 42*j**2 + 26*j - 2. Let w(h) = -h**5 - h**3 - h**2 + h - 1. Let v(g) = -l(g) + 2*w(g). Suppose v(c) = 0. Calculate c.
-3, 0, 1, 2
Let z = -31 - -36. Suppose 2*l + 0*l + 20 = 4*r, -z*r = 4*l + 1. Factor 17 + 26 + 10*i**2 - 53 + 5*i - 5*i**r.
-5*(i - 2)*(i - 1)*(i + 1)
Let f be (-268)/(-67) - (-30)/12*28/(-18). Let j(u) be the first derivative of 23 - 2*u - 7/6*u**2 - f*u**3. Suppose j(k) = 0. What is k?
-6, -1
Factor 16/7*o**2 + 604/7 + 2420/7*o.
4*(o + 151)*(4*o + 1)/7
Suppose 2*p = -3*a + 104, -4*p = -5*a - 55 + 199. Let t(y) = -4*y + 130. Let k be t(a). Factor -2/11*j**k + 8/11*j - 6/11.
-2*(j - 3)*(j - 1)/11
Let d = 18204/36413 - -5/72826. Factor 3 + d*q**2 + 7/2*q.
(q + 1)*(q + 6)/2
Let r(z) be the second derivative of -4*z**7/21 - 5*z**6/3 - z**5 + 95*z**4/6 + 104*z**3/3 + 20*z**2 - 205*z - 7. Find o such that r(o) = 0.
-5, -2, -1, -1/4, 2
Let v(k) be the first derivative of 25*k**4/2 - 1160*k**3/3 + 669*k**2 - 396*k + 1721. Factor v(y).
2*(y - 22)*(5*y - 3)**2
Let h(i) be the first derivative of i**7/2520 - i**6/216 + i**5/180 + i**4/9 - 3*i**3 + 2*i - 74. Let s(w) be the third derivative of h(w). Factor s(a).
(a - 4)*(a - 2)*(a + 1)/3
Let x(d) be the second derivative of -d**4/20 + 18*d**3/5 - 78*d**2 + 2379*d. Suppose x(n) = 0. Calculate n.
10, 26
Let r = -324 + 230. Let q = 97 + r. Factor 10*p**q + 17*p + 15*p + 16*p**2 - 8*p**3.
2*p*(p + 4)**2
Let p(o) be the third derivative of -2*o**7/105 + 151*o**6/30 - 146*o**5/3 - 68*o**2 + 14. Factor p(k).
-4*k**2*(k - 146)*(k - 5)
Let -11519 + 2*n**4 - 16*n**2 - 18*n + 11551 + 6*n**3 - 6*n = 0. Calculate n.
-4, -2, 1, 2
Suppose 2*j - 9 + 3 = -3*c, -2*j + 2*c - 4 = 0. Suppose -21*l + 34*l - 39 = j. Suppose -y + 0 - 3/2*y**2 - 1/2*y**l = 0. What is y?
-2, -1, 0
Factor 0 - 730/17*k + 2/17*k**2.
2*k*(k - 365)/17
Let u be (-8)/36 + 2 + (-59278)/18. Let d = -3287 - u. Solve 2/9*l**5 + 16/9 + 2/9*l**3 - d*l - 8/9*l**4 + 28/9*l**2 = 0 for l.
-2, 1, 2
Let m be 1278/42 - 31 - (7 + -10 - (-2)/7). Suppose -6/7*b**3 - 27/7*b**2 + 18/7*b + m = 0. Calculate b.
-5, -1/2, 1
Let l = 195 - 117. Let i = l + -52. Factor -i*x**2 - 9*x + 21*x + 22*x**2.
-4*x*(x - 3)
Let u = 821/711 - 21/79. Let d = -5651/288 - -635/32. Factor -2/9*x**3 + d*x + 8/9*x**2 - u.
-2*(x - 4)*(x - 1)*(x + 1)/9
Let f be -6 + (7 - -4) - (182/(-98) - -2). Find q such that -f*q - 32/7 - 2/7*q**2 = 0.
-16, -1
Let c(r) be the second derivative of 12/7*r**2 + 0 + 218*r + 33/140*r**5 + 18/7*r**3 - 3/2*r**4. Determine n so that c(n) = 0.
-2/11, 2
Let p(z) be the third derivative of 4/3*z**3 - 4/21*z**4 + 1/210*z**5 + 2*z**2 + 0*z + 15. Solve p(g) = 0.
2, 14
Let q(b) be the first derivative of b**4/2 + 670*b**3/3 + 27888*b**2 - 56448*b - 4268. Find d, given that q(d) = 0.
-168, 1
Let g(p) be the third derivative of p**5/30 + 155*p**4/12 - 158*p**3 + 57*p**2 + 18. Factor g(h).
2*(h - 3)*(h + 158)
Let j(d) be the third derivative of 2*d**7/105 + 4*d**6/15 + 8*d**5/5 + 16*d**4/3 + 32*d**3/3 - 998*d**2. Find k, given that j(k) = 0.
-2
Factor 0*h**5 - 5*h**3 - 38384*h**4 + 38388*h**4 + 2*h**3 - h**5.
-h**3*(h - 3)*(h - 1)
Factor 0 - 138*o + 3/4*o**3 + 63/2*o**2.
3*o*(o - 4)*(o + 46)/4
Let o(x) be the third derivative of -8/3*x**3 + 1/15*x**5 + 8*x**4 + 0*x + 4*x**2 + 2 - 2/5*x**6. Let o(j) = 0. What is j?
-2, 1/12, 2
Let s(r) be the third derivative of -4*r**8/63 + 32*r**7/63 + 203*r**6/90 + 19*r**5/6 + 7*r**4/4 + 2*r**2 - 1699*r. Find c such that s(c) = 0.
-3/4, -1/2, 0, 7
Let a(n) = -5*n**2 + 13140*n + 13043. Let j(k) = 15*k**2 - 39385*k - 39128. Let o(v) = 8*a(v) + 3*j(v). Factor o(r).
5*(r - 2608)*(r + 1)
Let r(n) be the third derivative of 7*n**5/15 - 449*n**4/6 + 128*n**3/3 + 1085*n**2. Find t such that r(t) = 0.
1/7, 64
Let v(n) = 5*n**3 + 11*n**2 - 7*n. Let a(p) = -3*p**2 - 5*p**3 + 4*p - 3*p**2 + p**3 + p**3. Let f(m) = -7*a(m) - 4*v(m). Determine k so that f(k) = 0.
0, 2
Let w(o) = -o - 1. Let q(h) = 6*h - 7. Let c be q(4). Let r(t) = c + 13*t + 2*t**2 - 10*t - 12. Let j(m) = r(m) + 5*w(m). Factor j(y).
2*y*(y - 1)
Let o(g) be the first derivative of g**4/26 + 34*g**3/13 + 504*g**2/13 + 216*g - 9654. What is s in o(s) = 0?
-39, -6
Let b(i) = i**3 - 4*i**2 - 10*i + 4. Let u be b(6). Factor 41*n - 3 - 40*n - 13*n**2 - n**3 + u*n**2.
-(n - 3)*(n - 1)*(n + 1)
Factor 0 + 42*y**3 + 45*y - 177/2*y**2 + 3/2*y**4.
3*y*(y - 1)**2*(y + 30)/2
Let n(d) be the first derivative of d**6/10 - 27*d**5/25 - 3*d**4/20 + 9*d**3/5 - 1080. Solve n(r) = 0.
-1, 0, 1, 9
Let t(n) = -n**2 + 20 - n**3 + 15 - n - 36. Let c(l) = -4*l + 5*l**3 + l**4 - 2*l**2 + 3*l**4 + 0*l + l. Let f(i) = -3*c(i) - 3*t(i). What is z in f(z) = 0?
-1, -1/2, 1
Let q(d) be the third derivative of d**8/336 + 3*d**7/70 - 23*d**6/60 + 37*d**5/30 - 17*d**4/8 + 13*d**3/6 + 2*d**2 + 86. Factor q(n).
(n - 1)**4*(n + 13)
Suppose -2*g - 5*x + 31 = 2*g, 5*g = 2*x + 14. Suppose 3*s = -2*t - 2, g*t + 6*s = 2*s. Factor 11*v - 21 + 21*v - 5 - 38 - 4*v**t.
-4*(v - 4)**2
Let w(t) be the third derivative of t**7/3780 + t**6/270 + t**5/45 - 9*t**4/8 + t**3/6 - t**2 - 24*t. Let v(y) be the second derivative of w(y). Factor v(f).
2*(f + 2)**2/3
Factor 3/4*b**4 + 945/2*b**2 - 129/4*b**3 - 2499*b + 2058.
3*(b - 14)**3*(b - 1)/4
Let j(s) be the first derivative of 48/5*s**5 + 1652/3*s**3 + 1372*s + 1323*s**2 + 141 + 106*s**4 + 1/3*s**6. Solve j(f) = 0 for f.
-7, -2, -1
Suppose -2/9*z**2 + 4132/9 + 2062/9*z = 0. Calculate z.
-2, 1033
Suppose -1306/5*m**2 + 0 - 546/5*m**3 - 688/5*m + 74/5*m**4 + 2/5*m**5 = 0. Calculate m.
-43, -1, 0, 8
Let j be 4 + (44 - 2)*21/252. Factor 0 + 6*t + j*t**2 + 3/2*t**3.
3*t*(t + 1)*(t + 4)/2
Find v such that -3/4*v**4 - 243/2 - 75/4*v**3 - 423/4*v**2 - 837/4*v = 0.
-18, -3, -1
Let t = -210496 + 210498. Factor 3/2 - 1/4*n**t + 1/4*n.
-(n - 3)*(n + 2)/4
Solve 3163*p**4 + 2*p**5 - 1589*p**4 + 28*p**3 - 1604*p**4 = 0.
0, 1, 14
Let j(i) = 2*i**2 + 17*i + 72. Let h be j(-3). Factor -h*d**2 + 90*d - 6*d**3 + 97 - 97 + 3*d**3.
-3*d*(d - 2)*(d + 15)
Let n(t) = 11*t**3 - t**2 - 21*t + 21. Let q be n(1). Suppose -o + 15 = q. Factor -o - 5/4*x**3 - 45/4*x - 15/2*x**2.
-5*(x + 1)**2*(x + 4)/4
Let k(u) = -u**2 + 22*u + 43. Let n be 644/((-21)/(-3))*2/8. Let d be k(n). Factor d*x + 13*x**2 - 8*x**2 - 10*x**2.
-5*x*(x - 4)
Let w(r) = 0 + 8 - 6 + 3*r**2 + r. Let y(o) = 10*o**2 + 2*o + 7. Suppose -31*t = -5*f - 30*t + 34, -4*t - 3 = -f. Let u(v) = f*w(v) - 2*y(v). Factor u(b).
b*(b + 3)
Let b(y) be the second derivative of 2*y**6/15 + 9*y**5/20 + 2*y**4/3 - 11*y. Let a(o) = 4*o**4 + 8*o**3 + 8*o**2. Let g(x) = 3*a(x) - 4*b(x). Factor g(n).
-4*n**2*(n + 1)*(n + 2)
Let x = -4977 + 39817/8. Suppose 4*c + 2 = 10. Find v, given that -x*v**c - 1/4 + 3/8*v = 0.
1, 2
Let b(x) be the second derivative of 1/50*x**5 + 0*x**3 + 1/210*x**7 - 14 - 1/50*x**6 - 2*x + 0*x**2 + 0*x**4. Determine d so that b(d) = 0.
0, 1, 2
Let v = 15771244 - 8800351633/558. Let b = -4/279 + v. Let 6*r**2 + b - 57/4*r = 0. Calculate r.
3/8, 2
Let w = -6 - -8. Suppose -3*d - w*h = 0, -5*d + 3*h + h + 22 = 0. Let -10*x**3 + 15*x**d - 14*x + 2*x**4 + 5 + 0*x**2 + 3*x**2 - 1 = 0. Calculate x.
1, 2
Suppose -243 + 198 = -132*j + 615. Let o(f) be the third derivative of 0 + 0*f - 2/165*f**j - 13/264*f**4 - 1/1320*f**6 + 3*f**2 - 1/11*f**3. Factor o(k).
-(k + 1)**2*(k + 6)/11
Let v(u) be the first derivative of -2/25*u**5 - u**4 + 0*u + 0*u**2 + 16 + 0*u**3. Factor v(c).
-2*c**3*(c + 10)/5
Let t(n) be the second derivative of n**4/12 - 207*n**3 + 385641*n**2/2 - 2*n - 32. Determine k, given that t(k) = 0.
621
Factor -3/5*m**2 - 141/5*m + 0.
-3*m*(m + 47)/5
Let f(p) be the third derivative of p**6/600 + 577*p**5/25 + 665858*p**4/5 + 6147201056*p**3/15 - 3296*p**2. Factor f(n).
(n + 2308)**3/5
Let g(m) = m**3 - 9*m**2 + 28*m - 15. Let k be g(5). Suppose k = 83*l - 224. Factor -6/7*z**l + 0*z**2 + 0 + 2/7*z - 4/7*z**4.
-2*z*(z + 1)**2*(2*z - 1)/7
Suppose m = 4*m - 12. Suppose 2*x - g = 3, -m*x + 6 + 7 = 5*g. Suppose -6*d**x + 9*d**2 - 4*d**2 - 6*d = 0. What is d?
-6, 0
Suppose 5*b + 13 = l - 8, 2 = -3*l + 2*b. Let y(o) = 7*o**3 + 15*o**2 - 22*o. Let a(s) = -20*s**3 - 45*s**2 + 65*s. Let k(v) = l*a(v) - 11*y(v). Factor k(w).
3*w*(w - 1)*(w + 6)
Suppose 4*a = 5*x + 149, 0 = -2*a + 4*x - x + 77. Let -20*r**2 - a*r + 19*r + 22*r**2 = 0. Calculate r.
0,