 2)/2
Let b = -1604 + 447515/279. Let m = b - -7/31. Determine y, given that -2/9*y**5 + 0 - 8/9*y**2 + 4/3*y**3 - 16/9*y + m*y**4 = 0.
-2, -1, 0, 2
Let b(z) be the third derivative of 75*z**8/224 + z**7/7 - 611*z**6/240 - 341*z**5/60 - 16*z**4/3 - 8*z**3/3 - 1659*z**2. Determine a so that b(a) = 0.
-4/5, -1/3, 2
Suppose 26*h - 32 = 18*h. Determine w so that -h*w**2 + 7 - 4*w**4 + 0 + 12*w - 5 + 0 + 6 - 12*w**3 = 0.
-2, -1, 1
Suppose 9*y = y + 24. Factor -4 + 3*h**4 - 26*h**3 + y*h - h**5 + 47*h**3 - 20*h**3 - 11*h**2 + 9*h.
-(h - 2)*(h - 1)**3*(h + 2)
Let n be (4/6)/(18/54). Suppose 4*w - 7 = 5*a - 0*a, a + 8 = 3*w. Suppose -3*o**2 - 6*o + 3*o**2 - n - w*o**2 + o = 0. What 