.
-2
Let l(n) be the first derivative of -2/27*n**3 + 46/9*n + 88 - 22/9*n**2. Let l(i) = 0. Calculate i.
-23, 1
Let i(u) be the first derivative of 0*u + 20/3*u**3 + 1 - 25/2*u**2 + 5/4*u**4. Factor i(z).
5*z*(z - 1)*(z + 5)
Let c = 897/215 - 854/215. Let c*p**3 - 4/5*p**2 - 2/5 + p = 0. What is p?
1, 2
Let l be 686/(-105)*(-10)/24. Let d = -20/9 + l. Factor -5/4*o + d*o**2 - 3/4.
(o - 3)*(2*o + 1)/4
Let o(y) be the first derivative of -y**4/20 + 3*y**3/5 - 12*y**2/5 - 143*y + 283. Let g(c) be the first derivative of o(c). Factor g(a).
-3*(a - 4)*(a - 2)/5
Let i(f) be the second derivative of -f**6/195 - 151*f**5/130 - 1320*f**4/13 - 52992*f**3/13 - 774144*f**2/13 + 506*f. Factor i(b).
-2*(b + 7)*(b + 48)**3/13
Let b = 65/9 - 17/9. Let t(n) = -6687*n - 33431. Let y be t(-5). Determine f so that -32/3 + 40/3*f**2 - 4/3*f**5 - 8/3*f**y + 20/3*f**3 - b*f = 0.
-2, -1, 1, 2
Solve -5*r**5 + 348100*r**2 + 0*r**5 - 51467*r**3 - 1155*r**4 + 8227*r**3 + 21427*r**3 - 41907*r**3 = 0.
-118, 0, 5
Let n(m) = 7*m - 29. Let s be n(5). Let -11 + s*g**3 - 2*g**2 + 8 - 16*g - 5 = 0. What is g?
-1, -2/3, 2
Let m be ((-24)/108)/(29/(-87)). Factor -8/3*h + 0 - m*h**3 + 10/3*h**2.
-2*h*(h - 4)*(h - 1)/3
Let i be (1 - 1) + 9*(-4)/(-180). Let d be 0/(10/(-30)*-9). Factor i*p**2 + d + p.
p*(p + 5)/5
Let i(w) be the second derivative of -1 - 4/15*w**4 + 0*w**2 - 90*w + 1/75*w**6 + 4/5*w**3 - 1/50*w**5. Suppose i(l) = 0. What is l?
-3, 0, 2
Let q(t) be the first derivative of -t**6/30 - t**5/4 - 2*t**4/3 - 2*t**3/3 - 23*t - 59. Let h(g) be the first derivative of q(g). Factor h(r).
-r*(r + 1)*(r + 2)**2
Factor -936149*m**3 + 936414*m**3 + 2*m - 2*m - 5*m**4 - 260*m**2.
-5*m**2*(m - 52)*(m - 1)
Let x(h) = 9*h - 43. Let y be x(7). Find p such that -2*p**3 - p**3 + 2*p**4 + 7*p**3 + y*p**3 + p**4 + 48*p**2 = 0.
-4, 0
Let j(v) be the first derivative of 3*v**3/7 + 93*v**2/14 + 30*v/7 + 803. Solve j(n) = 0 for n.
-10, -1/3
Let i(y) be the first derivative of 11*y**5/45 - 7*y**4/18 - y**3/27 + 112*y + 8. Let u(o) be the first derivative of i(o). Let u(l) = 0. Calculate l.
-1/22, 0, 1
Let b(x) be the first derivative of 4*x**5/5 - 10*x**4 + 32*x**3 - 44*x**2 + 28*x - 1100. Determine w so that b(w) = 0.
1, 7
Let j(d) be the second derivative of d**4/16 + d**3/2 - 231*d**2/8 - 10*d - 81. Suppose j(w) = 0. What is w?
-11, 7
Let d be 2 - (2/3)/(232/(-87) - -4). Determine j so that 1/6*j**5 + 0 - 7/6*j**2 + d*j**3 - 5/6*j**4 + 1/3*j = 0.
0, 1, 2
Let y(i) be the second derivative of 185*i**4/18 - 139*i**3/3 + 22*i**2/3 + 239*i + 3. Factor y(j).
2*(5*j - 11)*(37*j - 2)/3
Let -13 + 64 + 35 + 3*m**2 + m**2 - 80*m - 10 = 0. What is m?
1, 19
Let -5*h**2 - 17/4*h - 1/4*h**3 + 19/2 = 0. What is h?
-19, -2, 1
Let q(c) be the first derivative of -c**4/2 + 830*c**3/3 + 833*c**2 + 834*c - 3509. Factor q(k).
-2*(k - 417)*(k + 1)**2
Let f be ((-159)/(-21) - 9)/((-30)/(-42) + -1). Let j(l) be the second derivative of 0*l**3 + 1/3*l**4 + 14*l - 1/15*l**6 + 7/20*l**f + 0 + 0*l**2. Factor j(s).
-s**2*(s - 4)*(2*s + 1)
Let q(n) be the second derivative of n**6/75 - n**4/3 + 9*n**2/5 + 204*n + 4. Suppose q(w) = 0. Calculate w.
-3, -1, 1, 3
Let l be ((187/(-66))/17)/(3859/5431). Let m = 1/1362 - l. Let -m + 2/17*r**2 + 2/17*r = 0. Calculate r.
-2, 1
Let t(i) = 71*i**3 - 135*i**2 + 936*i - 1360. Let g(c) = -153*c**3 + 270*c**2 - 1873*c + 2720. Let a(w) = -6*g(w) - 13*t(w). Factor a(y).
-5*(y - 17)*(y - 8)*(y - 2)
Let a(o) be the first derivative of -o**3/9 + 97*o**2/6 - 190*o/3 + 6198. Factor a(f).
-(f - 95)*(f - 2)/3
Let j = -775 + 777. Let p(y) = 9*y**2 - 17*y + 2. Let u be p(j). Find f such that 1/3*f**5 + 0*f + 0*f**u - f**3 + 2/3*f**2 + 0 = 0.
-2, 0, 1
Solve -338*n + 34*n**2 - 3*n**5 - 290*n**2 - 448*n + 256*n**4 + n**5 + 602*n**3 + 186*n**3 = 0.
-3, -1, 0, 1, 131
Let t = 23257/28218 - -43/4703. Determine l so that -t*l**3 - 65/6 - 45/2*l - 25/2*l**2 = 0.
-13, -1
Let q(o) = -11*o**3 + 3543*o**2 - 626574*o - 3. Let r(c) = -9*c**3 + 3542*c**2 - 626576*c - 2. Let i(l) = 2*q(l) - 3*r(l). Let i(z) = 0. What is z?
0, 354
Let u(p) = -2*p**2 + 22*p - 1499. Let x(t) = -20*t**2 + 236*t - 13492. Let y(s) = -28*u(s) + 3*x(s). Determine z so that y(z) = 0.
-11, 34
Let k(b) be the first derivative of -4*b**5 - 1437*b**4/4 - 1202*b**3/3 + 357*b**2/2 + 142*b - 2602. Let k(z) = 0. Calculate z.
-71, -1, -1/4, 2/5
Let j(r) be the second derivative of -1/15*r**6 - 1/105*r**7 + 0*r**2 + 1/6*r**4 - 101*r + 4/15*r**3 - 3/50*r**5 + 0. What is q in j(q) = 0?
-4, -1, 0, 1
Factor 32 - 70*i**3 + 162*i + 29*i**3 - 182*i**2 + 29*i**3.
-2*(i - 1)*(i + 16)*(6*i + 1)
Let f(c) be the third derivative of 0*c**4 + 22*c - 9/5*c**6 + c**2 - 243/5*c**5 + 0 - 2/105*c**7 + 0*c**3. Solve f(s) = 0 for s.
-27, 0
Let x be (-12)/(-32)*(-4144)/(-333). Let x*j**2 - 1/3*j**3 - 65/3*j + 100/3 = 0. What is j?
4, 5
Factor 3/5*x**4 + 0 + 313/5*x**2 + 112/5*x - 68/5*x**3.
x*(x - 16)*(x - 7)*(3*x + 1)/5
Let i(y) = 27*y - 1. Let o(d) = d**2 - 69*d + 217. Let j(z) = 5*i(z) + 5*o(z). Solve j(l) = 0.
6, 36
Let g(h) = -h**2 - 107*h - 94. Let l(y) = -5*y**2 - 539*y - 468. Let p(b) = 33*g(b) - 6*l(b). Factor p(t).
-3*(t + 1)*(t + 98)
Let k(f) = 131*f - 7072. Let s be k(54). Let x(l) be the first derivative of -1/2*l**4 + 4*l + 6*l**s + 5 + 3*l**3 - 3/5*l**5. Factor x(q).
-(q - 2)*(q + 1)**2*(3*q + 2)
Factor 0 + 11/2*l**3 - l + 25/4*l**2 - 7/4*l**4.
-l*(l - 4)*(l + 1)*(7*l - 1)/4
Let l(o) = 1 - 39*o + 86*o - o**2 - 22*o - 24*o. Suppose -3*x - 15 = -0*x. Let b(n) = 6*n**2 - 5. Let h(d) = x*l(d) - b(d). Find v, given that h(v) = 0.
-5, 0
Let c(l) be the third derivative of l**6/120 + l**5/20 - 147*l**4/8 + 437*l**3/6 - 5507*l**2. Determine s so that c(s) = 0.
-23, 1, 19
Suppose -143*i = 113*i - 1024. Let t(d) be the first derivative of -2/3*d**3 + 0*d**2 + d**i - 2/5*d**5 - 34 + 0*d. Suppose t(p) = 0. Calculate p.
0, 1
Let h(x) be the second derivative of -x**4/72 + 47*x**3/9 + 191*x**2/4 + 681*x - 2. Factor h(a).
-(a - 191)*(a + 3)/6
Let m(x) be the second derivative of -x**5/50 - 8*x**4/5 + 379*x**3/15 - 66*x**2 - 10197*x. Factor m(h).
-2*(h - 6)*(h - 1)*(h + 55)/5
Let u(o) be the third derivative of -o**5/390 + 2261*o**4/78 - 5112121*o**3/39 - 30*o**2 - 4*o - 6. Factor u(p).
-2*(p - 2261)**2/13
Let x(c) be the third derivative of -13/24*c**4 - 17/120*c**6 + 1/3*c**3 + 2/5*c**5 - 2*c + 0 + 2/105*c**7 - 30*c**2. Determine d so that x(d) = 0.
1/4, 1, 2
Let s(m) be the first derivative of -m**6/18 - 2*m**5/15 + m**4 + 2*m**3 - 9*m**2/2 + 4946. Suppose s(t) = 0. Calculate t.
-3, 0, 1, 3
Let u(c) be the first derivative of c**8/448 + c**7/280 - c**6/160 - c**5/80 - 5*c**2/2 - 51. Let p(r) be the second derivative of u(r). Factor p(h).
3*h**2*(h - 1)*(h + 1)**2/4
Let q(g) be the second derivative of g**7/42 - 61*g**6/30 + 258*g**5/5 - 444*g**4 - 128*g. Factor q(v).
v**2*(v - 37)*(v - 12)**2
Let v be (6/(-3))/1 + 2 + 3. Suppose -137*q + 81*q - 25*q**2 - 15 + 91*q + 5*q**v = 0. Calculate q.
1, 3
Factor 429*n**2 + 245*n + 2*n**4 - 116*n**3 + 73*n + n**4 - 103*n**3 - 531*n.
3*n*(n - 71)*(n - 1)**2
Let j(x) be the second derivative of -6 + 40/3*x**3 - 5/2*x**4 + 7*x - 1/4*x**5 + 0*x**2. Find c such that j(c) = 0.
-8, 0, 2
Let l(q) be the second derivative of 125*q**5/2 + 1925*q**4/12 + 494*q**3/3 + 169*q**2/2 - 9*q + 1045. Find w, given that l(w) = 0.
-13/25, -1/2
Let o(b) be the third derivative of 0 + 2*b**3 - 46*b**2 + 0*b + 11/48*b**4 + 1/120*b**5. Determine y so that o(y) = 0.
-8, -3
Let c be 3381/414 - (-19244)/(-2856). Determine w, given that c*w**4 - 10/7*w**2 + 12/7*w + 0 + 2/7*w**5 - 2*w**3 = 0.
-6, -1, 0, 1
Let r(i) be the third derivative of -i**7/315 + 8*i**6/45 - 29*i**5/30 + 186*i**2 - 1. Factor r(m).
-2*m**2*(m - 29)*(m - 3)/3
Let x(r) = r**2 - 1. Let y(w) = w**2 - 26*w - 171. Let v = 154 - 140. Suppose -6*n + v*n = -24. Let z(l) = n*y(l) + 6*x(l). Factor z(s).
3*(s + 13)**2
Factor -38 + 19/2*k**2 + 1/2*k**3 - 2*k.
(k - 2)*(k + 2)*(k + 19)/2
Let 6 - p**4 - 47/4*p**3 - 61/4*p - 32*p**2 = 0. What is p?
-8, -3, -1, 1/4
Let l(s) be the second derivative of 0 + 2/3*s**3 - 16*s - 4/15*s**6 - 1/5*s**5 + 0*s**2 + 2/3*s**4. Determine w so that l(w) = 0.
-1, -1/2, 0, 1
Factor 0 - 1/10*n**3 - 12/5*n - 5/2*n**2.
-n*(n + 1)*(n + 24)/10
Let u = -1238433/5 + 247687.