ative of s(t). Factor g(z).
-4*z*(z - 1)**2*(z + 1)**2
Let f(p) be the first derivative of -6/5*p**5 + 15/4*p**4 + 0*p + 7 + 4*p**3 - 9/2*p**2. What is j in f(j) = 0?
-1, 0, 1/2, 3
Let y(a) = -a**2 - 10*a - 17. Let p be y(-7). Factor 15*t**3 - 2*t - 37*t**4 + 42*t**p + 2*t - 20*t**2.
5*t**2*(t - 1)*(t + 4)
Let r(n) be the third derivative of n**7/490 - n**6/140 - 2*n**5/35 + 9*n**4/28 - 9*n**3/14 - 251*n**2 + n. Let r(v) = 0. Calculate v.
-3, 1, 3
Let y(o) be the first derivative of -2*o**5/15 + 7*o**4/6 - 10*o**3/3 + 13*o**2/3 - 8*o/3 + 43. Suppose y(d) = 0. What is d?
1, 4
Let l(n) be the second derivative of -n**6/90 - 26*n**5/15 - 901*n**4/12 + 52*n**3/9 + 1352*n**2/3 - 596*n. Factor l(u).
-(u - 1)*(u + 1)*(u + 52)**2/3
Let u(r) = 2*r**2 - 2*r - 2. Suppose 0 = 16*f - 13*f + 3. Let z be u(f). Suppose 1/3*t**z + 0 - 1/3*t = 0. Calculate t.
0, 1
Let n(p) be the second derivative of p**8/3360 + p**7/630 + p**6/360 + 7*p**4/4 - 6*p. Let j(g) be the third derivative of n(g). Let j(k) = 0. Calculate k.
-1, 0
Suppose 2*y = -y. Let z be (-2 - y) + 1 + 3. Suppose 2*q**3 - 2*q + 2*q**z - 15*q**4 + 0*q**3 + 13*q**4 = 0. What is q?
-1, 0, 1
Factor 4*o**2 + 4652 - 4*o - 76*o - 4252.
4*(o - 10)**2
Let s(c) = -15*c**3 - 245*c**2 - 5*c + 240. Let m(q) = 7*q**3 + 122*q**2 + q - 120. Let w(z) = 5*m(z) + 2*s(z). Let w(n) = 0. What is n?
-24, -1, 1
Factor -35/4*m + 0 - 1/12*m**2.
-m*(m + 105)/12
Let g be (-756 - -753)*6/(-11). Find q such that g*q + 28/11 + 2/11*q**2 = 0.
-7, -2
Determine h, given that -56*h - 159*h + 50*h**4 - 180*h**3 - 5*h**5 + 188 + 290*h**2 - 128 = 0.
1, 3, 4
Let h = 70 - 64. Let q(r) = r**2. Let o(n) = -9*n**2 + 6*n. Let t(j) = h*q(j) + o(j). Solve t(i) = 0.
0, 2
Let l be (-26)/(-35) + (30/(-35))/6. Let b be (-39)/(-90) + (-2)/(-12). Suppose b*f**5 - 1/5 - 6/5*f**3 + l*f - 1/5*f**4 + 2/5*f**2 = 0. What is f?
-1, 1/3, 1
Let r(f) be the first derivative of -f**3/12 + 43*f**2/4 - 1849*f/4 + 141. Let r(c) = 0. What is c?
43
Let r(f) = f**3 - 3*f**2 - 4*f + 3. Let c be r(4). Factor 3*g**3 + 13*g**4 + g**c - 12*g**4 + 4*g**2.
g**2*(g + 2)**2
Determine n so that -3/2*n - 1/2*n**2 + 2 = 0.
-4, 1
Let s(a) be the third derivative of a**8/40320 + a**7/5040 - 11*a**5/60 + 12*a**2. Let r(b) be the third derivative of s(b). Factor r(i).
i*(i + 2)/2
Let v(i) = -5*i**2 - i + 3. Let y(q) = 5*q - 3 + 29*q**2 + 0 - 14. Let h(w) = -34*v(w) - 6*y(w). Factor h(s).
-4*s*(s - 1)
Suppose 48*x + 1151 = -12*x + 1271. Let l be 14/(-16) + 0 + 1. Factor 3/8*i + l*i**x + 0.
i*(i + 3)/8
Let f(s) = 988*s + 2967. Let i be f(-3). Factor 3/2*n**2 + 3/2*n**i + 0 + 1/2*n + 1/2*n**4.
n*(n + 1)**3/2
Let f(d) = -d**2 + 5*d + 2. Let s(c) = -7*c + 2. Let h be s(-4). Let q(l) = 2*l**2 + 37*l + h*l + 21 - 11*l**2 - 16*l. Let m(r) = 21*f(r) - 2*q(r). Factor m(w).
-3*w*(w - 1)
Let t(a) be the second derivative of -a**4/3 + 88*a**3/3 - 86*a**2 - a - 43. Factor t(s).
-4*(s - 43)*(s - 1)
Let n be -17 + 20 + (-1 - (-6)/(-4)). Let l(i) be the first derivative of 0*i - 1/9*i**3 - n*i**2 + 3. Factor l(x).
-x*(x + 3)/3
Let d(n) = 17*n**2 + 9*n + 12. Let c(y) = 20*y**2 + 8*y + 12. Let s(a) = -5*c(a) + 6*d(a). Solve s(r) = 0.
-6, -1
Let 14*c**2 + 88/3*c**5 + 64*c**4 + 142/3*c**3 + 4/3*c + 0 = 0. Calculate c.
-1, -1/2, -2/11, 0
Let u(h) be the first derivative of -9*h**4/4 - 20*h**3 + 54*h**2 + 96*h + 148. Determine x so that u(x) = 0.
-8, -2/3, 2
Let i be (20/2)/(24/12). Let z(g) be the second derivative of 1/30*g**6 - 1/6*g**3 - 1/12*g**4 + i*g + 1/20*g**5 + 0*g**2 + 0. Factor z(u).
u*(u - 1)*(u + 1)**2
Factor 36/7*r**2 + 66/7*r + 32/7 + 2/7*r**3.
2*(r + 1)**2*(r + 16)/7
Let g(n) be the first derivative of 5/21*n**3 + 1/7*n**2 - 7 + 4/35*n**5 - 11/28*n**4 + 0*n. Factor g(r).
r*(r - 2)*(r - 1)*(4*r + 1)/7
Let k(b) be the second derivative of -b**7/28 + b**6/4 - 3*b**5/4 + 5*b**4/4 - 5*b**3/4 + 3*b**2/4 + 4*b + 10. Factor k(m).
-3*(m - 1)**5/2
Let m(t) be the third derivative of -t**7/1260 + t**6/90 - 7*t**5/120 + 11*t**4/72 - 2*t**3/9 + 4*t**2 + 26. Factor m(z).
-(z - 4)*(z - 2)*(z - 1)**2/6
Let g be 9*8/252 + 92/(-28) + 5. Suppose g*k**2 - 4/5 + 6/5*k = 0. What is k?
-1, 2/5
Let b = -106711/71 - -1503. Let v = b + 278/213. Find f such that 8/3*f**2 + 0 + 0*f - v*f**3 = 0.
0, 2
Let t = -8619 - -17239/2. Factor 1/2*u**2 + 0 - t*u**4 + 1/2*u**3 - 1/2*u.
-u*(u - 1)**2*(u + 1)/2
Let z be 2/((45/81)/((-10)/(-12))). Let s(t) = 4*t**2 - 1. Let d be s(1). Find a, given that -d + z + 5*a + 3 + 3*a**2 + a = 0.
-1
Let j = -2/4899 - -122483/19596. Solve 15/4*k**2 + 5/4*k**5 + 5/4*k**4 + 0*k - j*k**3 + 0 = 0 for k.
-3, 0, 1
Let q(b) be the first derivative of -2*b**3/3 + 127*b**2 + 724. Let q(a) = 0. Calculate a.
0, 127
Let o(k) be the third derivative of k**6/280 + 11*k**5/140 + 5*k**4/8 + 25*k**3/14 - 100*k**2 - 2*k. Factor o(i).
3*(i + 1)*(i + 5)**2/7
Suppose 16 = 4*x - 0. Determine b so that -11*b**5 + 11*b**5 + 4*b**5 + 4*b**x = 0.
-1, 0
Let k(r) be the second derivative of 0*r**3 - 5/3*r**4 + 9*r + 0*r**2 - 27/2*r**6 + 9*r**5 + 0. Suppose k(c) = 0. What is c?
0, 2/9
Let k(i) = i**3 - 19*i**2 - 11*i - 2. Let s be k(20). Find z such that -3*z**2 + 100*z - s*z + 93*z - 12 = 0.
1, 4
Factor 20/3 - 55/3*d**2 + 35/3*d.
-5*(d - 1)*(11*d + 4)/3
Let c(z) be the third derivative of z**7/22680 - z**5/270 - 17*z**4/8 + 2*z**2 - 7*z. Let n(u) be the second derivative of c(u). Find j, given that n(j) = 0.
-2, 2
Let g(h) be the second derivative of h**9/13608 - h**8/360 + 7*h**7/180 - 343*h**6/1620 - 4*h**3 - 6*h. Let n(d) be the second derivative of g(d). Factor n(b).
2*b**2*(b - 7)**3/9
Let c(d) be the first derivative of 2/39*d**3 + 0*d + 1 + 1/13*d**2. Factor c(l).
2*l*(l + 1)/13
Let i be (26/(-3))/(4/(-12)). Suppose 2*u = -5*w + 3*u + 24, 0 = -5*w - u + i. Solve -3*a**2 + 3*a + 0*a + 6*a**4 - 3*a**w - 3*a**2 = 0 for a.
-1, 0, 1
Factor 6*s - 2/3*s**2 - 16/3.
-2*(s - 8)*(s - 1)/3
Let x(g) be the second derivative of -g**6/30 - 23*g**5/20 + 13*g**4/2 - 27*g. Factor x(k).
-k**2*(k - 3)*(k + 26)
Let m = -3672/7 - -526. Suppose -16/7*a + 8/7 - m*a**2 = 0. Calculate a.
-2, 2/5
Let s(i) be the first derivative of i**5/100 - 11*i**4/120 + i**3/5 + 3*i**2/2 - 10. Let n(a) be the second derivative of s(a). Find c such that n(c) = 0.
2/3, 3
Suppose 0 = -2*h + 5*k - 4, k - 4*k = -6. What is u in h + 82*u - 84*u + 0*u**3 + 2*u**3 - 6*u**2 + 3 = 0?
-1, 1, 3
Let l(y) = -2*y. Let i be l(-2). Let v = 483 + -481. Factor 1/6*g**v + 0*g**3 - 1/6*g**i + 0*g + 0.
-g**2*(g - 1)*(g + 1)/6
Let x = -227/26 - -1213/130. Factor -x*j**2 + 0*j + 0 + 3/5*j**3.
3*j**2*(j - 1)/5
Let f(t) be the first derivative of t**6/33 + 4*t**5/11 - t**4/2 + 159. Factor f(y).
2*y**3*(y - 1)*(y + 11)/11
Factor -30*z**4 + 5/4*z**5 + 180*z**3 + 0 + 0*z**2 + 0*z.
5*z**3*(z - 12)**2/4
Let a(s) = -2 + 1 + 1718*s - 1717*s - s**3. Let v(k) = -12*k**3 - 18*k**2 - 6*k - 9. Let o(d) = -9*a(d) + v(d). Factor o(w).
-3*w*(w + 1)*(w + 5)
Let d be 795/225 + 55/(-25). Solve -1/3*o**2 - 4/3 + d*o = 0 for o.
2
Let k be (-2)/((3 + -4)/2). Find h such that -2*h**2 - 3*h**3 + k*h**2 + h**4 + 0*h**2 = 0.
0, 1, 2
Factor -5/8*o**2 + 0 - 1/2*o**3 - 1/8*o**4 - 1/4*o.
-o*(o + 1)**2*(o + 2)/8
Let f(i) be the second derivative of 12*i**7/7 - 79*i**6/25 + 18*i**5/25 + 9*i**4/10 - 2*i**3/5 + i. Let f(b) = 0. What is b?
-1/3, 0, 1/4, 2/5, 1
Suppose 0 = -10*p - 56 + 76. Let u(s) be the first derivative of -1/2*s**4 + 1/2*s**p - 2/3*s**3 + s + 1/6*s**6 + 1/5*s**5 - 1. Factor u(d).
(d - 1)**2*(d + 1)**3
Suppose -r = -2*r, 0 = -2*z - 5*r. Suppose -2*p + 2*i - 4 = -p, z = 2*p - 3*i + 5. Determine a, given that -15/2*a**p - 3*a + 0 - 9/2*a**3 = 0.
-1, -2/3, 0
Let b(c) = c**3 - 11*c**2 + 17*c + 10. Suppose -3*v - 3*d + 21 = -d, -12 = 4*d. Let h be b(v). Find f such that h - 1/2*f**3 - 5/2*f + 2*f**2 = 0.
1, 2
Let t = 2/2837 - -5652/31207. Factor 0*m**3 + 0 - 2/11*m**5 + t*m**4 + 0*m + 0*m**2.
-2*m**4*(m - 1)/11
Suppose -4*w = 2*y, 25 = 3*y - 4*w + 15. Let d(n) be the second derivative of 1/40*n**5 - 7/24*n**4 - y*n + 4/3*n**3 - 3*n**2 + 0. Factor d(m).
(m - 3)*(m - 2)**2/2
Let u be 24/264 + 86/22. Let -1/4*q**u + 0*q**3 + 0 + 0*q + 1/4*q**2 = 0. What is q?
-1, 0, 1
Solve 29*v + 559*v**2 + 28 - 1112*v**2 + 554*v**2 = 0.
-28, -1
Let x = -78599/120 - -655. Let k(y) be the third derivative of -1/