- 8*g**2 - 3. Let a(t) = -3*u(t) - 20*y(t). Determine q so that a(q) = 0.
-1, 0
Let b(s) = -5*s**5 + 20*s**4 - 5*s**3 + 30*s**2 - 30. Let u(a) = -a**4 - a**2 + 1. Let m(i) = -b(i) - 30*u(i). Factor m(w).
5*w**3*(w + 1)**2
Factor 0*n - 1/3*n**2 - 1/3*n**3 + 0.
-n**2*(n + 1)/3
Let t(w) = -3*w**5 + 2*w**4 + 11*w**3 + w**2 + 2*w + 2. Let d(u) = 3*u**5 - u**4 - 10*u**3 - 2*u**2 - u - 1. Let l(n) = 5*d(n) + 4*t(n). Factor l(y).
3*(y - 1)**2*(y + 1)**3
Let j(f) be the first derivative of -f**4/3 + 2*f**3/3 - 2*f - 10. Let u(p) be the first derivative of j(p). Solve u(g) = 0 for g.
0, 1
Factor 0 - 2/13*w**2 + 4/13*w.
-2*w*(w - 2)/13
Let r = 5/76 - 525/38. Let j = 14 + r. Factor -1/2*z**4 + 1/4 - 3/4*z**2 + j*z - 5/4*z**3.
-(z + 1)**3*(2*z - 1)/4
Let b(d) = 64*d**2 + 160*d + 95. Let m(g) = -96*g**2 - 240*g - 142. Let r(i) = 8*b(i) + 5*m(i). Factor r(j).
2*(4*j + 5)**2
Let j(w) be the third derivative of w**5/20 - w**3/2 - 7*w**2. Solve j(l) = 0 for l.
-1, 1
Let v = 23 + -17. Let h(f) be the second derivative of 1/9*f**3 + 0*f**2 + 0*f**5 + 2/45*f**v + f - 1/63*f**7 - 1/9*f**4 + 0. Determine w, given that h(w) = 0.
-1, 0, 1
Let i(g) be the third derivative of -1/10*g**3 + 0*g + 1/60*g**4 - 8*g**2 + 1/300*g**5 + 0. Find w such that i(w) = 0.
-3, 1
Let w be (-7 + -4 - -7)/(-6). Let 2/3*y**3 - w*y**2 - 2/3*y + 2/3 = 0. Calculate y.
-1, 1
Let p(d) be the first derivative of 7*d**5/5 + 5*d**4/4 - 2*d**3/3 + 6. Let p(s) = 0. What is s?
-1, 0, 2/7
Let m(j) = j + 1. Let o(z) = -3*z**4 + 3*z**3 + 3*z**2 + 3*z + 6. Let y(s) = -6*m(s) + o(s). Factor y(v).
-3*v*(v - 1)**2*(v + 1)
Let f(o) be the second derivative of -o**7/105 + o**5/25 - o**3/15 - 3*o. Solve f(a) = 0.
-1, 0, 1
Let v(g) be the third derivative of g**8/896 + g**7/280 - g**5/80 - g**4/64 - 11*g**2. Factor v(i).
3*i*(i - 1)*(i + 1)**3/8
Let b(f) be the third derivative of f**5/100 - 42*f**2. What is y in b(y) = 0?
0
Suppose -2*h - 3*y + 1 = 0, -y + 5 + 7 = 3*h. Suppose -3*v - 11 = 2*c, 5*c + h*v = -7 - 8. Find q, given that -2/3*q**3 - 1/3 + 1/3*q**c + 2/3*q = 0.
-1, 1/2, 1
Let b(v) = -13*v - 11. Let i be b(-1). Factor 1/3*o**i + 2/3*o + 1/3.
(o + 1)**2/3
Let s(a) be the third derivative of 0*a + 0*a**5 + 0 - 3*a**2 - 1/6*a**4 + 1/3*a**3 - 1/105*a**7 + 1/30*a**6. Solve s(x) = 0 for x.
-1, 1
Let d be (4/(-10))/((-3)/15). Suppose 5*b**2 - 17*b**3 + d*b + 15*b**3 - 5*b**2 = 0. Calculate b.
-1, 0, 1
Let h(j) be the second derivative of -j**5/20 - j**4/4 + j**3/6 + 3*j**2/2 - 9*j. Factor h(r).
-(r - 1)*(r + 1)*(r + 3)
Let j(l) be the first derivative of l**6/360 - l**5/60 - l**3 + 2. Let f(d) be the third derivative of j(d). Factor f(u).
u*(u - 2)
Let i be (-177)/(-7) - 4/14. Let b be (2/(-5))/((-5)/i). Factor 2/7 + 2/7*m + 6/7*m**3 - 10/7*m**b.
2*(m - 1)**2*(3*m + 1)/7
Let v(j) = -65*j**2 + 125*j - 95. Let z(n) = 11*n**2 - 21*n + 16. Let a(s) = -6*v(s) - 35*z(s). Solve a(k) = 0 for k.
1, 2
Let p(b) be the second derivative of b**5/60 - 5*b**4/36 - b**3/18 + 5*b**2/6 + 20*b. Determine a so that p(a) = 0.
-1, 1, 5
Let a = -71 + 71. Factor -1/4*d**2 + a + 1/4*d.
-d*(d - 1)/4
Let y(c) be the second derivative of -c**6/120 + c**5/40 - c**3/12 + c**2/8 - 7*c. Factor y(m).
-(m - 1)**3*(m + 1)/4
Let p(d) = d**3 - d**2 + d + 1. Let w(y) = -90*y**5 + 15*y**4 + 15*y**3 - 5*y - 5. Let u(h) = -5*p(h) - w(h). Solve u(o) = 0 for o.
-1/2, 0, 1/3
Let x(o) be the second derivative of o**6/6 + o**5/4 - 16*o. Solve x(d) = 0 for d.
-1, 0
Let 2/7*t**2 + 0*t - t**3 + 0 = 0. Calculate t.
0, 2/7
Let m(p) be the third derivative of p**6/24 - 17*p**5/60 + 2*p**4/3 - 2*p**3/3 - 16*p**2. Find k such that m(k) = 0.
2/5, 1, 2
Factor 50*m + m**2 - 9 - 35*m - 3*m**3 - 4*m**2.
-3*(m - 1)**2*(m + 3)
Let c be 370/45 + 4/(-18). Let a = -4 + c. Determine s, given that -s**3 + 1/3*s**a + 0 + s**2 - 1/3*s = 0.
0, 1
Let c(l) = -l**3 + 5*l**2 + 13*l + 9. Let n be c(7). Let -13*i**2 + 6*i**n + 0*i - 3 + 8*i**2 + 2*i = 0. What is i?
-3, 1
Let f = 25/58 + 2/29. Let o be (2 + 32/(-12))/((-16)/6). Determine b so that 0*b + f*b**4 + 0 + 0*b**2 + 1/4*b**5 + o*b**3 = 0.
-1, 0
Let q(j) be the first derivative of 4*j**3/9 + 8*j**2/3 + 16*j/3 + 17. Factor q(a).
4*(a + 2)**2/3
Find d such that 1/2 + 1/2*d**2 - d = 0.
1
Let i be (49/105)/(3/6). Let x(k) be the first derivative of 2/3*k**2 - 2 - 2/3*k**3 - i*k**5 + 0*k - 2*k**4. Factor x(a).
-2*a*(a + 1)**2*(7*a - 2)/3
Let c(o) = o**2 - 21*o + 56. Let v be c(18). Solve 4/7*i**4 - 2/7*i**5 - 4/7*i**v + 2/7*i + 0*i**3 + 0 = 0.
-1, 0, 1
Determine c, given that 4 + 3*c + c + 2*c**4 + 10*c**3 + 14*c - 4*c + 18*c**2 = 0.
-2, -1
Let v(t) be the second derivative of t**4/8 - 3*t**3/2 + 27*t**2/4 + 12*t. Factor v(x).
3*(x - 3)**2/2
Let t(c) = -2*c**3 + 15*c**2 - 18*c + 8. Let r(n) = -8*n**3 + 61*n**2 - 72*n + 32. Let h(d) = -6*r(d) + 26*t(d). Find u, given that h(u) = 0.
1, 4
Suppose -d = v + 704, -5*d + 4*v = -3*d + 1396. Let a be (-2)/7 + d/(-105). Factor 14/5*c**3 + 22/5*c - 4/5 - a*c**2.
2*(c - 1)**2*(7*c - 2)/5
Factor 0 + 1/2*q**3 + q - 3/2*q**2.
q*(q - 2)*(q - 1)/2
Let r(z) be the first derivative of -z**4/4 + z**3/3 + 5*z**2/2 + 3*z - 9. Solve r(j) = 0.
-1, 3
Let a(q) = -q**2 - 6*q. Let l be a(-6). Suppose -3*f - f + 8 = l. Factor -w**f + w**3 - 2 + 2.
w**2*(w - 1)
Let f(c) be the second derivative of c**6/60 + 3*c**5/40 + c**4/8 + c**3/12 + 2*c. Factor f(h).
h*(h + 1)**3/2
Let g(r) = r**3. Let o(i) = -4*i**3 + 5*i**2 + 3*i - 9. Let m(p) = 10*g(p) + 2*o(p). Factor m(u).
2*(u - 1)*(u + 3)**2
Let w(u) be the third derivative of -4*u**2 + 0*u + 0 + 1/72*u**6 - 1/9*u**4 + 2/9*u**3 - 7/180*u**5. Factor w(l).
(l - 2)*(l + 1)*(5*l - 2)/3
Let 40/3*c**4 - 10*c**2 - 5/3*c + 5/3 + 20/3*c**3 = 0. What is c?
-1, -1/2, 1/2
Let b(a) be the third derivative of a**5/120 - a**4/12 + a**3/4 - 6*a**2. Factor b(i).
(i - 3)*(i - 1)/2
Let a(n) = 9*n**5 + 17*n**4 + 46*n**3 + 41*n**2 + 27*n + 9. Let g(h) = -h**5 + h**4 + h**2 - h - 1. Let y(l) = -a(l) - 5*g(l). Determine r so that y(r) = 0.
-2, -1, -1/2
Let m be -3 + (-36)/(-56)*-258. Let r = m + 170. Factor 10/7*k**2 - 2/7*k + 2/7*k**3 - 2/7 - 16/7*k**4 + r*k**5.
2*(k - 1)**3*(2*k + 1)**2/7
Suppose -y**2 - y**2 - y**2 + 733*y**3 - 732*y**3 = 0. What is y?
0, 3
Suppose -10*n - 6 = -26. Factor 3/5*u - 1/5*u**n - 2/5.
-(u - 2)*(u - 1)/5
Let p(v) be the second derivative of -7*v**5/360 - v**4/72 + v**2 - 2*v. Let b(c) be the first derivative of p(c). Factor b(m).
-m*(7*m + 2)/6
Suppose -36*h = -7*h - 58. Let l = -223/4 + 56. Find y, given that 1 + 13/4*y**h - 3*y - 3/2*y**3 + l*y**4 = 0.
1, 2
Suppose 0*x = 3*x - 3, 3*r + 2*x - 8 = 0. Let q(m) be the second derivative of -2/3*m**3 + m**2 + r*m + 1/6*m**4 + 0. Factor q(s).
2*(s - 1)**2
Find r such that 0*r**2 + 0*r + 1/6*r**3 - 1/6*r**4 + 0 = 0.
0, 1
Let y be (-11)/77 + 46/126. Let z = -1/19 - -85/171. What is j in -y*j + 0 + z*j**2 - 2/9*j**3 = 0?
0, 1
Find s, given that 30/7 + 6/7*s**3 + 6*s**2 + 66/7*s = 0.
-5, -1
Suppose 0 = -2*q - y + 7, 4 = q - 0*q + y. Find z, given that -65*z - 2*z**2 - z**4 + 4*z**q + 53*z + 2*z**4 + 9 = 0.
-3, 1
Factor -2/15*s**2 + 0 + 2/15*s**3 - 2/15*s**5 + 0*s + 2/15*s**4.
-2*s**2*(s - 1)**2*(s + 1)/15
Let 3*j**2 - 4*j**2 - 19*j - 23*j**2 + 9*j**3 + 27*j**4 + 7*j = 0. What is j?
-2/3, 0, 1
Let r(p) be the second derivative of -p**4/36 + 4*p**3/9 - 8*p**2/3 + 15*p. Factor r(k).
-(k - 4)**2/3
Let b(g) be the third derivative of -2/9*g**3 + 0*g + 2*g**2 + 0*g**5 + 1/180*g**6 + 0 - 1/12*g**4. Suppose b(c) = 0. Calculate c.
-1, 2
Suppose -35 = -0*q + 4*q - 3*s, 4*q - 4*s = -36. Let k = -6 - q. Factor 4*i**3 - k*i**5 - i + i - 2*i.
-2*i*(i - 1)**2*(i + 1)**2
Let h(s) be the third derivative of -s**11/498960 - s**10/226800 + s**5/12 - 2*s**2. Let o(m) be the third derivative of h(m). Factor o(f).
-2*f**4*(f + 1)/3
Let a be 5 + 2/6 + -5. Solve a*f - 1/6*f**2 + 0 = 0.
0, 2
Let w be (-10)/(-35) - 78/(-21). Find p such that -6*p**3 - 2*p + 17*p**4 - 15*p**4 + w*p**2 + 2*p**2 = 0.
0, 1
Suppose -h**3 + 1/3*h**4 - 1/3*h + 0 + h**2 = 0. What is h?
0, 1
Let g(f) = -10*f**3 + 5*f**2 - 10. Let a(x) = 11*x**3 - 4*x**2 + x + 10. Let y(s) = 5*a(s) + 6*g(s). Find h, given that y(h) = 0.
-1, 1, 2
Let b be (1 - -3)*(-1)/(-2). Factor -55*t + 53*t + 28*t**3 + t**2 - b*t**2.
t*(4*t + 1)*(7*t - 2)
Let y(b) be the third derivative of b*