1)/1). Let n(h) = p*v(h) - 2*m(h). Solve n(y) = 0.
-2, -1, 0, 1
Let d be (-70)/(-22) - -7*6/(-231). Let i(l) be the first derivative of 0*l**5 + 1/8*l**4 + 0*l - 1/12*l**6 - 2 + 0*l**2 + 0*l**d. Factor i(h).
-h**3*(h - 1)*(h + 1)/2
Let d(c) = -c**5 + c**4 + c**3 - c - 1. Let m(r) = 4*r**5 - 6*r**4 + 2*r + 2. Let h be 10/4 - 6/12. Let t(j) = h*d(j) + m(j). Let t(z) = 0. What is z?
0, 1
Let q(g) = -4*g**3 + 100*g**2 - 140*g + 60. Let f(p) = -p**3 + 20*p**2 - 28*p + 12. Let w(v) = 16*f(v) - 3*q(v). Find m, given that w(m) = 0.
1, 3
Let b be (-24)/60 - 66/10. Let v(o) = -o**3 - 7*o**2 - o - 2. Let k be v(b). Factor 0*c + 0 - 7/3*c**4 - c**k - 1/3*c**2 - 5/3*c**3.
-c**2*(c + 1)**2*(3*c + 1)/3
Factor -11*f**3 + 8*f**2 + 14*f**3 - 6*f**3 - 2*f**2.
-3*f**2*(f - 2)
Let l = 31/180 - -1/20. Factor -l*z**5 + 0 - 4/3*z**3 + 8/9*z**2 + 8/9*z**4 - 2/9*z.
-2*z*(z - 1)**4/9
Let p(q) be the second derivative of -q**6/120 + q**3/2 + 5*q. Let x(d) be the second derivative of p(d). Factor x(f).
-3*f**2
Let g(r) be the second derivative of 1/14*r**7 + 9/10*r**5 + 0 + 7*r + 1/2*r**3 - 2/5*r**6 - r**4 + 0*r**2. Determine v, given that g(v) = 0.
0, 1
Let b = 147 - 145. Find s, given that 0*s - 1/5*s**b + 1/5 = 0.
-1, 1
Factor 43*o**2 + 2 - 45*o**2 - 10 - 10*o.
-2*(o + 1)*(o + 4)
Let y(f) be the third derivative of f**6/30 - f**5/15 - f**4/6 + 2*f**3/3 - 6*f**2. Determine s, given that y(s) = 0.
-1, 1
Let l(p) be the third derivative of -8*p**2 + 1/540*p**6 + 0*p**3 + 1/108*p**4 + 0 - 1/135*p**5 + 0*p. Factor l(q).
2*q*(q - 1)**2/9
Suppose 0 = 5*x + 2*t - 19, -x - 3*t = -5 - 4. Let 1/3*j**2 - 1/3*j**x + 0 + 2/3*j = 0. Calculate j.
-1, 0, 2
Let p(n) = -24*n**2 - 57*n + 81. Let a(k) = 3*k**2 + 7*k - 10. Let d(q) = 33*a(q) + 4*p(q). Factor d(h).
3*(h - 1)*(h + 2)
Let l(p) = -14*p**3 + 51*p**2 - 68*p - 22. Let w(h) = 15*h**3 - 51*h**2 + 69*h + 21. Let o(b) = 6*l(b) + 5*w(b). Solve o(x) = 0.
-1/3, 3
Factor -4/5*a**4 + 0 + 3/5*a**3 - 4/5*a + 4/5*a**2 + 1/5*a**5.
a*(a - 2)**2*(a - 1)*(a + 1)/5
Suppose -6*i + 21 = i. Let j(g) be the first derivative of 1/4*g**2 - 2 + 1/4*g + 1/12*g**i. Factor j(o).
(o + 1)**2/4
Solve -4/5*l - 24/5 + 4/5*l**2 = 0.
-2, 3
Let u(n) be the third derivative of -n**7/210 - n**6/120 + n**5/60 + n**4/24 + n**2. Factor u(i).
-i*(i - 1)*(i + 1)**2
Let j(s) be the first derivative of -s**4/6 - s**3/3 + 2*s**2 - 4*s + 4. Let d(i) be the first derivative of j(i). Factor d(o).
-2*(o - 1)*(o + 2)
Factor -6/5*f + 8/5*f**2 + 0 - 2/5*f**3.
-2*f*(f - 3)*(f - 1)/5
Let g(w) = w + 4. Let k be g(-10). Let x be (-22)/k + (-6)/2. Determine d so that -2/3*d**3 + 2/3 - 2/3*d**2 + x*d = 0.
-1, 1
Factor 2/3*m**3 - 1/3*m**5 + 2/3*m**2 - 1/3 - 1/3*m - 1/3*m**4.
-(m - 1)**2*(m + 1)**3/3
Let u = -84/11 - -307/33. Find c such that -8/3 + u*c**3 - 22/3*c**2 + 28/3*c = 0.
2/5, 2
Let d(c) = c**3 + 5*c**2 + 2*c - 1. Let m(q) = -q**3 - q**2 - q - 1. Let v(z) = -d(z) - 2*m(z). Let b(a) be the first derivative of v(a). Factor b(w).
3*w*(w - 2)
Let o be (12/(-15))/((-2)/10). Let d be (-28)/(-21)*36/10. Factor 6/5*y**5 + d*y**3 + 12/5*y**2 + 0 + o*y**4 + 2/5*y.
2*y*(y + 1)**3*(3*y + 1)/5
Let f(n) = -5*n**2 + 5*n + 6. Let k(q) = 13 - q**2 + 12*q - 10*q**2 - q. Let r(l) = -l**2 - 2*l + 2. Let o be r(3). Let m(c) = o*f(c) + 6*k(c). Factor m(j).
-j*(j - 1)
Determine x so that 62/7*x**2 + 34/7*x**3 + 12/7 + 46/7*x + 6/7*x**4 = 0.
-3, -1, -2/3
Let f(y) = y**2 - 1. Let d(l) = -l. Let b be d(2). Let r(j) = j**3 - j**2 - j + 1. Let z(i) = b*f(i) - r(i). Factor z(o).
-(o - 1)*(o + 1)**2
Factor 20*t**4 + 138*t - 7*t**2 - 163*t - 3*t**2 - 10 + 20*t**3 + 5*t**5.
5*(t - 1)*(t + 1)**3*(t + 2)
Let q = 33 - 29. Let d(u) be the third derivative of -1/24*u**q - u**2 + 0 + 0*u - 1/120*u**6 + 0*u**3 - 1/30*u**5. Suppose d(f) = 0. What is f?
-1, 0
Let l be 1*(2 + 4) - 0. Suppose 3*r + 0 = l. Solve -r*w**3 + 7*w - 1 - w - 3 = 0.
-2, 1
Let z(t) be the first derivative of -4*t**5/15 - t**4/3 + 8*t**3/3 + 55. Factor z(p).
-4*p**2*(p - 2)*(p + 3)/3
Let j(y) be the first derivative of -4*y**3 + 10*y**2 + 8*y + 8. Factor j(c).
-4*(c - 2)*(3*c + 1)
Let t(v) = -2*v**2 - 9*v + 1. Let r be t(-4). Let j(q) be the first derivative of 3 + 2/5*q**r + 0*q**4 + 2*q - 4/3*q**3 + 0*q**2. Factor j(k).
2*(k - 1)**2*(k + 1)**2
Let r = -4 - -6. Factor -a**4 + 3*a**2 - r*a**3 - a**2 - 3*a**2.
-a**2*(a + 1)**2
Suppose p = -s, -p - 2*s - 20 = -4*p. Determine k, given that 6*k**4 - 15*k**2 + 4*k**3 + 8*k**4 - k**3 - 5*k**p - 3*k + 6 = 0.
-1, 2/3, 1
Let b(t) be the first derivative of -t**4/3 + 4*t**3/3 - 16*t/3 + 6. Factor b(k).
-4*(k - 2)**2*(k + 1)/3
Let m(t) be the first derivative of -t**6/90 + t**5/20 - t**4/18 - 4*t + 4. Let p(q) be the first derivative of m(q). Factor p(l).
-l**2*(l - 2)*(l - 1)/3
Factor 0*w + 5/6*w**2 + 3/2*w**3 - 1/6*w**5 + 0 + 1/2*w**4.
-w**2*(w - 5)*(w + 1)**2/6
Let m be 2 + (-16)/(-12) + -3. Let a(g) be the first derivative of 2/3*g**4 + 0*g + 2 - 1/9*g**3 - m*g**5 - 1/3*g**2. Suppose a(o) = 0. Calculate o.
-2/5, 0, 1
Let -4*q**2 + 2*q**2 - 2*q**2 = 0. What is q?
0
Let f(o) be the second derivative of o**8/560 + o**7/168 + o**6/240 + o**4/4 - 3*o. Let c(t) be the third derivative of f(t). Factor c(l).
3*l*(l + 1)*(4*l + 1)
Let m(l) be the second derivative of l**4/6 + 4*l**3/3 + 3*l**2 + 11*l. Determine y, given that m(y) = 0.
-3, -1
Factor 12/5 - 9*z**2 - 12/5*z.
-3*(3*z + 2)*(5*z - 2)/5
Let l(h) = h**4 + h**3 - h. Let r(t) = 14*t**4 + 9*t**3 - 7*t**2 - 9*t. Let f = -9 - -6. Let j(u) = f*r(u) + 21*l(u). Factor j(v).
-3*v*(v - 1)*(v + 1)*(7*v + 2)
Suppose 0 = -y + 2*y. Let n(j) be the third derivative of -j**2 - 1/12*j**4 + y*j - 1/30*j**5 + 0*j**3 + 0. What is h in n(h) = 0?
-1, 0
Let i(c) be the third derivative of -2*c**2 + 1/30*c**5 + 0*c**3 - 1/60*c**6 - 1/36*c**4 + 0 + 0*c + 1/315*c**7. Solve i(b) = 0 for b.
0, 1
Let p be -12*-1*2/18. Factor -p - 2*o - 2/3*o**2.
-2*(o + 1)*(o + 2)/3
Let q(m) = -10*m**3 - 10*m**2 - 7*m - 7. Let r(o) = -5*o**3 - 5*o**2 - 3*o - 3. Let j(s) = 3*q(s) - 7*r(s). Factor j(n).
5*n**2*(n + 1)
Let a be (-20)/(-6) + 10/15. Suppose -b + 2*b = 1, -4*b - a = -4*r. Factor 2 + 0 - 2*f**3 - 2*f - 4*f**r - 2.
-2*f*(f + 1)**2
Let z(t) be the third derivative of t**7/105 + t**6/60 - t**5/10 - t**4/12 + 2*t**3/3 - 22*t**2. Factor z(h).
2*(h - 1)**2*(h + 1)*(h + 2)
Suppose -5*l - 3*a = -4*l + 10, 4*l - 2*a = 16. Let f(p) be the second derivative of 0 - 3/20*p**5 - l*p - 1/4*p**4 + 0*p**2 + p**3. Factor f(x).
-3*x*(x - 1)*(x + 2)
Let z(l) = l**2 + 6*l - 1. Let a be z(-7). Let v(j) be the third derivative of 0 + 1/96*j**4 + 1/480*j**a + 0*j**3 + 0*j - 1/120*j**5 + j**2. Factor v(t).
t*(t - 1)**2/4
Let g(v) be the third derivative of v**6/48 - 7*v**5/120 + v**4/24 - 4*v**2. Solve g(s) = 0.
0, 2/5, 1
Factor 0*z + 4/17*z**3 + 0*z**2 + 2/17*z**4 + 0 - 2/17*z**5.
-2*z**3*(z - 2)*(z + 1)/17
Let y(d) be the first derivative of 2/25*d**5 - 4*d + 1/15*d**3 + 0*d**2 - 1/6*d**4 - 3. Let h(n) be the first derivative of y(n). Factor h(m).
2*m*(m - 1)*(4*m - 1)/5
Suppose -49 = -2*p + s - 0*s, -5*p = 3*s - 139. Let j = p - 26. Factor -2/7*n**4 + j*n**2 + 0*n + 2/7*n**3 + 0.
-2*n**3*(n - 1)/7
Let m = -1343/6 + 224. Factor 0*b + 0 + m*b**2.
b**2/6
Let h(q) be the third derivative of 0*q - 1/48*q**4 + 0*q**3 + 1/80*q**5 + 0 + 0*q**6 - 1/840*q**7 - 4*q**2. Let h(i) = 0. Calculate i.
-2, 0, 1
Let g = -125/3 - -42. Factor 0*m**3 + 0*m + 2/3*m**2 - g - 1/3*m**4.
-(m - 1)**2*(m + 1)**2/3
Let g(t) be the second derivative of -3*t - 1/105*t**7 + 0*t**4 - 1/30*t**6 + 0*t**3 + 0*t**2 - 1/50*t**5 + 0. Factor g(y).
-y**3*(y + 2)*(2*y + 1)/5
Suppose -2*h - 9 - 5 = -2*f, -2*f - 2*h = -22. Let c = f + -7. Solve -2*j**5 + 2*j**3 + 0*j + 1/2*j**4 - 1/2*j**c + 0 = 0 for j.
-1, 0, 1/4, 1
Let b(c) = c**3 - c. Let w(n) = 2*n**3 + 20*n**2 + 14*n - 36. Let a(h) = 2*b(h) + w(h). Factor a(r).
4*(r - 1)*(r + 3)**2
Let o be (2 + 5)*(1 + -3). Let p be (7/o)/(-1 + 0). Solve -p - 1/4*k**2 - 3/4*k = 0.
-2, -1
Let c(r) be the third derivative of r**6/540 + r**5/30 + r**4/4 + 5*r**3/6 - 5*r**2. Let t(u) be the first derivative of c(u). Solve t(a) = 0.
-3
Let j(s) be the first derivative of 3/8*s**4 + 0*s + 1/8*s**2 + 1/5*s**5 + 1/24*s**6 + 1/3*s**3 + 2. Solve j(y) = 0.
-1, 0
Let g be 1/(-15)*-10*(-12)/(-2). Factor 1/3 + 0*x**2 + 2/3*x*