-h**8/784 + 3*h**6/280 + h**5/70 + 7*h**2/2 - 28. Let r(m) be the second derivative of s(m). Factor r(z).
-3*z**2*(z - 2)*(z + 1)**2/7
Let z(m) = m**2. Let j(s) be the second derivative of -s + 0*s**3 - 11/12*s**4 + 4*s**2 + 0 - 1/10*s**5. Let o(w) = j(w) + 5*z(w). Find d such that o(d) = 0.
-2, 1
Suppose 0 = 4*j - 2*o + 6 + 10, 5*j - 5*o = -25. Let b be 3 - (j - -3)/(-1). Let -48*a**2 + 2 + 8*a**3 + 56*a**b + 12*a - 3 = 0. Calculate a.
1/4
Solve -1/3*r**2 - 2/3*r + 0 = 0.
-2, 0
Factor 40*w**2 - 77*w**2 + 38*w**2 + 108*w.
w*(w + 108)
Let d(n) = n**2 - n + 3. Let g(u) = -u**2 + 299*u + 10943. Let h(o) = 3*d(o) + g(o). Suppose h(a) = 0. What is a?
-74
Let v = -203 - -208. Let n be (-11)/(242/84) - (v - 9). Factor -4/11*t - 2/11*t**2 - n.
-2*(t + 1)**2/11
Let v = 485522/10493 + 22/1499. Let p = -46 + v. Let -8/7*r - 8/7 - p*r**2 = 0. What is r?
-2
Suppose -4*h - 8 = 4*i, -5*h = 8*i - 7*i + 18. What is y in 0 + 16/5*y + 4/5*y**i = 0?
-4, 0
Let i(n) be the first derivative of n**5/40 - n**4/16 - n**3/24 + n**2/8 + 110. Suppose i(w) = 0. What is w?
-1, 0, 1, 2
Let i(p) = p**3 - 5*p**2 - 6*p + 6. Let l be i(6). Suppose 2*m = -2*x + 4, 0*m + l = 3*m + 4*x. Factor 2*a - 4 + 7*a**2 + 10*a**m + a**2 + 12*a.
2*(a + 1)*(9*a - 2)
Let t(l) be the third derivative of 1/6*l**3 + 0 - 1/420*l**5 - 7*l**2 + 0*l + 1/28*l**4. Suppose t(d) = 0. Calculate d.
-1, 7
Let t(o) be the first derivative of 4 - 5/4*o**2 + 2*o + 1/6*o**3. Factor t(m).
(m - 4)*(m - 1)/2
Let c(j) be the third derivative of -1/60*j**5 - 1/3*j**3 + 0*j + 0 + 1/8*j**4 - 6*j**2. Factor c(o).
-(o - 2)*(o - 1)
Let d(r) = -25*r**3 - 1640*r**2 - 26565*r + 10888. Let i(u) = 1. Let y(a) = -d(a) - 2*i(a). Find n, given that y(n) = 0.
-33, 2/5
Let o(i) be the second derivative of -i**4/30 + 13*i**3/15 + 14*i**2/5 + 147*i. Suppose o(v) = 0. What is v?
-1, 14
Suppose w + 307 - 311 = 0. Determine f so that 1363*f**4 - 3*f**3 - 1367*f**w - 4*f**2 - 5*f**3 = 0.
-1, 0
Suppose 9*j = 6*j + 5*y + 17, -11 = -2*j + 3*y. Suppose 16/11*w**2 - 4/11*w**j + 0 - 8/11*w + 2/11*w**5 - 6/11*w**3 = 0. What is w?
-2, 0, 1, 2
Let z be 109/(-2) + 0 + (-1)/(-2). Let u = z - -56. Determine i, given that 0 - 4/3*i + 2/3*i**u = 0.
0, 2
Suppose 0 = -5*u + 8 + 17. Let r = -5 + u. Suppose r*n + 0*n + 2*n**2 + n**3 + n = 0. Calculate n.
-1, 0
Let r(a) be the third derivative of -a**8/112 - a**7/70 + a**6/20 + a**5/10 - a**4/8 - a**3/2 + 11*a**2. Determine n, given that r(n) = 0.
-1, 1
Let j be (-6)/9*12/(-2). Determine c, given that -3*c**2 + 6*c**3 + 0*c**2 + 428*c + 3*c**j - 434*c = 0.
-2, -1, 0, 1
Let o = 10 + -8. Find z, given that 6*z + z**2 - o*z**2 - 10 + 1 = 0.
3
Let j(g) = g**3 + 2*g**2 + g - 1. Let n(f) = 24*f**5 - 14*f**4 - 300*f**3 - 86*f**2 + 152*f - 34. Let x(o) = 10*j(o) - n(o). Find d, given that x(d) = 0.
-3, -1, 1/4, 1/3, 4
Find x such that -228/5*x + 3/5*x**2 - 231/5 = 0.
-1, 77
Factor -8/11*y**2 + 0 + 2/11*y**4 - 8/11*y + 2/11*y**3.
2*y*(y - 2)*(y + 1)*(y + 2)/11
Let o(i) be the third derivative of -i**5/30 - 5*i**4/12 - 2*i**3 + 18*i**2. Let w(y) = -y**2 - 5*y - 6. Let d(u) = 4*o(u) - 9*w(u). Let d(j) = 0. Calculate j.
-3, -2
Let u be ((-4)/(-6))/(196/(-147))*0. Factor 7/5*k**3 - k**4 - 2/5*k**2 + 0*k + u.
-k**2*(k - 1)*(5*k - 2)/5
Let n = 43 - -46. Let l = -173/2 + n. Factor 0 - 1/2*b**4 + 2*b + l*b**3 - 4*b**2.
-b*(b - 2)**2*(b - 1)/2
Let d be 216/660 - 8*(-13)/260. Let 10/11*q + d*q**2 + 4/11 + 2/11*q**3 = 0. What is q?
-2, -1
Let n(m) be the first derivative of 3/14*m**2 + 4/7*m**3 - 6/7*m - 6/35*m**5 - 3/14*m**4 + 5 + 1/14*m**6. Find x, given that n(x) = 0.
-1, 1, 2
Let w(g) be the second derivative of 2*g**2 + 7/12*g**3 - 33*g - 1/24*g**4 + 0. Solve w(f) = 0 for f.
-1, 8
Let w(b) = b**3 - 9*b**2 + 11*b - 18. Let z be w(8). Let c(p) = p**2 + 1. Let f(x) = 8*x**2 + 8*x + 12. Let o(y) = z*c(y) - f(y). Factor o(a).
-2*(a + 1)*(a + 3)
Let q(t) be the second derivative of t**4/96 - 25*t**3/24 + 625*t**2/16 + 16*t. Factor q(u).
(u - 25)**2/8
Suppose 25 = -d + 4*p, 4*d + 3*p = -0*d - 62. Let h = 20 + d. Suppose -1/4*o**5 - 5/4*o**h + o**4 + 0 + 0*o + 1/2*o**2 = 0. Calculate o.
0, 1, 2
Suppose -4*y - 3*w = -9, 5*y = 2*w - 4*w + 6. Suppose 0*c - 4/3*c**2 + 2/3*c**3 + y = 0. What is c?
0, 2
Let j be 27/(-126)*(-154)/66. Factor 7/4*n + j*n**2 - 1/4*n**3 + 1.
-(n - 4)*(n + 1)**2/4
Let 40 - 444*j**4 + 219*j**4 + 70*j**3 + 210*j**4 - 25*j**2 - 70*j = 0. Calculate j.
-1, 2/3, 1, 4
Let l = 857 - 7763/9. Let v = l + 109/18. Factor 0 - r + v*r**2.
r*(r - 2)/2
Let k be 0/((-1*8)/(-4)). Suppose k*f = -0*f - 4*f. Find w such that 0 - 1/6*w**4 + 0*w + 1/6*w**3 + f*w**2 = 0.
0, 1
Let d(w) be the third derivative of -1/60*w**5 - w**2 + 0*w + 0 - 8/3*w**3 + 1/3*w**4. Factor d(v).
-(v - 4)**2
Let n(z) be the third derivative of -2*z**7/105 - 7*z**6/30 + z**5/15 + 7*z**4/6 + 2*z**2 + 66. Let n(v) = 0. What is v?
-7, -1, 0, 1
Let v be (-14)/(-8) + 16/(-192) - 1. Factor 0 - 2/3*d**2 + v*d**4 + 2/3*d - 2/3*d**3.
2*d*(d - 1)**2*(d + 1)/3
Let d(w) be the third derivative of w**7/168 - w**6/48 - 7*w**5/48 - 5*w**4/24 - 122*w**2 + 2. Factor d(g).
5*g*(g - 4)*(g + 1)**2/4
Let k be (-9)/(-21) + (-175)/(-49). Factor 8*x - 6*x**3 + 0*x**4 + 9*x**4 - 7*x**k.
2*x*(x - 2)**2*(x + 1)
Let r(p) be the second derivative of -p**5/80 + 5*p**4/48 - p**3/4 - 631*p. Let r(j) = 0. What is j?
0, 2, 3
Factor z**2 + 2*z**3 + 2 - z**2 - 2*z**2 - 2*z.
2*(z - 1)**2*(z + 1)
Let p(j) be the second derivative of -1/6*j**4 + 0 + 10*j + 2/3*j**3 - j**2. Find l, given that p(l) = 0.
1
Let z(a) be the third derivative of 5*a**8/168 - 5*a**7/42 - 37*a**6/16 + 353*a**5/48 - 895*a**4/96 + 25*a**3/4 + 189*a**2. Let z(n) = 0. What is n?
-5, 1/2, 6
Suppose 5*z = 5*f - 5, 57*f + 12 = 60*f. Factor -1/8*s**5 - 1/4*s**2 + 0 + 1/8*s + 0*s**z + 1/4*s**4.
-s*(s - 1)**3*(s + 1)/8
Let r(k) = 6*k**3 + 24*k**2 + 15*k - 90. Let c(h) = -15*h**3 - 48*h**2 - 31*h + 178. Let q(i) = -3*c(i) - 7*r(i). Factor q(a).
3*(a - 8)*(a - 2)*(a + 2)
Let w(v) = v**3 - 32*v**2 - 110*v + 180. Let a be w(35). Factor 0*d**2 + 0*d - 3/8*d**a - 3/8*d**4 + 0 + 0*d**3.
-3*d**4*(d + 1)/8
Let o be (33/(-55))/(33/(-110)). Factor -9/4 - 21/4*z - 3*z**o.
-3*(z + 1)*(4*z + 3)/4
Let u(p) = 9*p**3 + 5*p**2 + 8*p - 4. Let a(y) = 20*y**3 + 10*y**2 + 17*y - 9. Let o(q) = 4*a(q) - 9*u(q). Find m, given that o(m) = 0.
-4, -1, 0
Let j(o) = -13*o - 2. Let v be j(-1). Suppose -v = -0*c - 4*c + 3*r, 3*c - 5 = -r. Find k, given that k**4 - 2*k**4 + c*k**3 + 4*k**2 - 6*k**2 + k**3 = 0.
0, 1, 2
Suppose -176/3*c - 4/3 + 89/3*c**2 = 0. What is c?
-2/89, 2
Let v(s) be the third derivative of 3*s**5/20 - 17*s**4/8 - 3*s**3 - 63*s**2. Factor v(d).
3*(d - 6)*(3*d + 1)
Let q be 54/4 - (-3876)/(-323). Factor 0 + 3*n + 0*n**3 + 9/2*n**2 - q*n**4.
-3*n*(n - 2)*(n + 1)**2/2
Let p(z) be the first derivative of -3*z**5/35 + 3*z**4/14 - z**3/7 - 107. Solve p(o) = 0 for o.
0, 1
Let y = -15162/5 - -3034. Factor -y*c + 2/5*c**2 + 0.
2*c*(c - 4)/5
Let w be 8*-5*(0 - -1). Let c be ((-6)/(-10))/((-8)/w). Factor c*f**2 - 3*f**2 + 6 - 3*f**3 + 3*f - 6*f**2.
-3*(f - 1)*(f + 1)*(f + 2)
Let j(b) be the first derivative of 7/2*b**2 + 2*b + 3/4*b**4 + 11 + 8/3*b**3. Factor j(h).
(h + 1)**2*(3*h + 2)
Let a(f) be the first derivative of -3*f**4/4 - 9*f**3 - 45*f**2/2 + 75*f - 125. Determine c, given that a(c) = 0.
-5, 1
Let b(n) be the first derivative of -n**3 - 3*n**2 - 3*n - 64. Factor b(i).
-3*(i + 1)**2
Let k = -44 - -47. Factor -2*f**2 + 32 + 5*f**3 - 3*f**k - 28 + 6*f - 8*f**3 - 2*f**4.
-2*(f - 1)*(f + 1)**2*(f + 2)
Let l(g) be the first derivative of -g**7/42 + g**6/30 + g**5/10 - g**4/6 - g**3/6 + g**2/2 + 18*g - 4. Let c(h) be the first derivative of l(h). Factor c(i).
-(i - 1)**3*(i + 1)**2
Let r(z) be the first derivative of -z**4/22 + 4*z**3/33 - z**2/11 + 18. Factor r(n).
-2*n*(n - 1)**2/11
Let x(t) = t**2 + t. Let l(h) = 2*h**2 - 9*h + 21. Let n(g) = 2*l(g) - 2*x(g). Let n(u) = 0. Calculate u.
3, 7
Let u = 1 - 7. Let k be ((-88)/66)/(4/u). Factor a**3 + 1/4*a**4 + 1/2*a + 5/4*a**k + 0.
a*(a + 1)**2*(a + 2)/4
Let a(g) = 45*g**3 + 771 + 771*g - 137*g**2 + 136*g**2 + 289*g**2. Let z(n) = 1 - 5*n**3 + n - n**4 + 4*n**3 + 0*n**4. Let i(o) = -a(o) + 3*z(o). Factor i(v).
-3*(v + 4)**4
Let t(s) = 2*s**4 + s**3. Let d(k) = -k**5 - 7*k**4 - 2*k**3 + k**2.