- 5*w**2. Let h(i) be the first derivative of j(i). Factor h(r).
-3*r**2*(r + 5)/7
Let o(z) be the second derivative of z**7/1260 - z**6/360 - z**5/30 - 7*z**4/4 + 16*z. Let x(b) be the third derivative of o(b). Factor x(s).
2*(s - 2)*(s + 1)
Suppose 0 = 3*i - 13 + 1. Suppose -4*x + 6*x - i = 0. Factor 0*g**3 + 2/9 + 2/9*g**4 - 4/9*g**x + 0*g.
2*(g - 1)**2*(g + 1)**2/9
Let z(o) be the second derivative of -o**9/30240 + o**8/8960 - o**6/2880 + o**4/12 - 5*o. Let h(r) be the third derivative of z(r). What is b in h(b) = 0?
-1/2, 0, 1
Let g(m) = -3*m**5 + m**4 - m**3 - 12*m**2 - 17*m - 10. Let n(f) = 5*f**5 - f**4 + f**3 + 17*f**2 + 26*f + 16. Let a(i) = -8*g(i) - 5*n(i). Factor a(h).
-h*(h - 2)*(h + 1)**2*(h + 3)
Suppose 0 = -4*c - 2*t + 1646, -5*t = 3*c - 6*c + 1228. Find q such that -4*q**2 + c*q - 411*q = 0.
0
Let c = 33 + -34. Let s be c + 3/(-6) - (-3)/2. Determine h so that 2/11*h**3 - 2/11*h + 2/11*h**4 + s - 2/11*h**2 = 0.
-1, 0, 1
Let x = -1117 + 1125. Let a(r) be the second derivative of 0 + x*r - 1/42*r**4 + 1/21*r**3 + 0*r**2. Factor a(f).
-2*f*(f - 1)/7
Let f(b) be the second derivative of -b**4/20 + 149*b**3/5 - 66603*b**2/10 + 15*b + 10. Factor f(w).
-3*(w - 149)**2/5
Factor 12 + 5054*g - 18*g**4 - 60*g**3 - 12 - 5102*g - 2*g**5 - 88*g**2.
-2*g*(g + 2)**3*(g + 3)
Let w(m) be the third derivative of -m**6/40 - m**5/8 + 9*m**4/16 + 9*m**3/2 + 7*m**2 - 4. What is g in w(g) = 0?
-3, -3/2, 2
Let r(x) be the first derivative of 2*x**5/55 + 3*x**4/22 - 14*x**3/33 - 15*x**2/11 + 36*x/11 - 136. Find i such that r(i) = 0.
-3, 1, 2
Let h = 10/47 + -33/376. Let b(t) be the second derivative of -3/16*t**4 - h*t**3 - 9/80*t**5 + 0 - 5*t - 1/40*t**6 + 0*t**2. Solve b(c) = 0.
-1, 0
Let q(v) be the third derivative of v**8/336 - 13*v**7/105 + 11*v**6/60 + 4*v**5/3 - 127*v**4/24 + 25*v**3/3 - 891*v**2. Determine a, given that q(a) = 0.
-2, 1, 25
Let r be (2/192)/((-39)/(-52)). Let w(c) be the second derivative of r*c**4 + 0 + 1/18*c**3 + 0*c**2 - 8*c. Factor w(d).
d*(d + 2)/6
Let k(r) = -22*r**2 + 3*r. Let v(p) = -5*p - 28*p - 2*p + 265*p**2. Let z(f) = 25*k(f) + 2*v(f). Factor z(w).
-5*w*(4*w - 1)
Suppose -2*g = 2*q - 3*q - 21, 2*g - 4*q = 6. Suppose g*p = 8*p + 10. Factor f**p - f**2 + 0*f**3 - 3*f**2 + 3*f**3.
3*f**2*(f - 1)
Factor 2/11*u**4 + 0 - 16/11*u**2 - 2/11*u**3 + 24/11*u.
2*u*(u - 2)**2*(u + 3)/11
Factor 7/11*b - 1/11*b**2 - 6/11.
-(b - 6)*(b - 1)/11
Find b such that -7/2*b - 1/2*b**3 - 5/2*b**2 - 3/2 = 0.
-3, -1
Let q(c) be the first derivative of 2/21*c**3 - 17/7*c**2 - 32 + 32/7*c. Let q(i) = 0. What is i?
1, 16
Let u(c) = c - 1. Let t(d) = -d + 2. Let y(s) = -3*t(s) - 4*u(s). Let b be y(-5). Factor 12/5*i**2 + 4/5*i**b + 0 + 8/5*i.
4*i*(i + 1)*(i + 2)/5
Let z(f) be the second derivative of 1/230*f**5 + 0 - 1/69*f**4 + 6*f - 4/23*f**2 - 7/69*f**3. Solve z(v) = 0 for v.
-1, 4
Let k = -1084 - -1090. Let w(d) be the first derivative of 1/8*d**k + 480*d**2 + 768*d + 160*d**3 + 3*d**5 + 30*d**4 + 6. Solve w(r) = 0.
-4
Let j(z) be the second derivative of z**5/60 + 151*z**4/36 + 2812*z**3/9 - 2888*z**2/3 - 130*z + 1. Factor j(v).
(v - 1)*(v + 76)**2/3
Let a = -26 + 22. Let c(w) = 3*w**2 + 3*w + 2. Let q be c(a). Factor -q + 15*b + 3*b**2 + 18 + 2*b**2.
5*(b - 1)*(b + 4)
Let h(r) = -2*r**2 + r + 4. Let p(j) = j. Let x(z) = 2*h(z) - 6*p(z). Factor x(o).
-4*(o - 1)*(o + 2)
Suppose 0 = n - 2*j - 3*j - 29, 5*n = 3*j + 35. Suppose 0 = -n*i - 3*i + 21. Solve 4/9*f**2 + 2/9*f + 0 + 2/9*f**i = 0 for f.
-1, 0
Let i be (-31)/(-3) - (0 + (-4)/6). Let y = -43/4 + i. Suppose y*t**3 + 0 + 0*t - 1/4*t**5 + 0*t**4 + 0*t**2 = 0. Calculate t.
-1, 0, 1
Let p(u) = -3*u**2 - 16*u. Let r(s) = -20*s**2 - 104*s. Suppose -5*f = 32 - 192. Let j(x) = f*p(x) - 5*r(x). Let j(b) = 0. Calculate b.
-2, 0
Let v(c) be the third derivative of -c**7/70 - c**6/10 + 3*c**5/20 + 9*c**4/4 + 143*c**2. Let v(g) = 0. Calculate g.
-3, 0, 2
Let t(c) be the third derivative of c**6/60 + 7*c**5/30 - 10*c**4/3 + 44*c**3/3 + 45*c**2. Factor t(q).
2*(q - 2)**2*(q + 11)
Let l(r) be the first derivative of 2*r**6/3 - 12*r**5 - 2*r**4 + 40*r**3 + 2*r**2 - 60*r - 111. Solve l(v) = 0 for v.
-1, 1, 15
Let f be ((-42)/4)/((-6)/12). Let j = 24 - f. Factor -8*k - k**2 - 3*k**j + 5*k**2 + k**3 + 4*k**2.
-2*k*(k - 2)**2
Let h be 33 + 304/(-9) + 0 + 1. Factor -4/9*l + 0 + h*l**3 - 2/9*l**2.
2*l*(l - 2)*(l + 1)/9
Let k = 172/207 - 14/23. What is v in -k*v**2 + 10/9*v - 4/3 = 0?
2, 3
Let s(l) be the second derivative of -85*l**4/12 + 115*l**3/3 - 60*l**2 - l + 168. Determine i so that s(i) = 0.
12/17, 2
Let m be (3 - -1) + -8 - -31. Factor 9*z - 6*z**2 + 18*z**3 + 6 + 0*z - m*z**3.
-3*(z - 1)*(z + 1)*(3*z + 2)
Let q(h) be the third derivative of 0*h + 0 - 8*h**2 + 0*h**3 - 1/12*h**4 - 1/60*h**5. Factor q(b).
-b*(b + 2)
Let n(d) = 2*d**3 - 330*d**2 - 2049*d - 3017. Let k(w) = -w**3 + 110*w**2 + 682*w + 1006. Let b(v) = -17*k(v) - 6*n(v). Factor b(x).
5*(x + 2)*(x + 10)**2
Let s(z) be the third derivative of 0*z**3 + 0 + 0*z**5 - 1/1155*z**7 + 0*z + 0*z**4 + 7*z**2 - 1/330*z**6. Determine g so that s(g) = 0.
-2, 0
Let o = 54961/4 - 13738. Solve -3/4*l**2 + 3/2 + 9/4*l - 3/4*l**4 - o*l**3 = 0.
-2, -1, 1
Let m = -29 + 43. Let y(w) = 14*w**3 - 37*w**2 + 8*w - 5. Let p(q) = 42*q**3 - 110*q**2 + 24*q - 14. Let v(h) = m*y(h) - 5*p(h). Factor v(u).
-2*u*(u - 2)*(7*u - 2)
Let m(v) be the first derivative of -v**4/28 - 2*v**3/7 + v**2/2 - 56. Factor m(o).
-o*(o - 1)*(o + 7)/7
Let o be -3 + (175/58 - 1) + 1. Let h = 27/116 + o. Solve -9/4*b**2 - h*b**3 - 27/4*b - 27/4 = 0.
-3
Suppose -20*z + 530 - 430 = 0. Factor 0*u + 0 + 1/7*u**z - 2/7*u**4 + 1/7*u**3 + 0*u**2.
u**3*(u - 1)**2/7
Factor 80/9 - 4/9*v**2 + 32/9*v.
-4*(v - 10)*(v + 2)/9
Let l = 995/48 + -62/3. Let v(c) be the first derivative of 0*c + 0*c**3 + 1/20*c**5 - 2 - l*c**4 + 0*c**2. Factor v(q).
q**3*(q - 1)/4
Factor -2*l**2 - 5*l**2 - 5*l**3 + 9 + 3*l**3 + 5*l**2 - 5*l**2.
-(l - 1)*(l + 3)*(2*l + 3)
Let t(v) = -15*v**2 + 27*v + 18. Let p(h) = 1. Let j(g) = 12*p(g) - t(g). Factor j(k).
3*(k - 2)*(5*k + 1)
Suppose -15 = 3*m + 75*t - 70*t, -15 = -m + 5*t. Let m + 6/5*u**2 - 4/5*u**3 - 2/5*u**4 + 0*u = 0. What is u?
-3, 0, 1
Let m = 9 - 6. Let y(j) = -5*j**3 - 15*j**2 + 5*j + 5. Let p(l) = -2*l**3 - 8*l**2 + 2*l + 2. Let x(g) = m*y(g) - 5*p(g). Factor x(q).
-5*(q - 1)*(q + 1)**2
Let q be 84/(-7) - (-17 - -3). Factor -3/5*v**q + 2/5*v + 1/5.
-(v - 1)*(3*v + 1)/5
Let y(f) be the third derivative of 2/15*f**5 - 4*f**2 - 4/105*f**7 + 1/84*f**8 - 1/6*f**4 + 0 + 0*f**6 + 0*f + 0*f**3. Factor y(c).
4*c*(c - 1)**3*(c + 1)
Let x(q) = -q**3 + 1. Let u(b) = -4*b**4 - 208*b**3 - 3264*b**2 - 16184*b + 19660. Let c(k) = -u(k) + 8*x(k). What is h in c(h) = 0?
-17, 1
Let g(c) be the first derivative of 1/2*c**2 + 4 + 0*c - 1/3*c**3. Let g(r) = 0. What is r?
0, 1
Let f(w) = w**2 + 16*w + 96. Let j(p) = p**2 + 17*p + 97. Let r(k) = -3*f(k) + 4*j(k). Suppose r(x) = 0. What is x?
-10
Let s(i) be the first derivative of 0*i - 1/32*i**4 - 1/20*i**5 + 1/12*i**3 + 4 - 1/2*i**2 - 7/480*i**6. Let x(a) be the second derivative of s(a). Factor x(c).
-(c + 1)**2*(7*c - 2)/4
Let a(w) be the second derivative of -2/15*w**6 - 2*w - 6/5*w**5 - 4*w**4 - 6*w**2 - 20/3*w**3 + 0. Factor a(r).
-4*(r + 1)**3*(r + 3)
Determine h so that -6/7*h**2 - 2/7*h**4 - 8/7*h + 8/7 + 8/7*h**3 = 0.
-1, 1, 2
Let z be (15/9)/(1/3). Suppose z*n - 4*p - 14 = 3*n, -5*p = 3*n + 1. Determine l so that 10*l**3 - 3*l**2 + 18*l - 19*l**2 - n - 2*l**2 - 1 = 0.
2/5, 1
Suppose b = f - 8, -5*b + 9 + 11 = f. Let k = f + -9. Suppose k - 9*j**2 - 4*j - 3*j**3 - 3 - 1 - 5*j = 0. Calculate j.
-1
Suppose 2*l = -3*d - 14, -3*l = 3*d + d + 21. Let y = -4 - l. Factor -3*u**y + 12 - 19*u + 5*u + 2*u**2 - 10*u + 13*u**2.
-3*(u - 2)**2*(u - 1)
Let o = -196 - -198. Let d be 0/(-32)*1/(o - 1). Determine x, given that -3/2*x + d + 2*x**2 - 1/2*x**3 = 0.
0, 1, 3
Find t, given that 4*t**5 - 11017*t**2 + 1 + 48*t**4 + 144*t**3 - 1 + 11145*t**2 = 0.
-8, -2, 0
Let k = 20411/61242 - -1/20414. Factor 3 + k*g**4 + 22/3*g**2 + 8*g + 8/3*g**3.
(g + 1)**2*(g + 3)**2/3
Let g(v) be the first derivative of -27*v**4/28 + 34*v**3/7 - 57*v**2/14 - 18*v/7 + 57. Factor g(c).
-3*(c - 3)*(c - 1)*(9*c + 2)/7
Let w(k) be the first derivative of 0*k + 5/16*k