- 2 + 0*v**3 - 27/5*v**6. Find r, given that i(r) = 0.
0, 2/9
Let i be (-6)/4*(-68)/(-3). Let y = i + 103/3. Factor 0*k**2 + 0*k + 2/3*k**4 + 1/3*k**3 + 0 + y*k**5.
k**3*(k + 1)**2/3
Let h(d) be the first derivative of d**3/3 - 3*d**2/2 - 4*d + 1. Factor h(i).
(i - 4)*(i + 1)
Let c(q) be the second derivative of 1/12*q**6 + 1/4*q**2 - 1/10*q**5 - 1/4*q**4 + 1/3*q**3 + 0 + 9*q. Factor c(z).
(z - 1)**2*(z + 1)*(5*z + 1)/2
Let h be ((-8)/10)/((-1)/30). Factor 8*i**2 - 26*i**2 + 6*i**4 - 8*i**3 - 8 + 4*i**3 + h*i.
2*(i - 1)**2*(i + 2)*(3*i - 2)
Let w(b) be the third derivative of 0*b**3 + 0 + 1/120*b**6 + 1/150*b**7 + 0*b + 1/300*b**5 + 1/560*b**8 + 0*b**4 - 4*b**2. Factor w(i).
i**2*(i + 1)**2*(3*i + 1)/5
Let f be ((-4)/(-3))/(6/9). Let o(r) be the third derivative of 1/120*r**6 + 1/8*r**4 + 1/20*r**5 + 1/6*r**3 - 2*r**f + 0*r + 0. Factor o(u).
(u + 1)**3
Let j(o) be the first derivative of -1 - 2/3*o - 1/9*o**3 + 1/2*o**2. Factor j(r).
-(r - 2)*(r - 1)/3
Let s(c) = -5*c**2 + 3*c. Let p(n) be the first derivative of 2*n**3 - 2*n**2 + 2. Suppose g = -2*g + 9. Let i(r) = g*p(r) + 4*s(r). Factor i(y).
-2*y**2
Let q be 6 - (2 - 0/(-2)). Let h(i) = -q*i**2 - 6*i - 21 - 2*i**2 + i. Let g(n) = -n**2 - n - 4. Let f(r) = 11*g(r) - 2*h(r). Factor f(l).
(l - 2)*(l + 1)
Let p(w) be the first derivative of w**3/2 - 21*w**2/2 + 147*w/2 - 14. Determine y, given that p(y) = 0.
7
Let j(w) be the first derivative of w**6/2 - 3*w**5/5 - 2. Determine m so that j(m) = 0.
0, 1
Let c(s) be the third derivative of -s**2 + 1/28*s**4 - 2/21*s**3 + 0 + 0*s + 1/210*s**5 - 1/140*s**6 + 1/735*s**7. Factor c(o).
2*(o - 2)*(o - 1)**2*(o + 1)/7
Let n(h) be the second derivative of 1/12*h**4 + 1/6*h**2 - 5*h + 1/60*h**5 + 0 + 1/6*h**3. Factor n(o).
(o + 1)**3/3
Let b(i) be the third derivative of i**8/112 - i**7/14 + i**6/4 - i**5/2 + 5*i**4/8 - i**3/2 + 14*i**2. What is q in b(q) = 0?
1
Factor -6/13*a**2 - 22/13*a - 20/13.
-2*(a + 2)*(3*a + 5)/13
Let d(c) be the third derivative of 1/105*c**7 + 1/15*c**5 + 0*c**3 + 7*c**2 + 0*c**4 + 0*c - 1/20*c**6 + 0. Factor d(j).
2*j**2*(j - 2)*(j - 1)
Let p be 4/(-10) - (-9)/10. Factor 1/2*s - p*s**3 - 1/2 + 1/2*s**2.
-(s - 1)**2*(s + 1)/2
Let t(i) = -i - 1. Let z be t(3). Let c = z + 4. Let -1/3*k**2 + c + 0*k = 0. What is k?
0
Let d(t) be the third derivative of -t**6/280 - 3*t**5/70 + t**4/56 + 3*t**3/7 - 18*t**2. Suppose d(n) = 0. What is n?
-6, -1, 1
Let h(p) = 2*p**2 - 40*p - 104. Let c(q) = -q**2 + 13*q + 35. Let g(s) = 8*c(s) + 3*h(s). What is a in g(a) = 0?
-4
Let c(x) be the first derivative of x**8/448 + x**7/70 + x**6/32 + x**5/40 + x**2/2 + 8. Let f(s) be the second derivative of c(s). Factor f(p).
3*p**2*(p + 1)**2*(p + 2)/4
Let l(x) be the second derivative of -x**7/70 + x**6/40 + x**5/10 - 3*x**2 + 8*x. Let v(y) be the first derivative of l(y). Solve v(s) = 0.
-1, 0, 2
Let u be 144/50*15/6. Let f = u + -38/15. Let 7/3*x + 7/3*x**5 - 2/3 - 2/3*x**4 - f*x**3 + 4/3*x**2 = 0. Calculate x.
-1, 2/7, 1
Let l(r) = 6*r**5 - 8*r**4 + 22*r**3 + 10*r - 10. Let v(q) = 2*q**5 - 3*q**4 + 7*q**3 + 3*q - 3. Let j(y) = -3*l(y) + 10*v(y). Determine o, given that j(o) = 0.
0, 1, 2
Let q(y) be the first derivative of y**6/15 - 4*y**5/25 - y**4/5 + 8*y**3/15 + y**2/5 - 4*y/5 + 2. Solve q(r) = 0.
-1, 1, 2
Let g(w) be the first derivative of w**6/30 - w**5/12 + w**4/24 + w**2/2 - 3. Let b(u) be the second derivative of g(u). Let b(v) = 0. Calculate v.
0, 1/4, 1
Let k(z) be the third derivative of z**8/84 - 6*z**7/35 + 4*z**6/5 - 16*z**5/15 + 31*z**2. Factor k(l).
4*l**2*(l - 4)**2*(l - 1)
Let k be (-934)/252 - (-4)/(-18). Let x = -24/7 - k. Find l such that 0 - x*l**2 + 0*l = 0.
0
Let -4/17*f**4 + 18/17*f**3 + 8/17*f + 0 - 24/17*f**2 = 0. What is f?
0, 1/2, 2
Let i(k) = 6*k**2 + 6*k. Let p be 0/(3/3) - -6. Let j(m) = -m**2 - m. Let h(s) = p*i(s) + 33*j(s). Let h(w) = 0. What is w?
-1, 0
Let j(d) be the first derivative of -59/12*d**4 + 1 - 104/15*d**5 + 1/3*d**3 - 8/3*d**6 + 1/3*d + 7/6*d**2. Solve j(m) = 0.
-1, -1/4, 1/3
Suppose 0 = -3*m + 5*f - f + 6, -4*m + 8 = -4*f. Factor 0 - 1/6*u**4 + 0*u**3 + 0*u + 1/6*u**m.
-u**2*(u - 1)*(u + 1)/6
Let v be 0/2 - (0 + 0). Suppose 5*f - j = 18, v = -4*f + 5*j + 3 + 3. Suppose 5*m**4 - m**f - 4*m**2 - 2*m**5 + 0*m + 2*m = 0. What is m?
-1, 0, 1
Let n = 37/2 - 329/18. Factor 0*i + 0 - n*i**2.
-2*i**2/9
Let h be -1*(-4 + (-4)/(-1)). Solve -2/9*d + h + 0*d**2 + 2/9*d**3 = 0 for d.
-1, 0, 1
Let l be (-39)/2 - 2/4. Let o = l + 23. Factor 3/2*b**o - 3/2*b - 3/4 + 0*b**2 + 3/4*b**4.
3*(b - 1)*(b + 1)**3/4
Suppose -4*a = 9*a. Solve -2/7 - 2/7*q**4 + a*q + 4/7*q**2 + 0*q**3 = 0 for q.
-1, 1
Let f = -61/15 + 22/5. Let r be 3 - 2 - (-2)/(-3). Factor -f*h - r*h**2 + 0.
-h*(h + 1)/3
Solve 9/8*c + 3/4 + 3/8*c**2 = 0 for c.
-2, -1
Suppose 4*v = 2*p - 8, 5*p + 6*v = v + 5. Factor -2*f - f**3 + 18*f**2 - 1 + 3*f - 17*f**p.
-(f - 1)**2*(f + 1)
Let s(k) be the first derivative of k**5/30 - k**4/6 + 2*k**2 - 3. Let o(n) be the second derivative of s(n). Factor o(h).
2*h*(h - 2)
Factor 3*w**2 + 3*w**5 - 18*w**2 - 272*w**3 + 3*w**4 + 263*w**3 - 6*w.
3*w*(w - 2)*(w + 1)**3
Let q(n) = n. Let x(f) be the second derivative of 7*f**4/12 - 7*f**3/6 + f**2 + 5*f. Let w(c) = 6*q(c) - 3*x(c). Let w(t) = 0. What is t?
2/7, 1
Factor 6*i - 21*i**2 - 36*i**3 - 14*i + 5*i + 8*i + 2.
-(3*i - 1)*(3*i + 2)*(4*i + 1)
Factor -20 + 20 - 12*m**3 - 4*m**5 - 12*m**4 - 4*m**2.
-4*m**2*(m + 1)**3
Let b(q) be the third derivative of -1/420*q**6 + 0*q**4 + 0*q**3 - 4*q**2 + 0 + 0*q - 1/210*q**5. Factor b(n).
-2*n**2*(n + 1)/7
Let m(t) be the second derivative of 1/110*t**5 + 0*t**3 - 1/66*t**4 - 2*t + 0*t**2 + 0. Determine q so that m(q) = 0.
0, 1
Suppose k - 1 = -5*v, 5*k - 4*v - 5 = -0. Let z be (k/2)/((-2)/(-16)). Factor 0 + 0*p + 1/3*p**3 - 1/3*p**z - 2/3*p**5 + 0*p**2.
-p**3*(p + 1)*(2*p - 1)/3
Let b(q) be the second derivative of 0*q**2 + 5*q + 0 + 1/4*q**4 - 1/2*q**3. Factor b(n).
3*n*(n - 1)
Suppose -y = -3*u, 3*y + u = 5 + 5. Factor 4*g - 6*g**y - 18 + 2*g**5 + 18 + 2*g**2 - 2*g**4.
2*g*(g - 2)*(g - 1)*(g + 1)**2
Let n(u) be the first derivative of 2*u**5/25 - u**4/10 - 4*u**3/15 - 1. Solve n(j) = 0.
-1, 0, 2
Let r(t) be the third derivative of t**8/840 - t**6/120 + t**5/60 + 5*t**4/24 + 5*t**2. Let j(d) be the second derivative of r(d). Factor j(x).
2*(x + 1)*(2*x - 1)**2
Let y(g) = 4*g**4 + 4*g**3 - 6*g**2 - 13*g + 8. Let r(k) = 7*k**4 + 8*k**3 - 11*k**2 - 25*k + 16. Let f(j) = -3*r(j) + 5*y(j). What is l in f(l) = 0?
-4, -2, 1
Suppose 2/7*d**5 - 4/7*d**3 + 2/7 + 2/7*d**4 + 2/7*d - 4/7*d**2 = 0. What is d?
-1, 1
Let x(h) be the third derivative of 0 + 0*h**5 + 0*h + 0*h**3 - 1/12*h**4 + h**2 + 1/60*h**6. Let x(k) = 0. Calculate k.
-1, 0, 1
Let s(l) be the first derivative of -l**6/15 + 3*l**5/20 - l**3/6 + 5*l - 2. Let p(n) be the first derivative of s(n). Factor p(v).
-v*(v - 1)**2*(2*v + 1)
Let z(a) be the first derivative of -2*a**6/3 - 4*a**5/5 + 2*a**4 + 8*a**3/3 - 2*a**2 - 4*a - 7. Factor z(c).
-4*(c - 1)**2*(c + 1)**3
Let u(i) = i**2 + i - 3. Let k be u(2). Let q(l) be the first derivative of 2*l - 4/3*l**k + 0*l**4 - 2 + 0*l**2 + 2/5*l**5. Suppose q(r) = 0. Calculate r.
-1, 1
Factor -94*o**2 - 101*o - 44*o**4 - 7*o**5 + 135*o - 75*o - 6 - 96*o**3.
-(o + 1)**3*(o + 3)*(7*o + 2)
Let v(t) be the third derivative of t**7/147 - t**6/30 + 2*t**5/35 - t**4/42 - t**3/21 - 8*t**2. Solve v(o) = 0 for o.
-1/5, 1
Suppose 80/3*p**3 - 50/9*p**4 + 64/3*p - 32/9 - 368/9*p**2 = 0. Calculate p.
2/5, 2
Let j(k) = 5*k**2 - 3*k. Let v be j(2). Let l be -1*(4/v + -2). Determine y, given that -l*y**5 + 2/7*y**4 - 2/7*y + 0 - 2/7*y**2 + 2*y**3 = 0.
-1, -1/3, 0, 1/2, 1
Let a(t) be the second derivative of t**7/140 - t**6/240 - t**5/40 + t**4/48 + 3*t**2/2 + t. Let z(s) be the first derivative of a(s). Let z(g) = 0. What is g?
-1, 0, 1/3, 1
Suppose -9 = 3*l - 4*l - 5*s, 2*l - 7 = s. Factor 2*n - 6*n**2 - n**3 - 2*n**l + 2*n**3 + 5*n**3.
-2*n*(n - 1)**3
Let b(w) = 11*w**4 + 4*w**3 - 5*w**2 - 3*w - 7. Let h(l) = 4*l**4 + l**2 - 2 - l - 5*l**2 + 2*l**2 + l**3. Let k(g) = -2*b(g) + 7*h(g). Factor k(s).
s*(s - 1)*(2*s + 1)*(3*s + 1)
Let l = 33/80 + -5/16. Let u(h) be the first derivative of 0*h - 2 + l*h**2 - 1/15*h**3. Suppose u(t) = 0. Calculate t.
0, 1
Let z(a) 