 second derivative of -1/100*y**5 + m - 1/20*y**4 - 1/10*y**2 + 7*y - 1/10*y**3. Factor l(x).
-(x + 1)**3/5
Let s = 43210/48591 - 2/5399. Factor 2/9*u**2 + 2/3*u - s.
2*(u - 1)*(u + 4)/9
Let h be (-253)/(-35) + 11/55 - 7. Factor 0 + h*m - 3/7*m**2.
-3*m*(m - 1)/7
Let b be 17/(-5)*(-30)/8*50/75. Solve 3/2*f**2 - 3 + b*f = 0 for f.
-6, 1/3
Let d(n) be the second derivative of -1/10*n**2 - 1/25*n**5 - 2/15*n**3 - 9*n - 1/150*n**6 - 1/10*n**4 + 0. Factor d(q).
-(q + 1)**4/5
Suppose -12*c = -11*c - 7. Factor -c*k**3 + 4*k**2 + 3*k**4 + 3*k**3 + 2*k**2 - 5*k**3.
3*k**2*(k - 2)*(k - 1)
Suppose 76*l**2 + 76*l**3 + 152*l**2 - 2*l**2 + 88 + 37*l**2 - 4*l**4 - 11*l**2 + 260*l = 0. Calculate l.
-1, 22
Let b be 2/(3 + 1)*12. Suppose b*p - 26 = -8. Let -17 - 21*u**2 - 39*u - p*u**3 - 10 - 6*u = 0. What is u?
-3, -1
Let m(x) = 11*x**2 + 518*x + 2523. Let w(q) = -15*q**2 - 519*q - 2523. Let k(h) = 3*m(h) + 4*w(h). Factor k(t).
-3*(3*t + 29)**2
Let r(d) be the second derivative of 1/70*d**5 - 34*d + 0 + 1/42*d**4 + 0*d**3 + 0*d**2. Factor r(z).
2*z**2*(z + 1)/7
Let d(z) be the second derivative of z**4/21 - 472*z**3/21 + 27848*z**2/7 - 742*z. Solve d(v) = 0 for v.
118
Let z = 458 - 2289/5. Factor -z*y**2 + 3/5*y + 4/5.
-(y - 4)*(y + 1)/5
Let w(b) be the first derivative of 2*b**5/45 + b**4/9 - 2*b**3/27 - 2*b**2/9 - 125. Factor w(z).
2*z*(z - 1)*(z + 1)*(z + 2)/9
Let z(n) be the second derivative of 9*n**6/10 - 18*n**5 - 83*n**4/4 - 7*n**3 + 146*n. Factor z(h).
3*h*(h - 14)*(3*h + 1)**2
Let m = 325 - 301. Suppose -8*c + m = 4*c. Factor -2 - 1/2*o**2 + c*o.
-(o - 2)**2/2
Let n(c) be the first derivative of -2*c**3/3 + 21*c**2 - 76*c - 21. Solve n(w) = 0.
2, 19
Let t(l) be the first derivative of -67/32*l**4 - 3/16*l**6 - 19/8*l**3 - 2 - 3/2*l**2 - 39/40*l**5 - 1/2*l. Find i such that t(i) = 0.
-1, -2/3
Let c be (328/1395)/(5 + (-26)/6). Let l = c + -3/155. Factor 1/3*q**4 + 0*q + 0 + l*q**5 - 5/3*q**3 + q**2.
q**2*(q - 1)**2*(q + 3)/3
Suppose 0 = 213*z - 118*z. Suppose 2/5*j**3 - 6/5*j**2 + 2/15*j**5 + 0*j + z + 2/3*j**4 = 0. Calculate j.
-3, 0, 1
Let f = 6700 + -6697. Suppose -1/2*c + 1/2*c**f - 1/4*c**2 + 1/4*c**4 + 0 = 0. What is c?
-2, -1, 0, 1
Let c(x) be the second derivative of x**8/1344 - x**6/480 + 2*x**2 + 5*x. Let y(g) be the first derivative of c(g). Solve y(s) = 0 for s.
-1, 0, 1
Suppose 3*d + 3 - 10 = j, 0 = 4*d - 5*j - 2. Suppose 5 = 4*z + 3*y, d*z - y = 1 + 6. Determine w, given that 1/4*w**3 + 1/2*w**z + 1/4*w + 0 = 0.
-1, 0
Let m be (8/(-3))/((-12)/54). Suppose -m + 8 = -q. Let 4*i**q - 2*i**2 - i**4 - i**4 = 0. What is i?
-1, 0, 1
Factor 36 + 26*u**2 + 2*u**4 - 2*u**3 + 50*u - 12 + 0*u**3 - 4*u**4.
-2*(u - 4)*(u + 1)**2*(u + 3)
Let u(o) = o - 4*o - 9 + 2 + 4*o**2. Let k(j) = -10*j**2 + 5*j**2 - 3*j - 6 + 8*j**2. Let s(v) = -5*k(v) + 4*u(v). What is z in s(z) = 0?
-2, -1
Let i(a) = -9*a**3 + 16*a**2 + 11*a + 6. Let w(k) = k**3 - 4*k**2 + k + 1. Let g(m) = i(m) + 4*w(m). Solve g(p) = 0 for p.
-1, 2
Let y = -162 - -3403/21. Let s(o) be the second derivative of -y*o**3 + 0 + 1/7*o**2 - 1/42*o**4 + 1/70*o**5 - 3*o. Factor s(n).
2*(n - 1)**2*(n + 1)/7
Factor -50*i**2 + 7*i**2 + 39*i**2 - 144*i + 304.
-4*(i - 2)*(i + 38)
Let 184*p**3 - 96*p + 21*p**4 + 4*p**5 - 36 - 351*p**3 - p**5 - 69*p**2 + 176*p**3 = 0. What is p?
-6, -1, 2
Let p be (-742)/(-3180)*(-8)/(-14). Let j(d) be the second derivative of -3/5*d**5 + 1/3*d**4 + 2*d**3 + p*d**6 - 9*d - 4*d**2 + 0. Let j(a) = 0. Calculate a.
-1, 1, 2
Let l(d) be the third derivative of d**7/840 - d**6/120 - 7*d**5/240 + 5*d**4/48 + 4*d**2 - 14. Factor l(r).
r*(r - 5)*(r - 1)*(r + 2)/4
Let s(l) be the third derivative of -13*l**8/1008 + l**7/21 - 7*l**6/120 + l**5/45 - 25*l**2 - l. Determine r, given that s(r) = 0.
0, 4/13, 1
Let o(h) be the third derivative of 0 - 1/1470*h**7 + 1/420*h**5 - 1/84*h**4 + 0*h - 1/2352*h**8 + 0*h**3 + 1/280*h**6 + 23*h**2. Let o(g) = 0. What is g?
-2, -1, 0, 1
Let i = 1/719 + 687/23008. Let v(m) be the third derivative of -i*m**4 + 0*m**5 + 0 + 1/160*m**6 + 0*m - 4*m**2 + 0*m**3. Factor v(q).
3*q*(q - 1)*(q + 1)/4
Factor -35912 + 48*s - 3*s**2 + 100*s + 161*s + s**2 + 227*s.
-2*(s - 134)**2
Let z(x) be the first derivative of 1/21*x**2 + 0*x + 15 + 1/21*x**6 + 4/63*x**3 - 2/21*x**4 - 4/105*x**5. Solve z(t) = 0 for t.
-1, -1/3, 0, 1
Let d(v) be the third derivative of 3/8*v**4 - 1/20*v**5 + 0 + 0*v - 13*v**2 + 2*v**3. Factor d(l).
-3*(l - 4)*(l + 1)
Let t = -19 + 1. Let h(p) = 13*p**3 - 11*p**2 - 48*p - 24. Let r(y) = 45*y**3 - 39*y**2 - 168*y - 84. Let d(u) = t*h(u) + 5*r(u). Solve d(c) = 0 for c.
-1, -2/3, 2
Let t(d) be the second derivative of -d**5/80 - d**4/32 + d**3/4 + 13*d**2/2 + d. Let z(q) be the first derivative of t(q). Factor z(c).
-3*(c - 1)*(c + 2)/4
Let n be 71/(-36) - (-14 - -12). Let h(g) be the second derivative of 0*g**3 - g - n*g**4 - 1/60*g**5 + 0*g**2 + 0. Factor h(a).
-a**2*(a + 1)/3
Let a = -24 - -28. Find v, given that 3*v**4 + 12*v**a + 6*v**5 - v**5 + 6*v**3 + 5*v**2 + 9*v**3 = 0.
-1, 0
Suppose i = 2*i - 3*h - 4, 3*h + 12 = 3*i. Factor -8*y**2 - 10*y**2 + 10*y**2 + 4*y**4 + i*y**3.
4*y**2*(y - 1)*(y + 2)
Let c = -92 + 97. What is s in 2*s**c - 9*s**3 + 2*s + s**5 - 310*s**4 - 3*s**2 + 309*s**4 = 0?
-1, 0, 1/3, 2
Suppose 227*f - 228*f + 3 = 0. Let v(n) be the first derivative of 3/5*n**2 + 1/5*n**f + 3/5*n - 2. Find t such that v(t) = 0.
-1
Let x(w) be the first derivative of w**3/3 + 37*w**2 - 377. Factor x(h).
h*(h + 74)
Let q(k) be the second derivative of -k**4/54 + 7*k**3/27 - 2*k**2/3 - 2*k - 3. Factor q(m).
-2*(m - 6)*(m - 1)/9
Let o be (-4)/(-14) + (-594)/(-77). Suppose -f - 6*x = -4*x + o, 3*f + 2*x = -4. Solve 8/3*u**4 - 26/3*u - 34/3*u**3 + 4/3 + 16*u**f = 0.
1/4, 1, 2
Let z(n) = -n**2 + n - 1. Let l(f) = 4*f**3 + 14*f**2 - 2*f + 6. Let y = -31 + 30. Let a(x) = y*l(x) - 6*z(x). Let a(g) = 0. What is g?
-1, 0
Let d(r) be the first derivative of r**5/20 - 7*r**4/6 + 10*r**3 - 36*r**2 - 23*r - 26. Let a(x) be the first derivative of d(x). Factor a(p).
(p - 6)**2*(p - 2)
Let n(f) = 7*f**4 + 7*f**3 - 2*f**2 - 6*f. Let c(i) = -13*i**4 - 13*i**3 + 7*i**2 + 11*i. Let t(j) = -6*c(j) - 11*n(j). Find q, given that t(q) = 0.
-5, 0, 4
Let a be (21/5)/((-57)/(-190)). Suppose 2*h**3 - 6*h**3 - a*h**2 + 10*h**2 = 0. Calculate h.
-1, 0
Let v = 127 - 122. Suppose l = -0*l - 2*s + 7, 2*s = 3*l - v. Let -16/7*z**l + 6/7*z**5 + 0*z + 0 + 8/7*z**2 + 2/7*z**4 = 0. Calculate z.
-2, 0, 2/3, 1
Factor 19*h**2 - 86*h**2 + 30*h**2 + 300*h + 40*h**2.
3*h*(h + 100)
Let b(c) = c**2 + 65*c - 501. Let i be b(-72). Solve 0 - 2/5*f**i + 0*f - 8/5*f**2 = 0 for f.
-4, 0
Factor -18723/2 - 3/8*f**2 - 237/2*f.
-3*(f + 158)**2/8
Factor -1150/13*q + 94/13*q**2 + 1058/13 - 2/13*q**3.
-2*(q - 23)**2*(q - 1)/13
Let m(i) be the first derivative of -i**6/39 + 28*i**5/13 - 646*i**4/13 + 4624*i**3/39 + 665. Factor m(t).
-2*t**2*(t - 34)**2*(t - 2)/13
Suppose -3*w = -6 - 3. Factor -9 + 14*i + 3*i**4 + 3*i**3 - 27*i**2 - w + 6*i + 13*i.
3*(i - 1)**3*(i + 4)
Let m = 1289/3 + -429. Let j(u) be the first derivative of 1 + u**2 + 0*u + m*u**3. Factor j(i).
2*i*(i + 1)
Let r(h) be the third derivative of h**7/840 - h**6/240 + 7*h**4/24 - 8*h**2. Let w(b) be the second derivative of r(b). Factor w(x).
3*x*(x - 1)
Suppose k - 9 = 9*t - 4*t, -k - 4*t = 0. Let c(q) = -q**2 + 10*q - 22. Let a be c(k). Factor -3/5*b**a - 3/5 - 6/5*b.
-3*(b + 1)**2/5
Suppose 5*f + 3*i - 34 = 0, 0*i = -2*f + i + 7. Suppose 2 = -r + f. Find t, given that 3 + t + 80*t**r - 45*t**2 - 8*t + 28*t**3 + t = 0.
-1/4, 1/3
Factor -6*i**5 + 5*i**5 - 25*i**4 - 227 + 6*i**5 + 227 + 45*i**2 + 15*i**3.
5*i**2*(i - 3)**2*(i + 1)
Let c(y) = 5*y**2 - 5*y + 11. Let f(i) = 10*i**2 - 11*i + 21. Let u(r) = 5*c(r) - 3*f(r). Let p(d) = 5*d**2 - 9*d + 7. Let t(m) = -4*p(m) - 3*u(m). Factor t(b).
-(b - 2)*(5*b - 2)
Let f(d) = -d**2 - 4*d + 8. Let k be f(-5). Solve 5*c - 9*c**k - 5*c**2 + 4 + 4*c + 2 - c**2 = 0 for c.
-1, -2/3, 1
Suppose 0 = -7*d - 18 + 46. Determine h, given that 3*h**4 - 5*h**4 - 4*h**3 - 5 + d*h + 7 = 0.
-1, 1
Factor 159*n - 13 - 153*n + 2*n**2 + 5.
2*(n - 1)*(n + 4)
Let g be (24/25)/((-6)/(-15)). Let y = -151 - -153. Determine u so that 7/5*u**y - g*u - 4/5 = 0.
-2/7, 2
Suppose 4*p - 244 = 172. Factor -4*z**3 - p*z + 201*z