y**a + 1/3*y**3 - 3/2*y**2. Determine i so that t(i) = 0.
-3, 1
Let v(u) be the third derivative of u**6/360 - 13*u**5/90 + 169*u**4/72 + 7*u**2 - 3. Let v(o) = 0. What is o?
0, 13
Let x(s) = -7*s**2 - 14*s. Let r(j) be the first derivative of j**3 + 7*j**2/2 - 27. Let p(q) = -10*r(q) - 4*x(q). Let p(c) = 0. What is c?
-7, 0
Factor -1/4*w**4 + 0 + 5/4*w**3 - 3/2*w**2 + 0*w.
-w**2*(w - 3)*(w - 2)/4
Let v**2 + 15*v**2 - 7*v**2 - v**3 - 30*v + 4*v**3 = 0. What is v?
-5, 0, 2
Let o(f) = f**3 - f**2 - 2*f. Let x(m) = 12*m**3 - 72*m**2 + 33*m + 21. Let h(i) = 3*o(i) - x(i). Factor h(p).
-3*(p - 7)*(p - 1)*(3*p + 1)
Let r be -115 + 112 + (-3)/(-1). Let w(o) be the second derivative of -1/22*o**5 + 0 + 0*o**2 + r*o**3 - 1/33*o**4 - 1/231*o**7 - 4/165*o**6 + 7*o. Factor w(d).
-2*d**2*(d + 1)**2*(d + 2)/11
Let q(x) be the third derivative of x**7/70 + 3*x**6/160 - 21*x**5/80 + 17*x**4/32 - 3*x**3/8 - x**2 - 15. Let q(n) = 0. What is n?
-3, 1/4, 1
Let v(o) be the second derivative of o**4/42 + 74*o**3/21 + 708*o. Solve v(c) = 0 for c.
-74, 0
Factor 7637*m**3 - 7642*m**3 + 3*m - 83*m - 85*m**2.
-5*m*(m + 1)*(m + 16)
Let y(a) be the third derivative of -a**6/280 - 3*a**5/70 + 19*a**4/56 + 12*a**3/7 - 189*a**2. Factor y(c).
-3*(c - 3)*(c + 1)*(c + 8)/7
Let n(k) = -2*k**2 + 11*k - 5. Let w be n(4). Suppose 3*d - 5 = w. Let -4*a**4 + 15 - 4*a + d*a**2 + 4*a**3 - 15 = 0. What is a?
-1, 0, 1
Let t(x) be the third derivative of x**8/336 - x**7/105 - x**6/15 - x**5/30 + 7*x**4/24 + 2*x**3/3 - x**2. Factor t(l).
(l - 4)*(l - 1)*(l + 1)**3
Let r(t) = 12*t**4 + 9*t**3 - 27*t**2 - 27*t. Let l(z) = -z**5 - 12*z**4 - 9*z**3 + 26*z**2 + 28*z. Let k(j) = 3*l(j) + 4*r(j). Let k(c) = 0. What is c?
-1, 0, 2, 4
Let a(y) be the second derivative of y**6/2520 + y**5/168 + y**4/42 - y**3/2 + 4*y. Let q(o) be the second derivative of a(o). Determine u, given that q(u) = 0.
-4, -1
Let n(w) = 27*w**2 + 21*w + 24. Let y(c) = -23*c**2 - 21*c - 26. Let g(s) = 5*n(s) + 6*y(s). Factor g(j).
-3*(j + 3)*(j + 4)
Let f(m) be the first derivative of -24 - 1/2*m**2 - m**3 - 1/4*m**4 + 3/5*m**5 + 0*m + 1/3*m**6. Factor f(p).
p*(p - 1)*(p + 1)**2*(2*p + 1)
Suppose -18*x + 15*x = -o + 3, 0 = 2*x + 2*o - 6. Factor -3/4*p**2 + 1/4*p**3 + x*p + 0.
p**2*(p - 3)/4
Let u(k) be the third derivative of -k**8/26880 + k**7/1680 + 15*k**4/8 + 5*k**2 + 2*k. Let m(r) be the second derivative of u(r). What is g in m(g) = 0?
0, 6
Let a be 3/(-1)*10/(-6). Factor 2*w**5 + 86*w + w**3 - 84*w + 0*w**3 - a*w**3.
2*w*(w - 1)**2*(w + 1)**2
Let f = 3 - 2. Let k = 92 - 92. Factor -3*j**3 + 6*j**2 + 1 + j**3 + f - 6*j + k*j**3.
-2*(j - 1)**3
Let n(g) be the second derivative of -g**6/45 - 2*g**5/5 + 7*g**4/3 - 44*g**3/9 + 5*g**2 - 218*g - 2. What is a in n(a) = 0?
-15, 1
Let c(w) be the third derivative of 1/20*w**5 + 0 + 8*w**3 + 11*w**2 + 0*w - w**4. Suppose c(r) = 0. What is r?
4
Let z(w) be the second derivative of w**4/30 + w**3/5 - 18*w**2/5 + 144*w. Factor z(t).
2*(t - 3)*(t + 6)/5
Let b(t) be the second derivative of -t**7/420 - t**6/60 - t**3/6 + 4*t. Let m(j) be the second derivative of b(j). Determine u so that m(u) = 0.
-3, 0
Let 732 + 0*l**2 - 98*l + 1537 - 505 + 4*l**2 - 70*l = 0. Calculate l.
21
Solve 39/5*b**3 + 102/5 + 249/5*b + 189/5*b**2 - 3/5*b**4 = 0.
-2, -1, 17
Let c(y) be the second derivative of -y**6/55 + 27*y**5/110 + 21*y**4/22 + y**3 - 22*y - 1. Find k, given that c(k) = 0.
-1, 0, 11
Let o(p) = 2*p**2 - 11*p - 8. Let u be o(6). Let i be (-1 + 4/3)*u/(-1). Solve 0 - 2/3*s + i*s**3 + 2/3*s**4 - 2/3*s**2 = 0.
-1, 0, 1
Let h = 2/115 + 111/230. Let p(b) = -b**3 + 8*b**2 + 19*b + 12. Let a be p(10). Factor h*o**4 + 0 + 0*o**3 - 3/2*o**a + o.
o*(o - 1)**2*(o + 2)/2
Let f(q) be the second derivative of q**5/300 - q**4/40 + q**3/15 + 31*q**2/2 + 2*q. Let k(a) be the first derivative of f(a). Factor k(w).
(w - 2)*(w - 1)/5
Let m(o) be the first derivative of 2*o**3/5 - 57*o**2/10 + 27*o - 126. Solve m(s) = 0 for s.
9/2, 5
Let t(k) be the third derivative of -k**6/60 - 11*k**5/30 + k**4 + 10*k**2 + k. Factor t(i).
-2*i*(i - 1)*(i + 12)
Suppose 45 = 5*r + 20. Let c(k) be the second derivative of -1/10*k**r - 1/3*k**3 + 0 + 0*k**2 - 1/3*k**4 - 9*k. Suppose c(g) = 0. Calculate g.
-1, 0
What is m in 6*m**5 + 5833*m - 5833*m - 2*m**4 = 0?
0, 1/3
Suppose 3*g + 16 = 2*i, 3*g = -7*i + 5*i - 8. Factor 96/7*a + 2/7*a**3 - 72/7 - 26/7*a**i.
2*(a - 6)**2*(a - 1)/7
Solve -1962*t - 4*t**3 - 4*t**2 + 4*t**2 + 1998*t = 0 for t.
-3, 0, 3
Suppose -2*q**2 - q**3 - 1/2*q**5 + 3/2*q + 2*q**4 + 0 = 0. What is q?
-1, 0, 1, 3
Let x be 1 + (-8)/(-4)*-1. Let p(v) = v**3 - v**2 + 1. Let r(d) = d**3 - 9*d**2 + 8*d - 3. Let j(o) = x*r(o) - 3*p(o). Solve j(w) = 0.
0, 1, 2
Let x(d) be the second derivative of d**4/4 + 7*d**3/2 + 9*d**2 + 35*d - 1. Factor x(f).
3*(f + 1)*(f + 6)
Let q(b) be the third derivative of -1/15*b**5 + 0*b + 0 - 1/20*b**6 + 0*b**7 + 20*b**2 + 1/168*b**8 + 0*b**3 + 0*b**4. Suppose q(x) = 0. What is x?
-1, 0, 2
Suppose -a + 0*a - 3 = 0. Let m(t) = -t + 1. Let v(o) = -o**3 + o**2 - 4*o + 4. Let z(l) = a*v(l) + 15*m(l). Find c such that z(c) = 0.
-1, 1
Let b(p) = -80*p**4 - 131*p**3 + 289*p**2 - 60*p + 9. Let l(q) = -20*q**4 - 33*q**3 + 72*q**2 - 15*q + 2. Let t(v) = -2*b(v) + 9*l(v). Factor t(m).
-5*m*(m - 1)*(m + 3)*(4*m - 1)
Let c = 3201 - 3201. Factor -1/11*i + c - 3/11*i**2 - 2/11*i**3.
-i*(i + 1)*(2*i + 1)/11
Find y, given that -33*y + 13 + 229 - 50 - 100*y**2 - 2*y**3 - 55*y - 2*y**3 = 0.
-24, -2, 1
Let m = -1122 + 3371/3. Factor m*z**2 + 1/3*z**3 + 1 + 7/3*z.
(z + 1)**2*(z + 3)/3
Suppose -g + 2*k + 6 = 0, -3*k - 8 = g - 3*g. Let p be g*9/24 + 3/1. Factor 3*s - 3/4*s**2 - p.
-3*(s - 3)*(s - 1)/4
Let x = 1160 + -3470/3. Suppose 8/3 + 2/3*v**4 + 8/3*v - x*v**2 + 2/3*v**5 - 10/3*v**3 = 0. What is v?
-2, -1, 1, 2
Let f(m) = -4*m**3 - m**2 + 5*m + 6. Let w(z) = 7 + 14*z - 10*z**3 + 0 - 2*z**2 - 2*z**3 + 10. Let p(y) = -17*f(y) + 6*w(y). Let p(n) = 0. What is n?
0, 1/4, 1
Suppose 4*r + 30 = -r. Let v(x) = -x**3 - 2*x**2 + 21*x - 12. Let w be v(r). Suppose 21/8*j**4 + 3/2 + w*j + 3/8*j**5 + 57/8*j**3 + 75/8*j**2 = 0. Calculate j.
-2, -1
Suppose -r + 3 = 1. Suppose r*c = -0*c + 4. Factor -d**4 + c*d**5 + d**4 - 5*d**5 + 3*d**3.
-3*d**3*(d - 1)*(d + 1)
Let i(g) = 4*g**2 - 153*g + 28. Let p(f) = -f**2 - 2*f + 4. Let c(r) = -2*i(r) - 14*p(r). Suppose c(w) = 0. Calculate w.
-56, 1/3
Let l(o) = -3*o**3 + 20*o**2 - 21*o + 9. Let i(b) = -4*b**3 + 22*b**2 - 20*b + 8. Let n(j) = -5*i(j) + 6*l(j). Factor n(y).
2*(y - 1)**2*(y + 7)
Suppose 2*j = 5*i + 7, -3*j = j - 2*i - 6. Let s = -17 + 19. Find b such that -2*b**4 - 1 - j + 5*b**2 - 2*b**2 + b**s = 0.
-1, 1
Let q(g) = g**2 + g - 1. Let j(o) = -o**3 - o**2 + 3. Suppose 0 = 4*p + 4, -4*p = 5*a - 3 + 17. Let u(l) = a*j(l) - 6*q(l). Let u(r) = 0. What is r?
-1, 0, 3
Suppose -144*z**2 - 2*z**4 + 70*z**2 - 7*z**3 + 75*z**2 + 7*z + z**4 = 0. What is z?
-7, -1, 0, 1
Let i(w) be the second derivative of -w**6/90 + w**5/15 - w**4/6 - w**3/2 + 6*w. Let a(x) be the second derivative of i(x). Factor a(b).
-4*(b - 1)**2
Let z be 4/3*(-1 - (-14)/(-4)). Let v(b) = 4*b**2 - 2*b. Let u(l) = 12*l**2 - 5*l. Let s(d) = z*u(d) + 17*v(d). Suppose s(t) = 0. What is t?
-1, 0
Let v(s) = s**2 + 3*s - 22. Let q be v(-7). Let c(n) be the second derivative of -1/2*n**3 + 0 + 0*n**2 + 1/4*n**4 - q*n. Solve c(m) = 0 for m.
0, 1
Solve 2738/7*t**2 + 18/7 + 444/7*t = 0 for t.
-3/37
Let u(q) be the first derivative of q**5/25 - 6*q**4/5 + 88*q**3/15 + 336*q**2/5 + 784*q/5 + 500. Factor u(j).
(j - 14)**2*(j + 2)**2/5
Factor -9*d + 3356 - 41*d - 44*d**2 + 2*d**3 - 3264.
2*(d - 23)*(d - 1)*(d + 2)
Let i(y) = 2*y**3 + y**2 - 2*y + 1. Let j be i(1). Let a be (-2)/(j*(-4)/14). Factor -5/2*n**4 + 2*n + 4*n**2 + 0 - a*n**3.
-n*(n - 1)*(n + 2)*(5*n + 2)/2
Suppose -4*k - 19/3*k**2 + 4/3 + 5*k**4 + 8/3*k**3 + 4/3*k**5 = 0. What is k?
-2, -1, 1/4, 1
Let o = -13 - -17. Factor 2*r - 2*r**2 - o*r - 3*r + 3*r**2.
r*(r - 5)
Let r(l) be the third derivative of -l**8/6720 + l**7/630 + 7*l**4/24 - 18*l**2. Let x(w) be the second derivative of r(w). What is t in x(t) = 0?
0, 4
Let p(t) = 2*t**2 + 3. Let i(r) = 15*r**2 + 445*r + 455. Let f(v) = -i(v) + 5*p(v). Suppose f(l) = 0. What is l?
-88, -1
Let v(y) = y**4 - y**3 - 2*y