*(i + 4)
Let l(h) be the first derivative of 0*h + 0*h**3 + 0*h**2 + 3/4*h**4 + 1/2*h**6 + 6/5*h**5 + 4. Factor l(q).
3*q**3*(q + 1)**2
Suppose -2*h + 40 = 3*h. Factor -3*l + 4 + 5*l**2 + h*l - l**3 + 3*l + 2*l**3.
(l + 1)*(l + 2)**2
Let v(x) be the first derivative of x**6/300 + 2*x**2 - 4. Let m(b) be the second derivative of v(b). Let m(g) = 0. Calculate g.
0
Find b, given that -2/13*b**2 + 2/13*b**3 - 8/13*b + 8/13 = 0.
-2, 1, 2
Let c = 72 - 72. Let h(l) be the second derivative of c*l**2 + 0 - 4*l - 1/36*l**3 - 1/36*l**4. Factor h(f).
-f*(2*f + 1)/6
Let c(f) = f**3 - 2*f**2 - 4*f - 1. Let n be c(4). Suppose 5*u + 5*g + n = 3*u, -4*u - g = 3. Factor u + 2 - 2*w**2 + 0*w**2.
-2*(w - 1)*(w + 1)
Let g(a) be the second derivative of a**4/114 - 4*a**3/57 + 4*a**2/19 - 19*a. Find t, given that g(t) = 0.
2
Determine l, given that -112*l**3 - 12*l**5 - 148*l**3 + 48*l + 132*l**2 - 45*l**3 + 93*l**4 + 89*l**3 = 0.
-1/4, 0, 2, 4
Let m be 16 + -11 - (-2)/(-1). Factor 2/5 + 2/5*s**4 + 0*s + 0*s**m - 4/5*s**2.
2*(s - 1)**2*(s + 1)**2/5
Let g be ((-2)/3*-6)/1. Suppose g*q - 3 = q. Factor -56*m**2 - 24*m - 2*m + q - 5 - 40*m**3.
-2*(2*m + 1)**2*(5*m + 2)
Let d = -22 - -48. Factor 66*f**2 + d*f**3 + 4 + 28*f + 44*f**3 + 25*f**4 + 3*f**2.
(f + 1)**2*(5*f + 2)**2
Let h = 0 + 0. Let i be 3*(32/30)/8. Factor -1/5*j**2 + h + i*j.
-j*(j - 2)/5
Let -4/13 - 18/13*p**2 + 22/13*p = 0. What is p?
2/9, 1
Let -1/6*l**3 - 4/3*l + 2/3 + 5/6*l**2 = 0. What is l?
1, 2
Let u(x) be the third derivative of -x**2 + 0*x + 0*x**3 - 49/120*x**6 + 7/30*x**7 + 0 + 1/6*x**4 - 1/15*x**5. Determine o, given that u(o) = 0.
-2/7, 0, 2/7, 1
Let w(b) be the second derivative of b**7/6300 - b**6/1800 - b**4/12 + 5*b. Let n(h) be the third derivative of w(h). Find g such that n(g) = 0.
0, 1
Let b = 1691/5 + -337. Factor b*j - 2/5*j**3 + 0*j**2 + 4/5.
-2*(j - 2)*(j + 1)**2/5
Factor 11*a - 23*a + 3*a**2 + 3*a**3 + 1 - 13.
3*(a - 2)*(a + 1)*(a + 2)
Find d such that 0 + 1/2*d**3 + 1/2*d**2 + 1/6*d**4 + 1/6*d = 0.
-1, 0
Suppose 0*y - 12 = -3*y. Factor -3*v**5 + 0*v**4 - 8*v**3 - 3*v**2 - y*v**4 - 5*v**4 - v**3.
-3*v**2*(v + 1)**3
Let -26*m**2 + 44*m - 40 + 5*m**3 - 4*m**2 + 16*m = 0. What is m?
2
Let y(u) = -3*u**3 - u + 2. Suppose 2*q = 3 + 5. Let t(x) = 13*x**3 - x**2 + 5*x - 8. Let d(m) = q*t(m) + 18*y(m). Suppose d(h) = 0. Calculate h.
-2, -1, 1
Suppose 0 = 3*f + 4*h - 18, 5*f - 5*h + h = -2. Suppose -7 - 3 = 5*l - 4*v, 2*l + 6 = f*v. Factor 14*s**3 - 3*s**l + s**5 - 5*s**4 + 5*s - 4*s**3 - 1 - 7*s**2.
(s - 1)**5
Suppose 4*i = -1 + 9. Let t be (1/2)/((-21)/(-36)). Factor -2/7 - 4/7*w + t*w**i.
2*(w - 1)*(3*w + 1)/7
Factor -36/5 + 12*w + 4/5*w**3 - 28/5*w**2.
4*(w - 3)**2*(w - 1)/5
Suppose -2*a = g + a - 103, -3*g + 2*a = -298. Let o = 704/7 - g. Solve o*i - 2/7 - 2/7*i**2 = 0.
1
Factor 84*r**2 - 137 + 36*r**3 - 18*r - 50*r + 149.
4*(r + 3)*(3*r - 1)**2
Factor -2/15*f**3 + 0 + 0*f + 2/15*f**2.
-2*f**2*(f - 1)/15
Let p(n) be the third derivative of n**7/1260 - n**6/90 + n**5/15 + n**4/12 + 3*n**2. Let b(j) be the second derivative of p(j). Factor b(z).
2*(z - 2)**2
Let i = 288/125 + 12/125. Determine f so that -24/5*f - 3/5*f**2 - i + 9/5*f**3 = 0.
-1, -2/3, 2
Let j(i) be the third derivative of i**7/210 - i**6/40 + i**5/30 + 6*i**2. Factor j(y).
y**2*(y - 2)*(y - 1)
Let b(p) be the second derivative of -p**7/7 - 11*p**6/15 - 37*p**5/30 - 5*p**4/6 - 2*p**3/9 - 6*p. Determine t, given that b(t) = 0.
-2, -1, -1/3, 0
Let j(h) be the second derivative of -h**5/40 - h**4/12 + h**3/12 + h**2/2 + 15*h. Factor j(c).
-(c - 1)*(c + 1)*(c + 2)/2
Let u(c) be the second derivative of -c**5/10 + c**4/2 + 73*c. Solve u(i) = 0 for i.
0, 3
Factor -14/15*i + 0 - 16/15*i**2 - 2/15*i**3.
-2*i*(i + 1)*(i + 7)/15
Let y(b) be the first derivative of -2 - 3/10*b**2 + 0*b**3 + 0*b + 3/20*b**4. What is a in y(a) = 0?
-1, 0, 1
Let t(d) = -14*d - 12. Let f be t(-1). Determine n, given that 3/5*n - 4/5*n**f + 1/5*n**3 + 0 = 0.
0, 1, 3
Let c be 14/(-7) + 5/1. Let d be 0 - (c + -3) - -3. Let 2/5*s**d - 2/5 + 2/5*s**2 - 2/5*s = 0. What is s?
-1, 1
Let v(f) = -f**3 + f**2 + 5*f + 5. Let j(r) = 2*r**2 + 6*r + 4*r**2 + 6 - 4*r**2. Let i = -14 + 8. Let p(h) = i*v(h) + 5*j(h). Factor p(s).
2*s**2*(3*s + 2)
Let f(r) be the third derivative of 0 + 2*r**2 + 1/24*r**3 - 1/96*r**4 - 1/240*r**5 + 1/480*r**6 + 0*r. Suppose f(q) = 0. What is q?
-1, 1
Suppose -39*n = -45*n. Factor n + 2/7*w**3 + 2/7*w**2 - 2/7*w - 2/7*w**4.
-2*w*(w - 1)**2*(w + 1)/7
Let o = 2/917 + 5492/4585. Determine t so that -4/5*t**4 + o*t**2 - 2/5 + 2/5*t**3 - 2/5*t = 0.
-1, -1/2, 1
Suppose -2 = 5*h - 12. Let 2*l**2 + 0*l**h - 5 + 0 + 3 = 0. What is l?
-1, 1
Let c(o) = -o**2 - o. Suppose 5*d - 16 = -2*n, 2*n + 3 = 5*d - 1. Let r(s) = -3*s + s**d - 2*s**2 - 5*s - s**2 + 2. Let a(j) = -4*c(j) + r(j). Factor a(h).
2*(h - 1)**2
Let a be (-3)/(352/(-280) + (-18)/(-21)). Factor -a*s**2 + 12*s + 3/2*s**3 - 6.
3*(s - 2)**2*(s - 1)/2
Let u(b) be the second derivative of b**5/20 - b**4/4 + b**3/2 - b**2/2 + 24*b. Factor u(y).
(y - 1)**3
Let c(i) be the first derivative of -i**4/42 + i**3/21 + 2*i**2/7 + 2*i - 3. Let f(r) be the first derivative of c(r). Factor f(q).
-2*(q - 2)*(q + 1)/7
Let a be (-17 + 9)/((-5)/1). Suppose 4/5*w**2 + a*w + 4/5 = 0. What is w?
-1
Let d = 156 + -3275/21. Let n(b) be the third derivative of -1/70*b**5 - b**2 + 1/28*b**4 + 1/420*b**6 + 0*b - d*b**3 + 0. Find m such that n(m) = 0.
1
Let q(s) be the second derivative of s**7/63 - 2*s**6/45 + s**4/9 - s**3/9 - 15*s. Determine t so that q(t) = 0.
-1, 0, 1
Factor -390*b**3 + 375*b**3 + 7*b**4 - 5*b**5 - 27*b**4.
-5*b**3*(b + 1)*(b + 3)
Let l(c) = -c**2 - c + 1. Let v be l(-2). Let a(b) = -1. Let k(d) = -3*d**2. Let n(x) = v*k(x) + 3*a(x). Factor n(w).
3*(w - 1)*(w + 1)
Let y(a) be the second derivative of a**4/24 + a**3/12 - a**2/2 - 4*a. Solve y(u) = 0 for u.
-2, 1
Let c be 112/21 - (-4)/(-1). Factor c - 2/3*m - 2/3*m**2.
-2*(m - 1)*(m + 2)/3
Suppose -7*i + 9 = -10*i. Let t be (i/(-12)*0)/2. Find l such that -2/5*l**3 + 1/5*l**4 + 1/5*l**2 + t + 0*l = 0.
0, 1
Let z(t) be the third derivative of t**8/1512 - 2*t**7/945 + t**5/135 - t**4/108 + 31*t**2. Factor z(k).
2*k*(k - 1)**3*(k + 1)/9
Let r be ((-30)/4)/(-1 + 1/(-1)). Factor -3/2 - r*x**2 + 21/4*x.
-3*(x - 1)*(5*x - 2)/4
Let y(d) = d**2 + 7*d - 5. Let g be y(-8). Suppose 0 = g*b - 0*b. Solve 1/2*k**2 + b - 1/2*k**3 + 0*k = 0 for k.
0, 1
Let b(r) be the first derivative of r**5/2 - r**4/8 - 5*r**3/6 + r**2/4 - 20. Let b(y) = 0. Calculate y.
-1, 0, 1/5, 1
Let c(t) be the third derivative of t**6/10 + 31*t**5/15 + 4*t**4/3 - 40*t**3/3 + 23*t**2 - t. Solve c(s) = 0 for s.
-10, -1, 2/3
Suppose -6*q + 8 = -2*q. Let l = 627/5 - 125. Find f such that 0*f**q + 0 + 2/5*f - l*f**3 = 0.
-1, 0, 1
Suppose -y - 2 + 12 = 0. Let d be 75/y + (-1)/(-2). Factor d*w + 2*w**3 - 22/3*w**2 - 8/3.
2*(w - 2)*(w - 1)*(3*w - 2)/3
Let n(m) be the first derivative of -m**6/720 + m**5/120 - m**4/48 - 8*m**3/3 + 6. Let t(k) be the third derivative of n(k). Let t(s) = 0. Calculate s.
1
Let s(x) = x**2 + 7*x - 3. Let t(v) = 3*v**2 + 6*v - 3. Let y(j) = 6*s(j) - 5*t(j). Let y(a) = 0. What is a?
1/3, 1
Let c(p) = p**3 - 5*p**2 - 2*p + 4. Let s be c(4). Let m = s - -24. Factor -2/7*d**m + 6/7*d**3 + 0 + 2/7*d - 6/7*d**2.
-2*d*(d - 1)**3/7
Suppose 55 = 2*j + 3*j. Let j*o**2 + o**4 - o + 2*o**3 - 12*o**2 - o**3 = 0. What is o?
-1, 0, 1
Factor -15*i**2 - i**3 + 5*i**3 + 9*i**3 + 2*i + 0*i**3.
i*(i - 1)*(13*i - 2)
Let u be (3/6)/((-1)/(-6)). Suppose -1 - 5 = -u*r. Determine s, given that 0*s**r - 2*s**3 + s**2 + s**3 = 0.
0, 1
Let c = 69 + -42. Let m be 6*1/(-3)*-1. Determine y, given that m*y**3 + c + 2*y**4 - 27 = 0.
-1, 0
Let x = -1 - -1. Suppose x = -h + 2*h - 2. Factor 5*l + 6*l**3 - l - 2*l**4 - 2*l - 6*l**h.
-2*l*(l - 1)**3
Let v(l) be the second derivative of -l**5/50 + l**4/2 - 21*l**3/5 + 49*l**2/5 - 13*l. Factor v(z).
-2*(z - 7)**2*(z - 1)/5
Factor 671*q**4 - q**3 - 669*q**4 + 2*q**3 + q**5.
q**3*(q + 1)**2
Let b(t) be the first derivative of -4*t**5/65 - 9*t**4/26 - 8*t**3/39 + 32. Factor b(r).
-2*r**2*(r + 4)*(2*r + 1)/13
Let s(u) = u - u**2 + 2 - 2 + 1. Let v(f) = -4*f**4 - f**3 + 10*f**2 - 5*f - 6. Let b = 1 + 0. Let q(x) = b*v(x) + 6*s(x). Let q(n) = 0. What is n?
-1