3
Let o(k) = -4*k**3 + 12*k**2 + 16*k - 12. Let v(q) = 12*q**3 - 34*q**2 - 50*q + 33. Let m(j) = 11*o(j) + 4*v(j). Factor m(x).
4*x*(x - 3)*(x + 2)
Find l, given that -1960 + 5936*l + 6/5*l**3 - 842/5*l**2 = 0.
1/3, 70
Let r(m) = 2*m - 20. Let n be r(35). Factor -132*o + n*o**2 + 340*o - 4*o**3 + 5*o**4 - 160 - 122*o**2 - o**4.
4*(o - 2)**3*(o + 5)
Let d(y) be the first derivative of 2*y**3/27 - 28*y**2/9 + 64*y/3 - 995. Suppose d(m) = 0. What is m?
4, 24
Let p(s) be the third derivative of -s**5/105 + 3*s**4/7 + 230*s**3/21 - 8*s**2 - s + 60. Factor p(o).
-4*(o - 23)*(o + 5)/7
Let i(y) be the first derivative of 2*y**3/3 - 118*y**2 - 726*y + 1667. Suppose i(w) = 0. What is w?
-3, 121
Let t(w) be the third derivative of -w**8/2184 + 33*w**7/455 - 173*w**6/52 + 7201*w**5/390 - 584*w**4/13 + 768*w**3/13 + 1298*w**2 + 2*w. Factor t(i).
-2*(i - 48)**2*(i - 1)**3/13
Let h(g) be the second derivative of g**6/6 + 13*g**5 - 55*g**4/3 - 15600*g**3 + 324000*g**2 - 1517*g. Factor h(s).
5*(s - 10)**2*(s + 36)**2
Let z(f) be the first derivative of f**7/105 - f**6/20 + f**5/15 + 23*f**2/2 + 87. Let p(o) be the second derivative of z(o). Let p(m) = 0. What is m?
0, 1, 2
Let m(t) = -16*t**3 - 38*t**2 + 23*t + 73. Let c(d) = 3*d**3 - d**2 + d + 1. Let p(v) = -7*c(v) - m(v). Find b, given that p(b) = 0.
-1, 2, 8
Suppose -2 + 3 = 2*t + 5*d, -5*t = 5*d - 10. Let -58*x**4 + 118*x**3 - 74*x**3 - 2*x**5 - 30*x**2 + 77*x**t + 9*x**5 = 0. Calculate x.
0, 2/7, 3, 5
Suppose 2*u + 18*v - 19*v = 271, 0 = u + v - 131. Factor -2072 + u - 10*k - 106*k - 2*k**2 + 256.
-2*(k + 29)**2
Let o be 14/18*264/154. Determine w so that 8*w**3 + 36*w + 12 - 4*w**4 - o*w**5 + 104/3*w**2 = 0.
-3, -1, 3
Let y = 1/2947 - -2941/17682. Let b(l) be the second derivative of y*l**4 + 0 - 20*l + l**3 + 0*l**2. Suppose b(v) = 0. What is v?
-3, 0
Let l(v) be the first derivative of v**4/4 + 158*v**3/3 - 323*v**2/2 - 480*v + 3678. Factor l(o).
(o - 3)*(o + 1)*(o + 160)
Let y = -18 - -20. Let r(m) = 1 + 2*m**4 + 3*m**4 - 7*m**4 + 4*m**3. Let g(h) = -h**4 + h**3 + 1. Let u(d) = y*r(d) - 2*g(d). Factor u(q).
-2*q**3*(q - 3)
Let k(o) be the first derivative of 2*o**5/45 + 7*o**4/18 + 4*o**3/9 - 5324. Factor k(p).
2*p**2*(p + 1)*(p + 6)/9
Let a be (-3)/(-1*(-18)/24) - -42. Suppose -a*m + 24 = -14. Factor -m + k**3 - 3/2*k + 3/2*k**2.
(k - 1)*(k + 2)*(2*k + 1)/2
Let d be 920/104 + 2/13. Factor d*s**3 - 50*s - 11*s**3 - 35*s**2 - 3*s**3.
-5*s*(s + 2)*(s + 5)
Let x(p) be the second derivative of 9/50*p**5 + 3*p + 17/30*p**4 - 13/75*p**6 - 4/5*p**2 + 17 - 3/5*p**3. Solve x(m) = 0.
-1, -4/13, 1
Let v(z) = -2*z**2 + 62*z - 111. Let t be v(29). Suppose 0 = -l + 5*x + 5, t*l + 9 = -5*x + 4. Factor 2/9*m**5 + 10/9*m**3 - 4/9*m**2 + l*m - 8/9*m**4 + 0.
2*m**2*(m - 2)*(m - 1)**2/9
Suppose -4 = 58*c - 120. Let t(z) be the first derivative of 6*z - 5/3*z**3 + 12 + 13/2*z**c. Factor t(y).
-(y - 3)*(5*y + 2)
Let m = 1738 + -625679/360. Let d(z) be the third derivative of 0 + 1/15*z**5 + 16*z**2 - 2/3*z**4 - m*z**6 + 32/9*z**3 + 0*z. Factor d(l).
-(l - 4)**3/3
Let s = 419 + -235. Solve -s*m**3 + 9*m + 4 + 187*m**3 - 5*m**2 + m**4 - 12*m = 0.
-4, -1, 1
Let y(o) be the third derivative of o**8/112 + 33*o**7/490 - 31*o**6/280 - 17*o**5/28 + 12*o**4/7 - 10*o**3/7 - 563*o**2 + o. Determine g so that y(g) = 0.
-5, -2, 2/7, 1
Let y = 277/150 + -17/25. Let f(u) be the second derivative of 10*u - 4*u**2 + 4*u**3 + 0 + y*u**4. Factor f(v).
2*(v + 2)*(7*v - 2)
Let m(p) be the first derivative of -60 - 1/4*p**4 + 5/3*p**3 + 0*p - 2*p**2. Factor m(b).
-b*(b - 4)*(b - 1)
Let n(o) be the third derivative of o**5/180 - 50*o**3 - 10551*o**2. Solve n(s) = 0 for s.
-30, 30
Suppose 0 = 12*f - 16*f + 12. Factor 146*r**2 - 32*r**4 + 15*r + 20*r**3 + 14*r**2 + 4*r**5 + 4*r**f + 85*r.
4*r*(r - 5)**2*(r + 1)**2
Suppose -1/6*b**5 + 5/2*b**4 + 19/2*b**2 + 0 - 49/6*b**3 - 11/3*b = 0. Calculate b.
0, 1, 2, 11
Let h(g) be the first derivative of g**4 + 20*g**3/3 - 16*g**2 - 192*g - 1459. Let h(x) = 0. What is x?
-4, 3
Let s(l) be the first derivative of -l**7/168 + 5*l**6/18 - 77*l**5/24 - 605*l**4/12 + 43*l**3/3 - 172. Let i(x) be the third derivative of s(x). Factor i(f).
-5*(f - 11)**2*(f + 2)
Suppose 618 = -38*m + 694. Let b(z) be the first derivative of 2/3*z**3 + 72*z - 12*z**m + 18. Factor b(d).
2*(d - 6)**2
Let l(g) be the second derivative of 5*g**4/12 + 45*g**3/2 + 230*g**2 + 2*g + 66. Factor l(u).
5*(u + 4)*(u + 23)
Let l be ((-176)/24 + 8)*363. Let d = l + -240. Factor 1/3*u**4 - 1/3*u + 1/3 + 2/3*u**3 - 2/3*u**d - 1/3*u**5.
-(u - 1)**3*(u + 1)**2/3
Suppose 3*b + r - 1 = -8, 2*b + 4*r = -28. Suppose -1/2*f**3 + 1/6*f**5 - 2/3*f - 4/3*f**2 + b + 1/3*f**4 = 0. Calculate f.
-2, -1, 0, 2
Let k(t) be the second derivative of -t**4/18 + 379*t**3/9 - 500*t**2 + 12659*t. Find b such that k(b) = 0.
4, 375
Let q be ((-186)/(-14570))/(2/96). Let f = q - 10/47. Factor 0 - 4/15*z**2 + 0*z - f*z**4 - 14/15*z**3.
-2*z**2*(z + 2)*(3*z + 1)/15
Let r(a) be the first derivative of a**3/5 - 213*a**2/10 + 42*a + 4701. Factor r(j).
3*(j - 70)*(j - 1)/5
Suppose 5*p - 22 = -3*w - 4, -30 = -5*w + p. Let m be ((-8)/(-10))/(7*w/105). Suppose -3*b + 96 + m*b - 96 - b**4 + b**2 + b**3 = 0. What is b?
-1, 0, 1
Determine m, given that 34/5*m - 12 + 2/5*m**3 + 24/5*m**2 = 0.
-10, -3, 1
Suppose -105 = -27*h + 6*h. Factor -3*o**4 - 53*o + 32*o + 25*o - 5*o**3 + 2*o**5 + 3*o**2 - o**h.
o*(o - 4)*(o - 1)*(o + 1)**2
Suppose -15*s = -20*s + 2*c + 17, -3*c - 3 = 0. Let b(w) be the third derivative of -1/180*w**4 + 0*w + 0 + 0*w**s - 8*w**2 - 1/450*w**5. Factor b(t).
-2*t*(t + 1)/15
Suppose 12*w + 2 = 38. Factor i**4 - w*i**4 + i**5 - 4*i**3 - 95 + 95 - i**4.
i**3*(i - 4)*(i + 1)
Let f(p) be the first derivative of 43 - 27/4*p - 63/16*p**2 - p**3 - 3/32*p**4. Determine n so that f(n) = 0.
-3, -2
Let m(b) be the third derivative of 55*b**2 + 4/105*b**7 + 0 + 1/168*b**8 - 1/15*b**5 - 2/3*b**3 + 1/15*b**6 + 0*b - 5/12*b**4. Find p, given that m(p) = 0.
-2, -1, 1
Let u = -12 + 16. Suppose -4*x - u*l = 0, -l = 3*x + 4*l + 6. Factor 4*h**3 - 3*h**5 - 4*h**3 - 3*h**2 + 6*h**2 + 3*h**3 - x*h**4.
-3*h**2*(h - 1)*(h + 1)**2
Let v(a) be the first derivative of 5*a**4/24 - 5*a**3/3 + 5*a**2 + 35*a + 99. Let r(j) be the first derivative of v(j). Let r(w) = 0. What is w?
2
Let r = 203 - 287. Let g be (-126)/r*(-1)/(-1). Factor g*d + 3/2 + 3/8*d**2.
3*(d + 2)**2/8
Let w(t) = -t**2 + 952*t - 933. Let b(u) = -4*u**2 + 4762*u - 4659. Let v(j) = -2*b(j) + 11*w(j). Factor v(r).
-3*(r - 315)*(r - 1)
Let i(v) be the first derivative of -2*v**5 - 69*v**4/2 - 74*v**3 - 35*v**2 + 24*v + 467. What is p in i(p) = 0?
-12, -1, 1/5
Let f(m) be the third derivative of -m**7/1995 + 13*m**6/1140 + 2*m**5/285 - 13*m**4/57 + 190*m**2 + 4*m. Suppose f(g) = 0. What is g?
-2, 0, 2, 13
Factor 55*c - c**5 - 109*c**3 + 252*c**2 - 5217*c**4 + 5235*c**4 - 251*c.
-c*(c - 7)**2*(c - 2)**2
Let m(y) be the third derivative of y**8/336 + 29*y**7/420 + 3*y**6/20 - 41*y**5/120 - 13*y**4/24 + 1459*y**2 - 2*y. Solve m(z) = 0.
-13, -2, -1/2, 0, 1
Suppose -5*v + 2*v - 5*d = -24, -3*v + d = -6. Solve v*r**4 + 12*r + 16*r**3 - 108*r + r**3 + r**3 = 0 for r.
-4, 0, 2
Let i(p) be the third derivative of -p**8/1008 + 19*p**7/630 + 41*p**6/360 + 7*p**5/60 + 2*p**2 + 967*p - 1. Determine y, given that i(y) = 0.
-1, 0, 21
Let n(l) be the first derivative of 10 - 4/5*l**3 - 2/5*l - 7/5*l**2. Solve n(g) = 0.
-1, -1/6
Let p(y) be the first derivative of -5*y**3/3 - 10875*y**2/2 + 10880*y - 2133. Suppose p(s) = 0. Calculate s.
-2176, 1
Suppose 1880 + 122086*g**2 - 244174*g**2 + 122090*g**2 - 134*g = 0. What is g?
20, 47
Let l be 22*14 - (3 - -5)/4. Suppose -l = -13*s + 4*s. Factor s*f**4 + 8 - 11*f**4 - 19*f**4 - 12*f**2 - 4*f**3 + 4*f.
4*(f - 2)*(f - 1)*(f + 1)**2
Let f(i) be the third derivative of 1/160*i**6 - 1/560*i**7 + 24*i**2 + 0*i**4 + 0*i**3 + 3/160*i**5 - 3*i + 0. Factor f(y).
-3*y**2*(y - 3)*(y + 1)/8
Let y(u) = 6*u**4 + 24*u**3 + 92*u**2 + 164*u + 76. Let l(j) = j**4 - j**2 + j - 5. Let n(w) = 4*l(w) - y(w). Factor n(z).
-2*(z + 2)**3*(z + 6)
Let w = 59221/306 - 1841/153. Factor 297/2*t + w - 63/2*t**2 + 3/2*t**3.
3*(t - 11)**2*(t + 1)/2
What is o in 6*o**2 + 0*o**5 + 35 - o**5 + 2*o**3 - 3*o**4 - 58 + 20 - o = 0?
-3, -1, 