f) = 7*r(f) - 5*t(f). What is j in x(j) = 0?
-1, 2
Let j be -1*1*(-7 - -4). Suppose -2*q + 25 = j*q. Factor 6*b**4 + b**5 + 3*b**3 + 24*b - 24*b + 2*b**q.
3*b**3*(b + 1)**2
Suppose 4*r - 2*r - r = 0. Let c(l) be the second derivative of l + r*l**2 + 0 + 1/9*l**3 + 1/18*l**4. Factor c(i).
2*i*(i + 1)/3
Let h(j) be the third derivative of j**5/100 + j**4/20 + j**3/10 + 4*j**2. Solve h(z) = 0 for z.
-1
Suppose 3*s + 3*i = 42, -s + 36 = 3*s - i. Suppose -2*f - f**4 + 13*f**4 - s*f**2 + 3*f + 2*f**3 - 5*f = 0. Calculate f.
-2/3, -1/2, 0, 1
Let n(c) be the first derivative of -5*c**6/2 + 7*c**5 - 5*c**4/2 - 10*c**3 + 25*c**2/2 - 5*c + 10. What is h in n(h) = 0?
-1, 1/3, 1
Let c(z) be the second derivative of -z**7/840 + z**6/60 - z**5/10 + z**4/12 + 3*z. Let h(k) be the third derivative of c(k). Suppose h(a) = 0. What is a?
2
Let i(s) = s**2 + s - 1. Let q(a) = -8*a**2 + 12. Let r(z) = -4*i(z) - q(z). Determine g, given that r(g) = 0.
-1, 2
Let g be 8/(-36) + 38/(-558). Let j = -1/217 - g. Suppose j*u**4 - 2/7 + 0*u**2 + 4/7*u**3 - 4/7*u = 0. What is u?
-1, 1
Let d(b) be the second derivative of -b**4/6 + 4*b**3/3 - 3*b**2 + 11*b. Factor d(j).
-2*(j - 3)*(j - 1)
Let d(s) = s**4 + 5*s**3 - s**2 - 5*s. Let h(q) = 4*q**3 - q - q - 2*q. Let i(o) = -3*d(o) + 4*h(o). Find z, given that i(z) = 0.
-1, 0, 1/3, 1
Let t(i) be the first derivative of 1/70*i**5 - 2*i - 1/21*i**3 + 0*i**2 - 1/42*i**4 + 3 + 1/105*i**6. Let s(k) be the first derivative of t(k). Factor s(o).
2*o*(o - 1)*(o + 1)**2/7
Let k(n) be the second derivative of -n**8/420 - n**7/70 + 2*n**5/15 - 3*n**3/2 + n. Let a(y) be the second derivative of k(y). Suppose a(d) = 0. Calculate d.
-2, 0, 1
Let v be 6/(-15)*(-20)/1. Let x(f) = f - 6. Let o be x(v). Determine y, given that -1 - 1 - 2*y + o + 2*y**2 = 0.
0, 1
Suppose 4*x = -5*s + 12, 22 = -5*x + 3*s - 0*s. Let i be 4/8 - 3/x. Factor -2/3*n**i + 2/3*n + 2/3 - 2/3*n**3.
-2*(n - 1)*(n + 1)**2/3
Solve -2*i**3 - 29/2*i + 21/2*i**2 + 3 = 0 for i.
1/4, 2, 3
Suppose -y = 2*p - 5*y + 20, 0 = -2*p - y + 5. Factor -3*r - 4 - r**2 + p*r - r.
-(r + 2)**2
What is a in -13*a**2 - 3 - 6*a + 15*a**2 + 3 = 0?
0, 3
Let x(s) be the second derivative of s**5/270 - s**4/27 + 4*s**3/27 - s**2 - 4*s. Let i(d) be the first derivative of x(d). Factor i(h).
2*(h - 2)**2/9
Let k(j) be the first derivative of 2/25*j**5 - 2/15*j**3 + 0*j**2 + 0*j - 1/15*j**6 + 1/10*j**4 - 2. Factor k(b).
-2*b**2*(b - 1)**2*(b + 1)/5
Factor 8 - 6*r**2 - 15*r + 2*r**2 - 4*r**2 - 28*r**3 + 43*r.
-4*(r - 1)*(r + 1)*(7*r + 2)
Factor 22*s**3 - 8*s**3 + 6*s - 28*s**2 + 0*s + 8*s**4.
2*s*(s - 1)*(s + 3)*(4*s - 1)
Let d = -23 - -71/3. Factor -d*h**2 + 4/3*h + 0.
-2*h*(h - 2)/3
Factor t**2 + 0*t**3 + 1/2*t**5 - 1/2*t - t**4 + 0.
t*(t - 1)**3*(t + 1)/2
Factor 45*i**2 - 285*i**3 + 10 + 310*i**3 + 0*i**4 + 35*i + 5*i**4.
5*(i + 1)**3*(i + 2)
Let s(w) be the third derivative of w**6/600 - w**5/100 + w**4/40 - w**3/30 - 4*w**2. Find a, given that s(a) = 0.
1
Let r(y) = 9*y**2 - 9*y - 10. Let c(b) = b**2 - b - 1. Let m(v) = 24*c(v) - 3*r(v). What is a in m(a) = 0?
-1, 2
Factor 2/3*z**5 - 2*z + 4/3*z**3 - 2*z**4 + 2/3 + 4/3*z**2.
2*(z - 1)**4*(z + 1)/3
Let a(q) = -q**3 + q**2 - 2*q - 2. Let s be a(-1). Let k(v) be the first derivative of 1/3*v**3 + v + 3 - v**s. Factor k(t).
(t - 1)**2
Let i(a) = a**3 - a**2 + a. Let n(y) = -16*y**3 + 67*y**2 - 85*y + 24. Let f(p) = -i(p) - n(p). Suppose f(b) = 0. Calculate b.
2/5, 2
Let m(z) be the first derivative of -4*z**3/3 + 16*z - 6. Factor m(f).
-4*(f - 2)*(f + 2)
Let n(c) be the first derivative of c**4/12 - 2*c**3/9 + c**2/6 + 13. Find f such that n(f) = 0.
0, 1
Solve 2/5*z**3 - 4/5 - 2/5*z + 4/5*z**2 = 0 for z.
-2, -1, 1
Let o(n) = 8*n**2 + 4*n + 8. Let t(b) = -3*b**2 - 1 + 0*b**2 + 2*b**2. Let g(d) = o(d) + 6*t(d). What is m in g(m) = 0?
-1
Factor b**2 - 9/2*b**4 + 0 + 7/2*b**3 + 0*b.
-b**2*(b - 1)*(9*b + 2)/2
Let d(w) = w**3 - 7*w**2 + 6*w. Let p(u) = 3*u**2 - 2*u. Let q be p(3). Let l(t) = -6*t**3 + 36*t**2 - 30*t. Let z(a) = q*d(a) + 4*l(a). Factor z(s).
-3*s*(s - 1)*(s + 2)
Let b(k) be the third derivative of -k**7/315 - k**6/180 + k**5/90 + k**4/36 + 5*k**2. Determine x, given that b(x) = 0.
-1, 0, 1
Let t = -8 + 3. Let z = t + 8. Solve -1/4*b**4 - 1/4*b + 0 + 1/4*b**2 + 1/4*b**z = 0 for b.
-1, 0, 1
Let z(d) be the second derivative of d**7/147 - 2*d**6/105 - d**5/35 + 2*d**4/21 + d**3/21 - 2*d**2/7 - 2*d. Suppose z(b) = 0. What is b?
-1, 1, 2
What is l in -6/5*l**3 - 24/5*l**2 + 0 - 24/5*l = 0?
-2, 0
Let m(x) be the third derivative of x**8/392 - 22*x**7/735 + 5*x**6/42 - 2*x**5/15 - x**4/4 + 6*x**3/7 - 12*x**2. Determine u so that m(u) = 0.
-2/3, 1, 3
Factor 5*i**3 + i**5 - 5*i**5 + 2*i**5 - 3*i**5.
-5*i**3*(i - 1)*(i + 1)
Suppose -g + 2*g = 2*q - 10, 3*q = -2*g + 8. Factor 0*t**3 + 0*t - 2/3*t**2 + 1/3*t**q + 1/3.
(t - 1)**2*(t + 1)**2/3
Let o(w) be the third derivative of w**5/90 + w**4/9 - 5*w**3/9 - w**2 - 1. Solve o(d) = 0 for d.
-5, 1
Let u(t) be the second derivative of -3*t**5/20 + 5*t**4/4 - 7*t**3/2 + 9*t**2/2 + 6*t. Determine m, given that u(m) = 0.
1, 3
Let k(s) be the second derivative of s**5/20 - s**4/12 + 2*s**2 + 5*s. Let x(w) be the first derivative of k(w). Factor x(m).
m*(3*m - 2)
Let o = -1 + -3. Let z be 2/o*(-4 + 3). Factor z*w + w**2 + 0.
w*(2*w + 1)/2
Let j(c) = 2*c**2 - 191*c - 889. Let q(b) = -b**2 + 64*b + 296. Let h(a) = -4*j(a) - 11*q(a). Factor h(p).
3*(p + 10)**2
Let w(a) be the second derivative of -a**7/126 - a**6/45 + a**5/5 - 7*a**4/18 + 5*a**3/18 - 8*a. Factor w(j).
-j*(j - 1)**3*(j + 5)/3
Factor 2*u**2 - 2*u**2 + 3*u - 12*u**2 - 10*u**3 + 6 + u**3.
-3*(u + 1)**2*(3*u - 2)
Let j be (-27)/15 + 2 - (-35)/75. Let v(b) be the first derivative of j*b**3 - b**2 + 1 - 4*b. Solve v(t) = 0.
-1, 2
Factor 2/3*m**4 - 1/3*m**2 - 1/3 - 1/6*m**5 + 5/6*m - 2/3*m**3.
-(m - 2)*(m - 1)**3*(m + 1)/6
Let z be (42/45)/(16/10). Let c(n) be the second derivative of -1/5*n**5 - n + 0 + z*n**4 - 1/2*n**2 - 1/3*n**3. Determine w, given that c(w) = 0.
-1/4, 1
Let a(i) = -3*i**2 + 2*i + 14. Let n(t) = 6*t**2 - 5*t - 29. Let j(y) = 5*a(y) + 2*n(y). Solve j(p) = 0 for p.
-2, 2
Let k(y) be the first derivative of -18*y**5/65 + 11*y**4/26 + 14*y**3/39 - 11*y**2/13 + 4*y/13 + 52. Let k(t) = 0. What is t?
-1, 2/9, 1
Let -8*f**4 - 15*f**3 + 5*f**5 + 43*f**3 - 7*f**4 - 18*f**3 = 0. Calculate f.
0, 1, 2
Let j(n) = -63*n**4 + 95*n**3 - 40*n**2 + 2*n + 3. Let t(o) = -188*o**4 + 285*o**3 - 120*o**2 + 7*o + 8. Let c(p) = -8*j(p) + 3*t(p). Find l such that c(l) = 0.
0, 1/4, 1/3, 1
Factor 0*v + 8*v**5 - 12*v**4 + 0 - 1/2*v**2 + 9/2*v**3.
v**2*(v - 1)*(4*v - 1)**2/2
Let v(c) = -2*c**2 - 11*c - 11. Let w(b) = -8*b**2 - 45*b - 45. Let x(m) = -26*v(m) + 6*w(m). Find d, given that x(d) = 0.
-2
Let z be (-82)/(-36) - (4 - 190/45). Factor z*f**2 - 1/2*f**3 + 2 - 4*f.
-(f - 2)**2*(f - 1)/2
Let m(h) = h**3 + 10*h**2 - 10*h + 7. Let l be m(-11). Let n be (l/35)/(8/(-20)). Let n*s**2 + 2/7*s + 0 = 0. What is s?
-1, 0
Suppose 2*u - 2*f - 12 = 0, 4*f + 15 = 5*u - 11. Factor -2 + 4*b + u*b**2 + 9*b + 0*b**2 - 15*b + 2*b**3.
2*(b - 1)*(b + 1)**2
Suppose 5*n - 21 + 1 = 0. Factor 0*y**4 - y + y**n + 3*y**2 - y**3 - 2*y**3.
y*(y - 1)**3
Let o(r) = -r - 19. Let c be o(-19). Factor 4/5*n**2 + c*n**3 - 2/5*n + 0 - 4/5*n**4 + 2/5*n**5.
2*n*(n - 1)**3*(n + 1)/5
Let 2/3*f + 2/3*f**2 + 0 = 0. What is f?
-1, 0
Let j(y) = y**3 - y**2 - 1. Let m(c) = 3*c**3 + 9*c**2 - 32*c + 1. Let q(o) = j(o) + m(o). Suppose q(h) = 0. Calculate h.
-4, 0, 2
Let o = 8 + -4. Factor -3*c**2 + 3*c**4 + 4*c**3 + 2*c**4 + o*c**4 - 6 + 15*c - 19*c**3.
3*(c - 1)**2*(c + 1)*(3*c - 2)
Let b(u) = 12*u**2 + 8*u - 12. Let z(k) = -k**2 - k. Let r(p) = -b(p) - 10*z(p). Factor r(v).
-2*(v - 3)*(v + 2)
Suppose 5*o + 21 = 3*g, -3*o - 9 = -0*o. Factor 0*x**2 + 0*x + x**g + 2*x.
x*(x + 2)
Let h(d) be the third derivative of d**6/2700 + d**5/450 + d**3/6 - 6*d**2. Let t(o) be the first derivative of h(o). Solve t(s) = 0.
-2, 0
Let l(z) = 199*z**4 - 7*z**3 - 29*z**2 + z. Let f(c) = -66*c**4 + 2*c**3 + 10*c**2. Let u(o) = -14*f(o) - 4*l(o). Solve u(r) = 0.
-1/4, 0, 1/2
Let p(u) be the first derivative of 5/6*u**6 + 0*u**2 + 9/4*u**4 - 12/5*u**5 - 2/3*u**3 - 8 + 0*u. Factor p(m).
m**2*(m - 1)**2*(5*m - 2)
Let s(y) = y - 1. L