+ 1)*(w + 6)
Let a(q) = -7*q - 4. Let y be a(-1). Suppose -y*s + 6 = 2*v, 3 = -3*v - 6. Find z, given that 0 + 1/5*z**3 - z**2 + 3/5*z + 1/5*z**s = 0.
-3, 0, 1
Let v(f) be the third derivative of -8/5*f**3 + 0 - 120*f**2 + 0*f - 1/75*f**5 - 4/15*f**4. Factor v(k).
-4*(k + 2)*(k + 6)/5
Let t(i) = -i**2 - 1. Let q be (-338)/(-104) + (-2)/8. Let h(o) = 8*o**2 + 7*o + 17. Let a(n) = q*h(n) + 21*t(n). Factor a(j).
3*(j + 2)*(j + 5)
Let r(v) be the third derivative of -v**7/42 + 49*v**6/3 - 4290*v**5 + 1436500*v**4/3 - 10985000*v**3/3 - 2*v**2 + 410*v. Factor r(s).
-5*(s - 130)**3*(s - 2)
Let u(q) be the first derivative of q**7/280 - q**6/15 - q**5/40 + q**4 + 7*q**3/3 - 4. Let m(p) be the third derivative of u(p). Factor m(s).
3*(s - 8)*(s - 1)*(s + 1)
Suppose 21 - 1/5*y**3 + 137/5*y + 31/5*y**2 = 0. What is y?
-3, -1, 35
Let i(t) be the third derivative of t**5/60 - 11*t**4/12 - 23*t**3/6 + 2*t**2 - 446. Factor i(s).
(s - 23)*(s + 1)
Let h = -245 - -251. Let k(f) be the third derivative of 2*f**2 + 0*f**3 + 0*f + 0 + 1/72*f**4 + 0*f**5 - 1/360*f**h. What is t in k(t) = 0?
-1, 0, 1
Factor 897*t - 330*t**2 + 1389*t**2 - 4 - 676*t**2 + 2 - 132*t.
(t + 2)*(383*t - 1)
Suppose -15*x - 15562 = -43882. Let g = -1886 + x. Factor -4/5*v**g + 0 - 8/5*v + 4/5*v**3.
4*v*(v - 2)*(v + 1)/5
Suppose -9 = -3*t + 3*p, 20*t = 19*t - 4*p + 3. Determine u so that -729*u + 0*u**2 + u**2 + t*u**2 + 705*u = 0.
0, 6
Factor 54/5*b - 76/5*b**2 + 44/5*b**3 - 2/5*b**5 - 6/5*b**4 - 14/5.
-2*(b - 1)**4*(b + 7)/5
Let v(n) be the second derivative of 0 + 3/2*n**2 + n**3 + 1/30*n**5 + 10*n + 1/3*n**4. Let b(s) be the first derivative of v(s). Factor b(h).
2*(h + 1)*(h + 3)
Let u(s) be the third derivative of s**5/120 + 169*s**4/96 + 7*s**3/2 + s**2 + 2034*s. Find t such that u(t) = 0.
-84, -1/2
Let v be 8/(-2) - 34/((-272)/56). Factor 26/7*n + 16/7*n**2 + 12/7 + 2/7*n**v.
2*(n + 1)**2*(n + 6)/7
Let d(x) = -22*x**3 - 60*x**2 + 96*x - 16. Let n(c) = c**3 + 2*c**2 - 2*c. Let q(b) = -d(b) - 2*n(b). Suppose q(s) = 0. Calculate s.
-4, 1/5, 1
Factor -2/9*y**3 + 142/9*y**2 + 608/9 + 752/9*y.
-2*(y - 76)*(y + 1)*(y + 4)/9
Suppose -6*y + 90 = 78. Factor 5*h**3 - 5*h**4 + 76*h - 18*h**4 + 9*h**3 + 36 + 53*h**y + 24*h**4.
(h + 1)*(h + 2)**2*(h + 9)
Let j(x) be the first derivative of -x**5/15 - 81*x**4/4 - 77. Solve j(a) = 0 for a.
-243, 0
Let l(k) = -k**4 + 13*k**3 - 105*k**2 + 96*k + 5. Let x(r) = -14*r**3 + 104*r**2 - 96*r - 4. Let m(t) = -4*l(t) - 5*x(t). Find o such that m(o) = 0.
-8, 0, 3/2, 2
Let c(q) = -q + 22. Let n be c(18). Suppose 2*d - n = d. Let 84*m**4 - 42*m**d - 38*m**4 - 8*m**2 + 4 = 0. What is m?
-1, 1
Let p = -56203 - -224815/4. Factor 3/4*m**3 + 0 + 0*m - p*m**2.
3*m**2*(m - 1)/4
Let r be (4 - 176/36)/(10 - 416/39). Suppose 7/3*l**2 + l**4 - r*l + 10/3*l**3 - 4/3 = 0. What is l?
-2, -1, 2/3
Let j = 369 - 351. Find g, given that 10*g**4 - 10*g**2 - 8*g**2 - 25*g**4 - 9*g**3 + 24*g + j*g**4 = 0.
-2, 0, 1, 4
Factor 92*w + 1378/15 + 2/15*w**2.
2*(w + 1)*(w + 689)/15
Let z be 115/45 - (-8)/18. Suppose -67*l + 106*l - 10*l**4 + 13*l**4 - 15*l**z - 9*l**2 + 30 = 0. Calculate l.
-1, 2, 5
Let c(s) be the first derivative of s**7/112 + s**6/40 - s**4/16 - s**3/16 + 49*s + 66. Let l(z) be the first derivative of c(z). Factor l(k).
3*k*(k - 1)*(k + 1)**3/8
Let j(d) = -d**2 - 268*d + 144. Let k(p) = 2*p**2 + 402*p - 204. Let h(m) = 8*j(m) + 5*k(m). Factor h(o).
2*(o - 66)*(o - 1)
Suppose -152 = -72*r + 34*r. Let j(q) be the first derivative of -8/3*q**3 + 0*q + 9*q**r - 14 + 0*q**2. Factor j(p).
4*p**2*(9*p - 2)
Let r(s) be the second derivative of -s**6/72 + s**5/8 + 5*s**4/6 + 53*s**3/6 - 2*s - 70. Let c(l) be the second derivative of r(l). Let c(z) = 0. Calculate z.
-1, 4
Let s be 4/3 - 36/(-54). Suppose -5*a + 2 + 17 = s*g, -2*g + 3*a = 5. Factor -2/3 - 2/3*n**3 + 2/3*n**g + 2/3*n.
-2*(n - 1)**2*(n + 1)/3
Let v(d) = 5*d**3 + 20*d**2 + 45*d + 15. Suppose 22 = 12*u + 10. Let o(l) = l**2 - l - 1. Let r(p) = u*v(p) + 15*o(p). Factor r(s).
5*s*(s + 1)*(s + 6)
Factor -9628/5*d - 11587298/5 - 2/5*d**2.
-2*(d + 2407)**2/5
Let y be (-10)/45*-3 + 68/6. Solve -c**2 - c**2 - 4 + c**2 + y*c - 7*c = 0 for c.
1, 4
Let a = 25885 - 25867. Factor 3/2*o**3 - 21 - a*o**2 - 81/2*o.
3*(o - 14)*(o + 1)**2/2
Let q(j) be the third derivative of 0 + 1/540*j**6 + 121*j**4 + 0*j - 10648*j**3 - 11/15*j**5 + 165*j**2. Factor q(a).
2*(a - 66)**3/9
Let z(k) = -3*k - 2. Let r be (4 - 4) + 1 - 3. Let o be z(r). Factor -92*v + 2*v**3 + o + 86*v + 0.
2*(v - 1)**2*(v + 2)
Let x be ((-1287)/42 + 30)*(-1 - 4/24). Determine w, given that 9/4*w - 5/4 - x*w**2 - 1/4*w**3 = 0.
-5, 1
Let 0 - 10/7*i**5 + 256/7*i**3 + 2*i**4 - 96/7*i + 136/7*i**2 = 0. Calculate i.
-4, -1, 0, 2/5, 6
Let u(h) be the second derivative of 4*h**6/15 - 167*h**5/10 + 217*h**4/3 - 193*h**3/3 - 78*h**2 - 745*h + 3. Let u(j) = 0. What is j?
-1/4, 1, 2, 39
Determine r, given that 28*r - 120*r**2 + 179*r - r**3 - 246 - 18*r + 138*r + 40*r = 0.
-123, 1, 2
Let n(t) be the second derivative of -t**8/2800 + t**7/210 - t**6/48 + 51*t**4/4 + 81*t + 1. Let z(i) be the third derivative of n(i). Factor z(o).
-3*o*(2*o - 5)**2/5
Let i(q) be the second derivative of q**4/3 + 1000*q**3/3 - 1002*q**2 + 1831*q. Suppose i(r) = 0. Calculate r.
-501, 1
Suppose -11*w + 10*w - 62 = -32*w. Let h(o) be the first derivative of 3/4*o**4 + 29 + 0*o + 0*o**3 - 3/2*o**w. Let h(v) = 0. What is v?
-1, 0, 1
Let d be (((-100)/90)/(-5))/(33/297). Determine g, given that 8/5 + 26*g**d - 20*g**3 - 56/5*g = 0.
2/5, 1/2
Let y be 12159/1930 - 42/15. Factor 19/2*a**2 - 5/4*a**3 - 19/4*a - y.
-(a - 7)*(a - 1)*(5*a + 2)/4
Let o = 491 + -8337/17. Factor -2/17*t**4 - o*t**3 + 0 + 0*t - 12/17*t**2.
-2*t**2*(t + 2)*(t + 3)/17
Let x(y) be the second derivative of y**5/70 + 92*y**4/21 + 901*y**3/21 + 1074*y**2/7 + 2939*y. Factor x(o).
2*(o + 2)*(o + 3)*(o + 179)/7
Suppose -70*a**2 + 24*a**4 + 30*a**3 + 3*a**5 + 0*a**3 - 84*a - 2*a**5 + 11*a**3 + 88 = 0. Calculate a.
-22, -2, 1
Let d(r) be the first derivative of -27*r**4/4 - 17*r**3 + 87*r**2/2 - 9*r + 403. Suppose d(j) = 0. What is j?
-3, 1/9, 1
Let f(i) = -i**2 - 12*i - 23. Let m be f(-7). Suppose 10*z - 4*z - m = 0. Factor -72*b**2 + 147*b**z - 71*b**2 - 4.
4*(b - 1)*(b + 1)
Let r(a) be the second derivative of -a**5/20 + 19*a**4 - 151*a**3/2 + 113*a**2 + 5*a - 73. Suppose r(s) = 0. Calculate s.
1, 226
Suppose 155*g = 488 + 287. Let r(u) be the second derivative of 0 + 1/50*u**6 - 3/100*u**g + 0*u**4 + 0*u**3 - 23*u + 0*u**2. Factor r(z).
3*z**3*(z - 1)/5
Let -91/5*u**2 + 44/5*u**3 + 46/5*u + 0 + 1/5*u**4 = 0. Calculate u.
-46, 0, 1
Let n(f) = 126*f - 1002. Let j(h) = 189*h - 1502. Let b(c) = 5*j(c) - 8*n(c). Let p be b(8). Factor -24/5*q + 18/5 + 6/5*q**p.
6*(q - 3)*(q - 1)/5
Suppose -13*b = 13*b - 15*b. Let k(i) be the second derivative of 0 + 2/5*i**5 + 0*i**2 + b*i**3 + 17*i + 1/3*i**4 + 2/15*i**6. What is r in k(r) = 0?
-1, 0
What is u in -37/5*u**2 + 0 - 11/5*u**4 - 14/5*u - 1/5*u**5 - 33/5*u**3 = 0?
-7, -2, -1, 0
Let l(y) be the third derivative of -y**8/784 - 17*y**7/490 + 7*y**6/40 + 197*y**5/140 - 33*y**4/7 - 342*y**3/7 + 65*y**2. What is g in l(g) = 0?
-19, -2, 3
Determine l, given that 2640/7*l**3 + 3/7*l**4 + 2302128/7 + 586056/7*l**2 + 2312640/7*l = 0.
-438, -2
Let p(y) be the second derivative of y**7/1575 + y**6/900 - y**5/225 - 21*y**2 - 4*y + 2. Let b(k) be the first derivative of p(k). Factor b(z).
2*z**2*(z - 1)*(z + 2)/15
Solve 1617*v**5 - 588 + 1247*v**5 - 457*v**4 - 35495*v**2 - 1328*v**4 - 399*v**4 + 3220*v**5 - 8456*v - 35411*v**3 = 0.
-7/6, -2/13, 3
Let j(h) be the first derivative of -8/5*h**5 + 69 + 0*h**2 + 0*h + 0*h**3 - 3/2*h**4 - 1/3*h**6. Find w, given that j(w) = 0.
-3, -1, 0
Let p(t) be the first derivative of t**4/6 - 8*t**3/9 - 19*t**2/3 - 28*t/3 + 2858. Factor p(r).
2*(r - 7)*(r + 1)*(r + 2)/3
Let r be (34/(-85))/(2/(-20)). Suppose r*b + o = 12, 0 = 2*b - b + 5*o + 16. Factor 22*k + 3*k**2 - 22*k + 1 - b*k**2.
-(k - 1)*(k + 1)
Let r be 1/(2/(-5)*(32 + -2)*-2). Let d(x) be the third derivative of 0*x + r*x**4 + 0 + 1/360*x**5 + 0*x**3 + 23*x**2. Factor d(o).
o*(o + 6)/6
Let u(f) be the first derivative of f**5/10 + 5*f**4/6 + 2*f**3/3 - 8*f**2 + 182*f - 192. Let d(v) be the first derivative of u(v). Fact