- 1)**2/9
Let i(z) be the first derivative of -7*z**2/2 - 62*z + 86. Let t be i(-11). Find v such that -75/2 + t*v - 3/2*v**2 = 0.
5
Let k(g) be the third derivative of -g**5/240 + 53*g**4/24 - 211*g**3/24 + 1839*g**2. Factor k(u).
-(u - 211)*(u - 1)/4
Let h = 334102/25879 + -196/3697. What is m in -22/7 - 8/7*m**2 + h*m = 0?
1/4, 11
Let f(l) be the second derivative of -l**7/105 - 8*l**6/75 + 9*l**5/10 - 6*l**4/5 - l - 328. Determine w, given that f(w) = 0.
-12, 0, 1, 3
Let r(w) be the third derivative of w**6/30 - 22*w**5/15 + 7*w**4/2 - 23*w**2 + 4. Determine n, given that r(n) = 0.
0, 1, 21
Let f(d) be the first derivative of 3*d**4/32 - 17*d**3/8 - 15*d**2/4 + 27*d/2 + 1002. Find j such that f(j) = 0.
-2, 1, 18
Let w(g) be the third derivative of g**6/30 - 336*g**5/5 + 56448*g**4 - 25288704*g**3 - g**2 - 1030*g. Factor w(k).
4*(k - 336)**3
Factor 19*f + 6*f**3 + 9*f**3 - 101*f**2 - 97*f**2 - 46*f + 186*f**2.
3*f*(f + 1)*(5*f - 9)
Let s(m) be the first derivative of -m**5/5 + 5*m**4/3 - 14*m**3/3 + 6*m**2 + 4*m + 38. Let x(u) be the first derivative of s(u). Factor x(g).
-4*(g - 3)*(g - 1)**2
Let c(a) be the third derivative of -24*a**2 + 13/4*a**4 + 1/2*a**3 + 0 + 0*a + 5/4*a**5. Solve c(o) = 0 for o.
-1, -1/25
Let u(d) = d**3 + 6 - 3 + d - 2*d**2 + 1. Let l be u(2). Let 7*n**4 + 2*n**4 + 55*n**3 - 5 - 45*n**5 + l*n**4 - 25*n + 15*n**3 - 10*n**2 = 0. Calculate n.
-1, -1/3, 1
Let w(q) = 9*q**2 + 13*q + 1. Let b be w(-2). Let o be (-2)/b - ((-952)/264)/7. Solve -1/3*a + o*a**2 + 0 = 0 for a.
0, 1
Let a(w) = w**2 + w - 9. Let y(o) = 2*o**2 - 5*o - 4. Let m be y(-1). Let p be a(m). Solve -2*n**p - 7*n**2 - 7*n**2 + 2*n - 1 + 15*n**2 = 0 for n.
-1, 1/2, 1
Let v(x) = 5*x**3 - 54*x**2 - 188*x - 135. Let j(t) = t**3 + 2*t**2 + 2*t - 1. Let p(l) = 3*j(l) - v(l). Factor p(m).
-2*(m - 33)*(m + 1)*(m + 2)
Let f(r) be the first derivative of 28*r**5/5 + 124*r**4 + 332*r**3/3 - 68*r**2 + 43. Factor f(y).
4*y*(y + 1)*(y + 17)*(7*y - 2)
Let i(g) be the first derivative of g**4 + 112*g**3 - 1440*g**2 + 5888*g - 1518. Factor i(r).
4*(r - 4)**2*(r + 92)
Let b(u) be the second derivative of -47*u**6/6 + 23*u**5/2 + 20*u**4 - 115*u**3/3 - 5*u**2/2 + 2406*u. Find r, given that b(r) = 0.
-1, -1/47, 1
Let z = -171 - -123. Let c be (-1 + 168/171)*z. Find t, given that -4/19*t**3 - 2/19*t**4 + 8/19 + 6/19*t**2 + c*t = 0.
-2, -1, 2
Let s = -2 - -6. Suppose 5*a - 2*v = 35, -s*a + 37 - 6 = -v. Let 22*i - 6*i + 23*i + 5*i**3 - 35*i**3 + 9 - a*i**5 + 30*i**2 - 39*i**4 = 0. What is i?
-3, -1, -1/3, 1
Let f = 7009/2 - 3504. Let w(z) be the first derivative of -2/7*z + 2/21*z**3 - 12 - f*z**2 + 1/4*z**4. Factor w(x).
(x - 1)*(x + 1)*(7*x + 2)/7
Let f(g) = -532*g + 28731. Let l be f(54). Suppose -144/7*u + 39/7*u**2 - 3/7*u**l + 108/7 = 0. What is u?
1, 6
Let -180 - 180*b - 8*b**3 - 34*b**2 - 8*b**3 + 11*b**3 - 21*b**2 = 0. What is b?
-6, -3, -2
Suppose -3*g + 577 - 115 = 3*x, 2*x = 4*g - 604. Let l be (37/((-10545)/g))/((-2)/5). Factor 0*b - 16/9*b**4 + 4/9*b**2 + 0 - l*b**3.
-4*b**2*(b + 1)*(4*b - 1)/9
Let o = -1164760 - -6988561/6. Factor -11/6*v**2 - 2/3 + o*v**5 + 1/2*v**4 - 2*v - 1/6*v**3.
(v - 2)*(v + 1)**3*(v + 2)/6
Let w(b) = -b**3 - 23*b**2 - 110*b + 36. Let n be w(-16). Let j be (1/2)/((-3)/(-18)). Find i such that 2*i**j + 4*i**3 + 0*i**3 + 2*i**n - 6*i - 2*i**2 = 0.
-3, -1, 0, 1
Let n(l) be the first derivative of 44*l**3/21 - 142*l**2/7 + 240*l/7 - 1411. Find q, given that n(q) = 0.
1, 60/11
Let g = -85111/4 - -21286. Let -15/4*w**2 + g*w - 27/2*w**3 - 3/2 = 0. Calculate w.
-1, 2/9, 1/2
Let b = -9 + 12. Suppose -110 = -3*p - b*k - 41, -4*p - 5*k = -95. Find h, given that -33*h + p - 5*h**3 - 37*h + 9*h**2 + 25*h + 21*h**2 = 0.
1, 4
Let t(f) be the first derivative of -2*f**3/33 + 16*f**2/11 + 533. Let t(d) = 0. What is d?
0, 16
Let c(h) be the third derivative of -h**6/75 - 9*h**5/50 - 19*h**4/30 - h**3 - 2608*h**2. Determine w, given that c(w) = 0.
-5, -1, -3/4
Suppose 0 = -2*m - 0*x + 2*x + 46, m - 11 = 5*x. Factor -5*j**4 - m + 126 - 14 + 74 - 110*j**2 - 45*j**3.
-5*(j - 1)*(j + 2)*(j + 4)**2
Suppose 4*u + 6*h - 2*h = 0, -h = 2*u. Let g be (-6 - -5)*15/10*-1. Factor g*m**2 - 3/2*m + u.
3*m*(m - 1)/2
Let q(f) be the third derivative of f**5/330 - 17*f**4/66 + 64*f**3/33 - 1065*f**2. Factor q(i).
2*(i - 32)*(i - 2)/11
Solve 48*g**3 + 20*g**4 - 50*g**4 - 45*g - 3*g - 40*g**2 + 26*g**4 + 44 = 0 for g.
-1, 1, 11
Suppose -345*y**3 + 0 + 0*y + 0*y**2 - 3/4*y**4 = 0. What is y?
-460, 0
Let l(r) = -5*r**3 + 58*r**2 - 248*r + 432. Let h(z) = -z**3 + 5*z**2 + 2*z. Let n(a) = 2*h(a) - l(a). Factor n(d).
3*(d - 6)**2*(d - 4)
Let w(r) be the first derivative of 5*r**4/4 - 40*r**3/3 - 155*r**2/2 - 110*r - 1144. Let w(h) = 0. Calculate h.
-2, -1, 11
Let y(n) = n**3 + 638*n**2 - 21766*n + 40960. Let a(k) = -640*k**2 + 21765*k - 40960. Let p(j) = -6*a(j) - 5*y(j). Factor p(o).
-5*(o - 64)**2*(o - 2)
Suppose 137 = 3*c + 122. Factor -6 - 255*j**3 - 70*j + 162*j**c + 19*j - 19*j - 300*j**2 - 270*j**4 - 285*j**3.
2*(j - 3)*(3*j + 1)**4
Let q(g) be the third derivative of -g**6/120 - 43*g**5/20 + 197*g**4/12 - 44*g**3 + 1574*g**2. Factor q(n).
-(n - 2)*(n - 1)*(n + 132)
Let m be (1896/320 - 6)/((-99)/275). Let n(l) be the second derivative of 5/48*l**4 + 0*l**2 - 1/24*l**6 + m*l**3 + 7*l - 1/16*l**5 + 0. Factor n(q).
-5*q*(q - 1)*(q + 1)**2/4
Let f = -23/8 + 25/8. Suppose 4*p - 4*b = -4, -7*b - 25 = -5*p - 12*b. Let 1/2 - f*l**p - 1/4*l = 0. What is l?
-2, 1
Let s(c) be the first derivative of -375*c**6/2 - 30*c**5 + 1225*c**4/4 + 142*c**3/3 - 50*c**2 + 8*c + 1595. What is f in s(f) = 0?
-1, -2/5, 2/15, 1
Let o(d) = -10*d**3 - 17*d**2 - 16*d - 10. Let n be o(-6). Suppose n + 10*k**2 - 1634 + 5*k**4 - 15*k**3 = 0. Calculate k.
0, 1, 2
Let r(w) be the first derivative of -3*w**5/40 - w**4/4 + 3*w**3/4 + 43*w - 48. Let t(c) be the first derivative of r(c). Factor t(f).
-3*f*(f - 1)*(f + 3)/2
Let k(h) be the third derivative of -1/5*h**6 + 0*h**3 + 5/6*h**4 - 4/15*h**5 + 1/84*h**8 + h**2 + 8/105*h**7 - 18*h + 0. Solve k(d) = 0 for d.
-5, -1, 0, 1
Let f be (10/(-12))/((-13 - -18)/(-30)). Let s(k) be the first derivative of 0*k - 1/21*k**3 + 31 + 1/7*k**2 - 1/14*k**4 + 1/35*k**f. Factor s(i).
i*(i - 2)*(i - 1)*(i + 1)/7
Let n(s) be the first derivative of s**6/40 + 2*s**5/15 - s**4/6 + 53*s**3/3 - 22. Let q(u) be the third derivative of n(u). Factor q(w).
(w + 2)*(9*w - 2)
Suppose -2*p**5 + 56*p**4 + 1084*p**2 - 88948*p + 150*p**3 + 88228*p - 568*p**3 = 0. What is p?
0, 1, 4, 5, 18
Let q be 7 + (-8 - -4)*(-1173)/(-12). Let r = -381 - q. Factor -1 + 4*j**2 + 3/2*j + 3/2*j**r.
(j + 1)*(j + 2)*(3*j - 1)/2
Factor -81/2*j - 3/2*j**2 - 108.
-3*(j + 3)*(j + 24)/2
Let c = 171 + -162. Suppose 4*u + 2*p = -2, -3*u + 5*p = 8*p + c. Factor -6/5 - 3/5*m + 3/5*m**u.
3*(m - 2)*(m + 1)/5
Let t be (-111)/74*(-4)/1080. Let r(a) be the third derivative of 0*a + 31*a**2 + 0*a**3 + 0 + 1/45*a**5 + t*a**6 + 0*a**4 - 1/315*a**7. What is b in r(b) = 0?
-1, 0, 2
Let k = 3035792/5 + -607136. Factor k*l + 116/5 - 4/5*l**2.
-4*(l - 29)*(l + 1)/5
Let m(z) be the first derivative of -2*z**3/3 - 1166*z**2 - 2330*z - 3144. Suppose m(h) = 0. What is h?
-1165, -1
Let g = -5208 + 5213. Let a(k) be the second derivative of -1/24*k**4 + 0*k**2 + 0 + 1/60*k**6 + 11*k - 1/24*k**3 + 1/168*k**7 + 0*k**g. Factor a(i).
i*(i - 1)*(i + 1)**3/4
Let l be ((-112)/(-32))/((-805)/(-460)). Find r, given that 5/4*r**3 - 25 + 45/4*r**l - 15*r = 0.
-10, -1, 2
Let p(d) = -10*d - 12*d - 16*d - 1 + 37*d. Let w be p(-4). Let 0*x - 2*x**4 + x - w*x**3 + 31*x**2 - 31*x**2 = 0. Calculate x.
-1, 0, 1/2
Let d be (51/30)/((-305)/(-25) - (6 + 6)). Factor 1/2*c**2 + 8 - d*c.
(c - 16)*(c - 1)/2
Suppose -2*h + 83 = y + 521, 5*y + 2*h + 2182 = 0. Let g = 439 + y. Factor -8/5 + 8/5*o**2 + 2/5*o**g - 2/5*o.
2*(o - 1)*(o + 1)*(o + 4)/5
Factor -10420 + 18*n**3 - 22*n**3 + 108*n**3 - 127505*n**2 + 53*n**3 + 88*n**3 - 72920*n.
5*(n - 521)*(7*n + 2)**2
Let t be ((-23020)/(-149630))/((-4)/2 - 34/(-13)). Determine q so that -1/4 - t*q**4 - 3/2*q**2 - q**3 - q = 0.
-1
Let d = 36 - 34. Find f, given that d*f - 42*f**2 + f + 8*f**3 + 7*f = 0.
0, 1/4, 5
Let g(a) = -11*a**2 - 268*a - 107. Let y(h) = -12*h**2 - 332*h - 108. Let w(r) = 6*g(r) - 5*y(r). Find b, gi