5 - d. Solve k + r + k**2 - 3*k + 1 = 0 for k.
1
Suppose -3*w = 2*l + w, 4*l + w - 7 = 0. Let t be 4/20*(0 + l). Factor -t*n**2 - 4/5*n + 0.
-2*n*(n + 2)/5
Let b(t) = -t. Let h = -6 - -2. Let f be b(h). Factor v**f - 5*v**2 + 2*v**2 + 7*v**4 - 3*v**2 + 2*v.
2*v*(v + 1)*(2*v - 1)**2
Let o = -304/5 - -61. Factor 2/5*f - 1/5 - o*f**2.
-(f - 1)**2/5
Let k(x) = x**4 + 14*x**3 + 4*x**2 + 4*x. Let f(w) = 2*w**4 + 41*w**3 + 13*w**2 + 11*w. Let i(t) = 4*f(t) - 11*k(t). Factor i(z).
-z**2*(z - 4)*(3*z + 2)
Let o(s) be the first derivative of s**7/70 + 3*s**6/50 + 9*s**5/100 + s**4/20 + s - 2. Let p(g) be the first derivative of o(g). Factor p(b).
3*b**2*(b + 1)**3/5
Let w(p) be the third derivative of -p**8/4320 - p**7/3780 + p**5/15 - 4*p**2. Let n(h) be the third derivative of w(h). Factor n(q).
-2*q*(7*q + 2)/3
Let k(f) be the third derivative of f**6/1260 + f**5/140 + f**4/42 + 5*f**3/6 + 5*f**2. Let s(x) be the first derivative of k(x). Factor s(m).
2*(m + 1)*(m + 2)/7
Let z = -7 - -19. Let j(n) = -n**4 + n**3 - n**2 + 1. Let g(x) = 3*x**4 - 2*x**3 + 3*x**2 - 4. Let d(w) = z*j(w) + 3*g(w). Factor d(c).
-3*c**2*(c - 1)**2
Let n(m) = -m**2 - 4*m - 3. Let o be n(-3). Factor o*y + 0 + 2*y**2 + 8 - 8*y.
2*(y - 2)**2
Let f(z) be the second derivative of 0*z**3 - 1/168*z**7 + 1/48*z**4 - 4*z - 1/120*z**6 + 1/80*z**5 + 0 + 0*z**2. Solve f(b) = 0.
-1, 0, 1
Let s(d) be the first derivative of -d**6/10 - 3*d**5/25 + 9*d**4/20 + d**3 + 3*d**2/5 - 1. Determine t, given that s(t) = 0.
-1, 0, 2
Let w(h) = h**2 + h. Let z(d) = -10*d**2 - 30*d - 20. Let v(f) = 15*w(f) + z(f). Suppose v(i) = 0. What is i?
-1, 4
Let w(o) be the third derivative of 0*o**3 - 1/330*o**5 - 5*o**2 - 1/66*o**4 + 0 + 0*o. Determine r so that w(r) = 0.
-2, 0
Let i = 13 + -27. Let w(v) = -2*v**2 + 3*v - 3. Let d = -1 + 7. Let m(g) = -5*g**2 + 7*g - 7. Let a(j) = d*m(j) + i*w(j). Factor a(q).
-2*q**2
Let x be (-1)/(12/4) - 2/(-6). Let y(z) be the second derivative of 1/90*z**5 + 0*z**2 + 3*z + x + 1/27*z**3 - 1/27*z**4. Find w such that y(w) = 0.
0, 1
Factor 10/3*h**2 + 16/3*h + 2/3*h**3 + 8/3.
2*(h + 1)*(h + 2)**2/3
Let j = 154 - 60. Solve -j*b**2 + b**3 + 94*b**2 - b**5 = 0 for b.
-1, 0, 1
Let g(v) be the third derivative of v**7/30 - 11*v**6/240 + v**5/60 + v**2. What is x in g(x) = 0?
0, 2/7, 1/2
Suppose 6*m = 5*m - 3*m. Factor m + 10/3*d**2 - 8*d**3 + 4/3*d.
-2*d*(3*d - 2)*(4*d + 1)/3
Let z(h) = h**3 + 2*h**2 - 4*h - 5. Let g(q) = q**3 + 2*q**2 - 3*q - 4. Let b(f) = -f - 12. Let x be b(-16). Let t(r) = x*z(r) - 5*g(r). Factor t(d).
-d*(d + 1)**2
Let l = 27/46 + -2/23. Let c(t) be the first derivative of -l*t**4 + 2/5*t**5 + 0*t**2 + 0*t**3 + 0*t - 2. Factor c(i).
2*i**3*(i - 1)
Let s(u) be the second derivative of -4*u**6/15 + 11*u**4/6 + 3*u**3 + 2*u**2 + 4*u. What is h in s(h) = 0?
-1, -1/2, 2
Let v be 105/135 - (-2)/(-6). Find o, given that v*o**3 - 8/9 + 0*o + 2*o**2 - 2/3*o**4 = 0.
-1, 2/3, 2
Let p(w) be the second derivative of w**6/80 - w**4/16 + 3*w**2/16 - 14*w. Find x such that p(x) = 0.
-1, 1
Solve 48*w**3 + 3*w**4 - 12*w - 3*w**2 - 39*w**3 + 3*w**2 = 0 for w.
-2, 0, 1
Find b, given that -6/7*b + 4/7 + 2/7*b**2 = 0.
1, 2
Let x = 3298/9 - 366. Let o(g) be the first derivative of x*g - 4/9*g**3 + 1/9*g**2 + 1 + 1/9*g**6 + 8/45*g**5 - 2/9*g**4. Solve o(b) = 0 for b.
-1, 2/3, 1
Let s(x) be the first derivative of -x**7/525 + x**5/75 - x**3/15 - 5*x**2/2 - 1. Let n(q) be the second derivative of s(q). Suppose n(w) = 0. Calculate w.
-1, 1
Let l(x) be the second derivative of -x**3/6 + x**2/2 + 2*x. Let t(c) = -c**2 + c. Let n(o) = l(o) + t(o). Let n(g) = 0. What is g?
-1, 1
Solve -2/3 + s + 0*s**2 - 1/3*s**3 = 0 for s.
-2, 1
Let v = -130/7 - -19. Factor 3/7*f + 0 - v*f**5 - 6/7*f**2 + 0*f**3 + 6/7*f**4.
-3*f*(f - 1)**3*(f + 1)/7
Let k(x) be the second derivative of x**2 + 5*x - 1/30*x**6 - 5/6*x**3 + 1/4*x**4 + 0 + 1/20*x**5. Find c such that k(c) = 0.
-2, 1
Let a(k) be the second derivative of k**7/126 - 2*k**6/45 + k**5/60 + 7*k**4/18 - 10*k**3/9 + 4*k**2/3 + 5*k. Let a(t) = 0. Calculate t.
-2, 1, 2
Let c be (6/(-1))/((-3)/3). Solve c*k**2 + 1 + 4 + 2*k**3 - 3 + 6*k = 0 for k.
-1
Let s(r) = -r - 4. Let z(n) = -n**3 - 5*n**2 + 8*n + 5. Let o be z(-6). Let i be s(o). Factor 6*x**3 + 9*x - 9*x**2 - 3*x**i + 23 - 26.
3*(x - 1)**3
Let p(i) be the second derivative of 0*i**2 + 0 + 5*i + 1/18*i**4 + 1/27*i**3 - 1/45*i**6 - 1/18*i**5 + 4/189*i**7. Find n such that p(n) = 0.
-1, -1/4, 0, 1
Let t(j) be the first derivative of 2*j**6/3 + 8*j**5/5 + j**4 - 14. Factor t(v).
4*v**3*(v + 1)**2
Let i be (1/7)/(3/2). Let z(v) be the first derivative of -1/7*v**2 + 0*v - i*v**3 + 2. Suppose z(w) = 0. Calculate w.
-1, 0
Let j(p) = p**2 + p - 4. Let w be j(3). Suppose -g + w = g. What is z in 2*z**2 - g*z**4 - 2*z**3 - 2*z**4 - 2*z**2 + 4*z**2 = 0?
-1, 0, 2/3
Let r be 658/(-224) + 6/2. Let y(q) be the third derivative of -1/6*q**3 - 1/120*q**5 + 0*q + 0 - q**2 - r*q**4. Factor y(i).
-(i + 1)*(i + 2)/2
Let t(w) be the first derivative of -w**4/16 - w**3/12 + w**2/8 + w/4 - 3. Factor t(j).
-(j - 1)*(j + 1)**2/4
Let g(n) = 26*n. Let q be g(1). Let v = 80/3 - q. Solve -8/3 - 16/3*y - 10/3*y**2 - v*y**3 = 0.
-2, -1
Let b = 0 - -1. Let 0*s + 0*s - 3*s**3 - s**4 + 2*s + b + s**3 = 0. Calculate s.
-1, 1
Let i(f) be the third derivative of 0*f**5 + 2/33*f**3 + 0 - 5*f**2 + 1/44*f**4 + 0*f - 1/660*f**6. Factor i(z).
-2*(z - 2)*(z + 1)**2/11
Let c = 1 + -1. Let n = 43/91 + 5/182. Factor n*w + 3/4*w**2 + c*w**3 - 1/4*w**4 + 0.
-w*(w - 2)*(w + 1)**2/4
Suppose -10 = -3*z + 38. Let v = -16 + z. Let v - 1/4*p**3 + 0*p + 1/4*p**4 - 1/4*p**2 + 1/4*p**5 = 0. What is p?
-1, 0, 1
Let s(f) be the first derivative of 4/5*f**2 + 0*f + 21/10*f**4 - 16/5*f**3 + 2 + 98/25*f**5. Factor s(j).
2*j*(j + 1)*(7*j - 2)**2/5
Suppose 2*v + 15 = -v. Let z(a) = 5*a**3 - 4*a**2 - a - 3. Let l(p) = -9*p**3 + 8*p**2 + p + 5. Let h(t) = v*z(t) - 3*l(t). Factor h(o).
2*o*(o - 1)**2
Factor 4*r**3 + 1 + 0 - 4*r + 0*r**3 - r**2.
(r - 1)*(r + 1)*(4*r - 1)
Let t(q) be the first derivative of -q**6/6 - 6*q**5/5 - 13*q**4/4 - 4*q**3 - 2*q**2 - 7. Factor t(v).
-v*(v + 1)**2*(v + 2)**2
Suppose h + 3*c = 13, -4*h + 2 = -3*c - 5. Suppose 0 = -0*a + 3*a - 12. Factor 10*i**3 - i - 7*i**a + 3*i**2 - h*i**2 - i**4.
-i*(i - 1)*(2*i - 1)*(4*i + 1)
Let t(b) = 5*b**4 - 6*b**2 + 5. Let r(p) = -81*p**4 + 96*p**2 - 81. Let v(q) = 2*r(q) + 33*t(q). Suppose v(i) = 0. What is i?
-1, 1
Let d(k) be the first derivative of 2*k**3/45 + k**2/15 + 11. Solve d(q) = 0.
-1, 0
Let w be (-2)/3*(-4 - -2). Let f(v) be the first derivative of 2 + v**2 + 0*v - w*v**3. Factor f(a).
-2*a*(2*a - 1)
Let t be -1*5/15 + 1. Factor 0*u + 0 + 2/3*u**2 + 0*u**3 - t*u**4.
-2*u**2*(u - 1)*(u + 1)/3
Let p be 3/6 - (-20)/8. Let n(l) be the first derivative of -1/4*l**2 + 0*l**p + 1/8*l**4 + 2 + 0*l. Factor n(w).
w*(w - 1)*(w + 1)/2
Let q be (4/126*6)/2. Let a(z) be the first derivative of -2 - 4/7*z - q*z**3 - 3/7*z**2. Find t such that a(t) = 0.
-2, -1
Let q(k) be the second derivative of k**4/12 - 2*k**3/3 + 3*k**2/2 - 11*k. Factor q(t).
(t - 3)*(t - 1)
Let n be (10/(-2) - -4)*6/(-5). Let u = 197/480 + -1/96. Solve -n*w - u*w**2 - 4/5 = 0.
-2, -1
Factor 0*w + 0 + 1/5*w**5 + 1/5*w**2 + 3/5*w**3 + 3/5*w**4.
w**2*(w + 1)**3/5
Let r(h) = -h**3 - h**2 + 7*h - 5. Let q(y) = 0*y**3 - y**2 + 10*y - 6 - 2*y - y**3. Let c(l) = -6*q(l) + 7*r(l). Find d, given that c(d) = 0.
-1, 1
Let a(y) be the second derivative of y**4/51 - 5*y**3/51 + 2*y**2/17 + 14*y. Factor a(m).
2*(m - 2)*(2*m - 1)/17
Let k(r) be the first derivative of -r**3/9 + r**2/2 - 2*r/3 + 11. Factor k(g).
-(g - 2)*(g - 1)/3
Find z, given that 1/4*z**2 - 1/2*z - 3/4 = 0.
-1, 3
Let b(c) = -c**2 + 1. Let d(x) = 2*x**2 + 2*x. Let l(z) = b(z) - d(z). What is k in l(k) = 0?
-1, 1/3
Let o = 3 + -1. Factor 5*x**5 + 0*x - 4*x - 4*x**3 + 6*x**4 + 3*x - 6*x**o.
x*(x - 1)*(x + 1)**2*(5*x + 1)
Let g(k) = k - 17. Let u be g(19). Let q(f) be the first derivative of 3 - f**u + 8/5*f**5 - f**6 - 4*f**3 + 4*f + 2*f**4. Let q(i) = 0. Calculate i.
-1, -2/3, 1
Factor -9/4*p**2 + 3/4*p**3 + 3/2*p + 0.
3*p*(p - 2)*(p - 1)/4
Factor 4/9*v - 2/9*v**2 - 2/9.
-2*(v - 1)**2/9
Let o(n) be the second derivative of -n**7/1050 + n**5/150 - n**3/30 + 4*n**2 + 5*n. Let k