, 1
Factor 128*q - 26*q**3 + 2*q**4 + 8*q**3 + 7*q**3 - 3*q**3 + 6*q**3 - 32*q**2.
2*q*(q - 4)**2*(q + 4)
Let k(i) = 3*i + 10*i - 13*i - 1 + 3*i**2. Let x be k(1). Find h, given that 2/5 - 1/5*h - 1/5*h**x = 0.
-2, 1
Let l(a) be the second derivative of 49/16*a**2 + 1/96*a**4 + 0 - 7/24*a**3 + 17*a. Factor l(m).
(m - 7)**2/8
Let o(p) be the second derivative of 10*p**4 + 20*p + 80/3*p**3 + 1/6*p**6 + 0 + 2*p**5 + 40*p**2. Solve o(a) = 0 for a.
-2
Let m(k) = -k**2 + 4*k + 17. Let u be m(6). Suppose -l + 4*f - u*f + 1 = 0, -5*f = -l + 7. Determine i, given that 24/7*i + 2/7*i**3 - 12/7*i**l - 16/7 = 0.
2
Let w(r) be the first derivative of -2*r**6/3 - 124*r**5 - 8110*r**4 - 197880*r**3 - 546210*r**2 - 530604*r - 542. Factor w(n).
-4*(n + 1)**2*(n + 51)**3
Let x = -104 - -106. Let u(z) be the second derivative of 0*z**x + 3*z + 0 + 1/30*z**4 - 1/30*z**3 - 1/100*z**5. Factor u(q).
-q*(q - 1)**2/5
Let n(w) be the first derivative of 2*w**3/3 + 39*w**2 - 164*w - 154. Factor n(m).
2*(m - 2)*(m + 41)
Let r(d) be the second derivative of -9*d**4/4 - 10*d**3 - 6*d**2 + 26*d. Factor r(v).
-3*(v + 2)*(9*v + 2)
Let m(n) be the second derivative of n**4/102 + 71*n**3/51 + 22*n - 1. Factor m(j).
2*j*(j + 71)/17
Let a(u) = 3*u - 19. Let k be a(11). Factor k*p + 6 + 15*p**2 - 6*p + 6*p + 7*p.
3*(p + 1)*(5*p + 2)
Let r be (-24)/(-54) - 7/(-126)*82. Let m(k) be the second derivative of 0*k**2 + k + 4/9*k**3 + 1/30*k**r + 2/9*k**4 + 0. Determine a, given that m(a) = 0.
-2, 0
Let n(l) = -l + 1. Let s(a) = 4*a**2 - 98*a - 21. Let y(b) = -6*n(b) + 2*s(b). Solve y(g) = 0 for g.
-1/4, 24
Factor 3*a + 1/3*a**2 + 8/3.
(a + 1)*(a + 8)/3
Suppose -3*n + 0 - 3 = 2*m, 3*n = 3*m - 18. Suppose 0 = 5*j - m*x - 19, 2*j - 1 = 4*x - 5*x. Solve 2/3 - 1/6*l**j + 0*l = 0 for l.
-2, 2
Let p(u) = -u**2 + 13*u + 10. Let w be p(11). Factor 9*t**3 + 4*t + 4*t + 13*t**3 - 8*t**3 + w*t**2.
2*t*(t + 2)*(7*t + 2)
Let c(m) be the third derivative of m**5/12 + 95*m**4/6 + 3610*m**3/3 - m**2 - 109*m. Factor c(b).
5*(b + 38)**2
Suppose -2*m + 11 = 3*y, -5*y + 5*m + 14 = 4. Let g(c) be the first derivative of 12/5*c**2 - 2/25*c**5 + 3/5*c**4 - 8/5*c - 3 - 26/15*c**y. Factor g(f).
-2*(f - 2)**2*(f - 1)**2/5
Factor 12*b + 8*b**4 - 16*b**3 - 419 + 419 - 8*b**2 + 4*b**5.
4*b*(b - 1)**2*(b + 1)*(b + 3)
Let p(s) be the first derivative of s**6/3 - 29*s**5/5 + 113*s**4/32 - 7*s**3/12 - 72. Factor p(g).
g**2*(g - 14)*(4*g - 1)**2/8
What is t in -8*t - 15*t**5 + 9*t**3 - 22*t**5 + t**3 + 35*t**5 = 0?
-2, -1, 0, 1, 2
Let o be 12/(-30) - 54/(-45). Let 8/5*u**2 - o*u**5 - 4/5*u - 4/5*u**4 - 4/5 + 8/5*u**3 = 0. Calculate u.
-1, 1
Solve 2*d**2 + 110*d**2 + 43*d**3 - 39*d**3 + 156*d - 328 + 56*d**2 = 0.
-41, -2, 1
Let z(t) be the third derivative of 3*t**8/784 + 13*t**7/490 + 3*t**6/70 - 3*t**5/35 - 2*t**4/7 - 2*t**2 + 92. Suppose z(j) = 0. What is j?
-2, -4/3, 0, 1
Suppose -12*z + 10*z = 0. Let t(c) be the third derivative of 1/30*c**5 + 1/180*c**6 + 1/9*c**3 + z*c + 1/12*c**4 + 6*c**2 + 0. What is b in t(b) = 0?
-1
Let r(p) = -p**2 - 1214*p + 1221*p + 2 + 2*p**2. Let m be r(-7). Determine q so that 1/7*q + 1/7*q**m + 0 = 0.
-1, 0
Let s(z) be the first derivative of z**7/280 + z**6/120 - 3*z**3 - 6. Let f(l) be the third derivative of s(l). Find y such that f(y) = 0.
-1, 0
Let n = -10724/3 - -3576. Factor n*l - 2*l**2 + 2/3*l**3 + 0.
2*l*(l - 2)*(l - 1)/3
Let w(r) = -7*r + 44. Let c = -54 - -60. Let i be w(c). Factor 3/4*p**3 - 3/4*p - 3/2*p**i + 3/2.
3*(p - 2)*(p - 1)*(p + 1)/4
What is h in -98*h**2 - 86*h + 96 - 66*h**2 - 314*h + 12*h**2 + 36*h**3 = 0?
-2, 2/9, 6
Let n(f) be the first derivative of f**5/10 - 3*f**4/2 + 5*f**3 + 25*f**2 + 14*f - 32. Let d(y) be the first derivative of n(y). Factor d(w).
2*(w - 5)**2*(w + 1)
Let z(q) be the third derivative of 1/12*q**4 - 1/120*q**6 - 11*q**2 + 0*q**3 - 1/60*q**5 + 0 + 0*q. Factor z(x).
-x*(x - 1)*(x + 2)
Let v(u) = u**2 + 5*u + 4. Let w be v(-5). Suppose -7*o + 9 = -w*o. Factor 11*a**2 - 5*a - 8 - 36*a**o + a - 3*a**2 + 40*a**3.
4*(a - 1)*(a + 1)*(a + 2)
Suppose 15 = -t - 5*d + 42, 19 = 2*t + 3*d. Let k be 0/(-2 + 1 - -3). Factor -4*u + k*u + t*u - 2*u**3 + 4*u.
-2*u*(u - 1)*(u + 1)
Let j(m) be the second derivative of 34*m - 1/30*m**5 + 0 + 0*m**2 - 1/30*m**6 + 0*m**4 + 0*m**3 - 1/126*m**7. Factor j(h).
-h**3*(h + 1)*(h + 2)/3
Let f(z) = -2*z**4 + 10*z**3 - 10*z**2 - 4*z. Let u(d) = -d**4 + d**3 - d**2. Let p be -2*(-1)/(-2) - 0. Let v(w) = p*f(w) + 6*u(w). Factor v(a).
-4*a*(a - 1)*(a + 1)**2
Solve 2*p + 4 + 1/4*p**2 = 0 for p.
-4
Let m = -46201/7 - -6611. Factor 0 - 4*p**5 - 4/7*p**2 - 60/7*p**3 + 8/7*p - m*p**4.
-4*p*(p + 1)**3*(7*p - 2)/7
Let c(d) be the first derivative of 4*d**5/5 - 8*d**4 + 8*d**3/3 + 64*d**2 + 84*d + 94. Factor c(b).
4*(b - 7)*(b - 3)*(b + 1)**2
Let o = -75 - -54. Let w = o + 65/3. Factor -w*m**2 + 0 - 2/3*m.
-2*m*(m + 1)/3
Let j(w) = -9*w**2 - 754*w - 28129. Let s(v) = 19*v**2 + 1509*v + 56259. Let d(z) = 9*j(z) + 4*s(z). Determine o so that d(o) = 0.
-75
Let n = -19039 + 19039. Factor 1/6*s**2 - 2/3 + n*s.
(s - 2)*(s + 2)/6
Let u(i) be the first derivative of 1/24*i**3 - 1/80*i**5 - 1/24*i**4 - 9*i - 1 + 1/4*i**2. Let k(f) be the first derivative of u(f). Factor k(a).
-(a - 1)*(a + 1)*(a + 2)/4
Factor 0 + 1/8*a**3 - 1/8*a**2 + 0*a.
a**2*(a - 1)/8
Let d(r) be the third derivative of r**7/70 - 19*r**6/120 + 47*r**5/90 + 4*r**4/9 - 64*r**3/9 + 10*r**2 + 20*r. Let d(s) = 0. Calculate s.
-1, 2, 8/3
Let d be (0 + -1)/((-1)/2). Suppose 0 = -108*l - 11*l - 8*l. Factor 3/5*b**3 + 4/5*b + l + 8/5*b**d.
b*(b + 2)*(3*b + 2)/5
Let n = -17255 + 86276/5. Find u, given that n*u**2 - 1/5 - 1/5*u + 1/5*u**3 = 0.
-1, 1
Let t = -23523 + 23526. Suppose 2/5*s + 4/5*s**2 - 4/5 - 2/5*s**t = 0. What is s?
-1, 1, 2
Suppose 7*l - 9*l + 10 = 0. Factor c**3 - 2*c**2 - l*c**3 - 2*c**2.
-4*c**2*(c + 1)
Factor 3/2*q**2 + 12 + 27/2*q.
3*(q + 1)*(q + 8)/2
Let j(l) be the second derivative of 3*l**6/10 + 3*l**5/2 + l**4 - 4*l**3 - 593*l. Factor j(k).
3*k*(k + 2)**2*(3*k - 2)
Let j(m) be the second derivative of m**6/15 - 21*m**5/25 + 101*m**4/30 - 28*m**3/5 + 4*m**2 - 252*m. Determine w so that j(w) = 0.
2/5, 1, 2, 5
Let n be ((-12)/22)/(22/(-242)). Let d = -17 + 26. Factor -n*b**4 + b**4 + d*b**2 - 12 + 2*b**4 - 6*b**3 + 12*b.
-3*(b - 1)**2*(b + 2)**2
Suppose 199 + 179 = 9*u. Let k be (-8)/u*1/2*-3. What is i in -6/7*i + 4/7 + k*i**2 = 0?
1, 2
Let h(a) be the first derivative of 16 + a**4 + 2/3*a**3 + 0*a + 2/5*a**5 + 0*a**2. Factor h(m).
2*m**2*(m + 1)**2
Let v(h) be the third derivative of -h**7/840 + h**6/120 - h**5/40 + h**4/24 - h**3/24 - 23*h**2 + 2*h. What is k in v(k) = 0?
1
Suppose -2/17*g**4 - 2/17*g**5 - 18/17 + 20/17*g**2 + 20/17*g**3 - 18/17*g = 0. Calculate g.
-3, -1, 1, 3
Let n(w) be the first derivative of 3*w**5/20 - w**4/4 - w**3/2 + w**2 - 9. Let g(p) be the second derivative of n(p). Suppose g(t) = 0. What is t?
-1/3, 1
Let r(n) = -3*n**2 - 33*n + 150. Let m(g) = -5*g**2 - 65*g + 300. Let z(k) = -2*m(k) + 5*r(k). Factor z(t).
-5*(t - 3)*(t + 10)
Let a(d) be the first derivative of d**6/15 - d**5/5 + d**4/6 - 12*d + 2. Let j(v) be the first derivative of a(v). Suppose j(r) = 0. Calculate r.
0, 1
Let v(a) = 3*a**5 + 6*a**4 - 6*a**3 - 30*a**2 - 39*a - 15. Let w(o) = -o**4 - o**3 + o**2 - o - 1. Let r(i) = -v(i) + 3*w(i). What is j in r(j) = 0?
-2, -1, 2
Let j(u) = -27*u**2 + 160*u - 292. Let p(r) = -9*r**2 + 53*r - 98. Let w(h) = 4*j(h) - 11*p(h). Let w(m) = 0. What is m?
3, 10/3
Let l(w) = 2*w**2 + 3*w + 1. Let v be l(-2). Suppose -2*t - 3 = -v*t. Suppose -2*d**4 - 2*d**t + 2*d**2 - 42*d + 2*d**5 + 42*d = 0. Calculate d.
-1, 0, 1
Let z(g) be the second derivative of 4*g**2 + 1/6*g**4 + 0 - 6*g - 4/3*g**3. Find j, given that z(j) = 0.
2
Let n(h) be the third derivative of -5*h**8/1008 + h**7/21 - 13*h**6/72 + h**5/3 - 5*h**4/18 - 18*h**2. Suppose n(o) = 0. What is o?
0, 1, 2
Solve 3/5*x**3 + 9 + 93/5*x + 51/5*x**2 = 0 for x.
-15, -1
Suppose 2*s = 3*d + 6*s - 72, 0 = -5*d - 5*s + 120. Factor 2 + 4*a**4 + 8*a**2 - 6 + 4*a**3 - d*a**2 + 14*a - 2*a**5.
-2*(a - 1)**4*(a + 2)
Let s(a) be the second derivative of a**4/4 + 5*a**3/6 - a**2 + 158*a. Factor s(f).
(f + 2)*(3*f - 1)
Factor -13/6 + 29/12*s - 1/4*s**2.
-(s - 1)*(3*s - 26)/12
Let x = -57389/63