- a*k**2 - 5*k.
-4*k*(13*k + 2)
Let k(y) be the first derivative of 21/2*y**2 + 21 - 49/4*y**3 - 3*y. Suppose k(i) = 0. What is i?
2/7
Let f(c) = -3*c**3 + 41*c**2 - 24*c - 16. Let r(u) = 23*u**3 - 327*u**2 + 193*u + 128. Let s(l) = 51*f(l) + 6*r(l). Find q, given that s(q) = 0.
-2/5, 1, 8
Let j(o) be the first derivative of -o**5 - 105*o**4/2 + 220*o**3 - 335*o**2 + 225*o + 265. Determine d, given that j(d) = 0.
-45, 1
Let r = 141 + 1580. Let 5*t**2 + 2*t + r - 7*t**3 - 1721 = 0. Calculate t.
-2/7, 0, 1
Let z(f) be the first derivative of -2*f**5/5 - f**4/2 + 4*f**3/3 - 56. Factor z(o).
-2*o**2*(o - 1)*(o + 2)
Let r be (18/(-15))/(-2 + 8/5). Let h(l) be the second derivative of 1/90*l**6 - 1/12*l**4 + 0*l**2 + 0*l**5 + 5*l + 1/9*l**r + 0. Factor h(o).
o*(o - 1)**2*(o + 2)/3
Let u(o) = -3*o**2 + o - 1. Let g(m) = -20*m**3 - 61*m**2 - 23*m + 8. Let z(a) = g(a) - 2*u(a). Solve z(c) = 0 for c.
-2, -1, 1/4
Suppose -14 = -5*p - 4. Suppose -5*h = -t + 7, h = -2*h - 3. Let 0*b + 4*b - p*b - t*b**2 + 2*b = 0. What is b?
0, 2
Let f(v) be the second derivative of -v**7/21 + v**6/15 + v**5/10 - v**4/6 + 57*v. Factor f(h).
-2*h**2*(h - 1)**2*(h + 1)
Let m(z) = -z**4 - 226*z**3 + 16*z**2 + 10298*z - 36015. Let b(r) = 150*r**3 - 10*r**2 - 6865*r + 24010. Let n(p) = -8*b(p) - 5*m(p). Factor n(h).
5*(h - 7)**3*(h + 7)
Let q(x) be the first derivative of x**7/105 + x**6/75 - x**5/10 + x**4/10 + 2*x + 18. Let k(h) be the first derivative of q(h). Find v, given that k(v) = 0.
-3, 0, 1
Let f = 114/65 - -24/13. Let l be -9*20/50 - -6. Factor 12/5*p**3 + 3/5*p**4 + 3/5 + f*p**2 + l*p.
3*(p + 1)**4/5
Let f(s) = -s**2 + 224*s + 2645. Let n(i) = -3*i**2 + 447*i + 5290. Let p(h) = 13*f(h) - 6*n(h). Factor p(z).
5*(z + 23)**2
Let c(p) be the first derivative of -2*p + 1/66*p**4 - 1/33*p**3 + 0*p**2 - 1. Let q(n) be the first derivative of c(n). Factor q(x).
2*x*(x - 1)/11
Let u(z) = -z**4 + z**2 + z. Let p(r) = -3*r**3 + 2*r**3 + 2 + 6*r + 8*r + 12*r**2 - 10*r**4. Let s(c) = 2*p(c) - 18*u(c). Let s(i) = 0. Calculate i.
-1, 2
Let h(m) be the second derivative of m**4/12 - 13*m**3/9 + 8*m**2/3 + 1001*m. Suppose h(f) = 0. Calculate f.
2/3, 8
Let i(f) be the first derivative of 5*f**6/69 + 2*f**5/115 + 104. Factor i(y).
2*y**4*(5*y + 1)/23
Let r(i) = 4*i**2 + 336*i - 4704. Let b(d) = d**2 + 168*d - 2352. Let v(z) = 5*b(z) - 2*r(z). Let v(o) = 0. What is o?
28
Let g(i) be the second derivative of -i**7/105 + i**6/60 + i**2 + 2*i. Let h(j) be the first derivative of g(j). Factor h(a).
-2*a**3*(a - 1)
Suppose 11 + 1 + 128*h**3 + 13 - 12*h**4 + 32*h + 8 - 184*h**2 + 3 = 0. Calculate h.
-1/3, 1, 9
Suppose -3*x = -k + 7, 4*k - 28 = -4*x - x. Factor -1/5*m**4 + 1/5*m**2 + 2/5*m**3 - 2/5*m + x.
-m*(m - 2)*(m - 1)*(m + 1)/5
Factor -2048*t - 65536/3 - 2/3*t**3 - 64*t**2.
-2*(t + 32)**3/3
Let h(a) be the second derivative of -1/42*a**4 + 8*a + 0*a**2 + 0 - a**3 + 1/140*a**5 - 1/1260*a**6. Let r(y) be the second derivative of h(y). Factor r(l).
-2*(l - 2)*(l - 1)/7
Let s = -100 + 124. Let 12*z**3 + 2*z**4 + 22 - 23 + 26*z**2 + s*z + 9 = 0. What is z?
-2, -1
Let i(z) be the second derivative of z**7/2520 + z**6/720 + 5*z**4/4 - z. Let f(u) be the third derivative of i(u). Factor f(q).
q*(q + 1)
Let a(l) be the third derivative of l**8/168 + l**7/105 + 17*l**2 - 1. Factor a(o).
2*o**4*(o + 1)
Let m be 336/(-63)*3/(-2). Factor 46*x**2 + 31*x**3 + m*x - 10*x**2 - 3*x**3.
4*x*(x + 1)*(7*x + 2)
Let x(k) be the second derivative of k**5/60 - 53*k**4/36 + 103*k**3/18 - 17*k**2/2 - 731*k. What is i in x(i) = 0?
1, 51
Let g(x) = -162*x - 168. Let p(s) = -s**2 + 163*s + 168. Let n(z) = 2*g(z) + 3*p(z). Find k such that n(k) = 0.
-1, 56
Let l(b) be the third derivative of -3/64*b**4 + 0*b - 13*b**2 + 0 + 1/4*b**3 - 1/160*b**5. Factor l(p).
-3*(p - 1)*(p + 4)/8
Let n(f) be the first derivative of -5*f**2 + 36 + 1/2*f**4 + 4*f + 2*f**3 - 2/5*f**5. Find d such that n(d) = 0.
-2, 1
Let q(c) = 5*c**4 - 73*c**3 + 71*c**2 - 3*c + 3. Let f(j) = 5*j**4 - 72*j**3 + 69*j**2 - 2*j + 2. Let z(x) = -3*f(x) + 2*q(x). Find k, given that z(k) = 0.
0, 1, 13
Suppose -5*f - 1 = -11. Let w(n) be the second derivative of -f*n**2 - 4*n - 2*n**3 + 3/4*n**4 + 7/20*n**5 + 0. Factor w(m).
(m - 1)*(m + 2)*(7*m + 2)
Let t(v) = -v**2 + 2*v + 29. Let q be t(6). Suppose -15 = q*x, x + 13 = 4*b + b. Factor -2/3*l**b + 0*l**3 + 0*l + 1/3 + 1/3*l**4.
(l - 1)**2*(l + 1)**2/3
Find w such that -4030*w**3 + 30 + 330*w + 4036*w**3 - 92*w**2 - 130 = 0.
1/3, 5, 10
What is f in -83/7*f**2 - 60/7 - 20/7*f**3 - 124/7*f - 1/7*f**4 = 0?
-15, -2, -1
Let m(z) be the second derivative of 7*z - 9/2*z**2 + 0 + 1/4*z**3 + 1/8*z**4. Find p, given that m(p) = 0.
-3, 2
Let l(v) be the second derivative of -2/3*v**3 + 1/36*v**4 + 0 + 6*v**2 - 5*v. Determine p so that l(p) = 0.
6
Let d(i) = i**2 - 294*i - 10. Let k(x) = -146*x - 4. Let u(n) = -4*d(n) + 10*k(n). What is o in u(o) = 0?
-71, 0
Let n(z) be the first derivative of 0*z**5 - 3 - 2/21*z**3 + 1/420*z**6 + 0*z - 1/2*z**2 - 1/28*z**4. Let k(j) be the second derivative of n(j). Factor k(g).
2*(g - 2)*(g + 1)**2/7
Let b(f) be the third derivative of 81*f**6/40 - 63*f**5/20 - 17*f**4/8 - f**3/2 + 362*f**2. Factor b(q).
3*(q - 1)*(9*q + 1)**2
What is v in -12/5*v + 0 + 12/5*v**3 - 1/5*v**2 + 1/5*v**4 = 0?
-12, -1, 0, 1
Find h such that -24389/2 - 2523/2*h - 1/2*h**3 - 87/2*h**2 = 0.
-29
Factor -19 + 247*c - 45 - 56 + 47*c + 15*c**2.
3*(c + 20)*(5*c - 2)
Let n(j) be the third derivative of -1/140*j**6 + 4*j**2 + 0 + 0*j + 1/784*j**8 + 0*j**3 - 1/490*j**7 + 0*j**4 + 0*j**5. Factor n(l).
3*l**3*(l - 2)*(l + 1)/7
Let l be (-26 - 3114/(-120))*(-3 + -1). Determine f, given that l*f**2 + 1/5*f + 0 = 0.
-1, 0
Let y = -73708/7 + 10531. Suppose -3/7*s**4 + 9/7*s**3 + 6/7 - y*s - 3/7*s**2 = 0. Calculate s.
-1, 1, 2
Let j(o) be the third derivative of -o**5/330 + o**4/12 + 4*o**3/11 + 2*o**2 - 7. Factor j(z).
-2*(z - 12)*(z + 1)/11
Let g(p) be the second derivative of 0 - 4/3*p**3 - 1/45*p**6 - 1/5*p**5 - 13/18*p**4 - 4/3*p**2 - 4*p. Factor g(b).
-2*(b + 1)**2*(b + 2)**2/3
Suppose 3 = 3*w - 6. Suppose -9 = w*h - 3*l, -2*h + 3*l + 24 = 7*l. Let -8 + 2*m**2 - 3*m**h + 3*m**2 = 0. What is m?
-2, 2
Let t be -5*4*(-2 - (-35)/20). Let n(l) be the second derivative of -1/180*l**6 + 1/18*l**4 - 1/60*l**5 + 1/18*l**3 + 0 - 1/4*l**2 - t*l. Factor n(x).
-(x - 1)**2*(x + 1)*(x + 3)/6
Let w = 2472 + -2472. Factor 0 + w*v + 2/7*v**2.
2*v**2/7
Let x = 1093/1220 + -15/61. Let q = x - 1/20. Factor 1/5 - 2/5*h - q*h**2.
-(h + 1)*(3*h - 1)/5
Determine c, given that 2*c**3 + 5*c**2 + 328*c**4 - 330*c**4 + 3*c**2 - 8*c + 0*c**3 = 0.
-2, 0, 1, 2
Determine w so that 2/13*w**4 + 0*w - 8/13*w**3 + 0*w**2 + 0 = 0.
0, 4
Suppose 0 = -12*l + 14*l - 8. Let z be (-45)/(-12) - l/(-16). Factor -3*r**4 - r**3 + 0*r**4 + 2*r**z.
-r**3*(r + 1)
Let y(o) = -19*o**2 - 115*o. Let x(h) = 10*h**2 + 58*h. Let d(u) = 11*x(u) + 6*y(u). Suppose d(q) = 0. What is q?
-13, 0
Let r = -29773 + 29777. Factor -25/4 - 1/4*i**r + 10*i - 2*i**3 - 3/2*i**2.
-(i - 1)**2*(i + 5)**2/4
Let a be ((-4)/6)/((-6)/27). Let 10*n - 5*n**2 + 6*n**3 + 4*n**a - 15*n**3 = 0. What is n?
-2, 0, 1
Let f = 5277/20 - 1318/5. Factor -f*x**2 + 1 + 0*x.
-(x - 2)*(x + 2)/4
Let j(r) be the first derivative of 20*r - 5/3*r**3 + 19 + 15/2*r**2. Determine s so that j(s) = 0.
-1, 4
Factor 0 + 2*y**3 + 11/2*y - 45/2*y**2.
y*(y - 11)*(4*y - 1)/2
Suppose -2*h = -3*x + 6, -8*h = 4*x - 9*h - 8. Let n be (5/30)/(x/18). Let 1/2*w**2 + 0 - n*w = 0. What is w?
0, 3
Factor 0*f + 1/5*f**5 + 0 + 3/5*f**4 + 1/5*f**2 + 3/5*f**3.
f**2*(f + 1)**3/5
Let m(q) be the third derivative of q**6/60 - q**4/4 + 2*q**3/3 - 49*q**2. Let m(w) = 0. What is w?
-2, 1
Find k, given that -2*k**5 - 110*k**3 + 6*k**5 + 119 + 936*k**4 + 115*k**2 + 280*k - 19 + 6*k**5 - 971*k**4 = 0.
-2, -1, -1/2, 2, 5
Let g(p) be the second derivative of p**8/1344 + p**7/504 - p**6/18 - p**5/2 - 5*p**4/3 + 13*p. Let u(d) be the third derivative of g(d). Factor u(k).
5*(k - 3)*(k + 2)**2
Let x be -8*(-2)/(-64) + -1 + (-17)/(-4). Determine p, given that -2/3*p**x - 8/9*p - 16/9 + 20/9*p**2 = 0.
-2/3, 2
Let m(f) be the third derivative of f**7/630 - f**6/90 + 2*f**4/9 - 8*f**3/9 + 170*f**2. Determine u, given that m(u) = 0.
-2, 2
Let q(u) be the se