9th Grade
How do you subtract polynomials?
{
"voice_prompt": "",
"manuscript": {
"title": {
"text": "How do you subtract polynomials?",
"audio": "How do you subtract polynomials?"
},
"description": {
"text": "To subtract polynomials, you rewrite the expression by distributing the minus sign and then combine like terms. Let’s go through it step-by-step.",
"audio": "To subtract polynomials, you rewrite the expression by distributing the minus sign and then combine like terms. Let’s go through it step-by-step."
},
"scenes": [
{
"text": "First, what’s a polynomial? It’s an expression made of one or more terms — each with a number, a variable, and a non-negative integer exponent.",
"latex": "a_nx^n + a_{n-1}x^{n-1} + \\dots + a_1x + a_0"
},
{
"text": "Now let’s subtract two polynomials: (3 times x squared plus 2 times x minus 5) subtracting (x squared minus 4 times x plus 3).",
"latex": "(3x^2 + 2x - 5) - (x^2 - 4x + 3)"
},
{
"text": "Step one: remove the parentheses by distributing the negative sign to every term in the second polynomial.",
"latex": "3x^2 + 2x - 5 - x^2 + 4x - 3"
},
{
"text": "Step two: combine like terms. Match the x squared terms, the x terms, and the constants.",
"latex": "(3x^2 - x^2) + (2x + 4x) + (-5 - 3)"
},
{
"text": "Step three: simplify. 3 times x squared minus x squared = 2 times x squared, 2 times x plus 4 times x = 6 times x, and negative 5 minus 3 = negative 8.",
"latex": "2x^2 + 6x - 8"
},
{
"text": "So the result is 2 times x squared plus 6 times x minus 8. That’s the simplified difference of the two polynomials.",
"latex": "2x^2 + 6x - 8"
},
{
"text": "Let’s try a longer example: (5 times x cubed minus 2 times x squared plus 7 times x minus 4) - (2 times x cubed plus 3 times x squared minus x plus 6).",
"latex": "(5x^3 - 2x^2 + 7x - 4) - (2x^3 + 3x^2 - x + 6)"
},
{
"text": "Distribute the negative sign: (5 times x cubed minus 2 times x squared plus 7 times x minus 4 minus 2 times x cubed minus 3 times x squared plus x minus 6)",
"latex": "5x^3 - 2x^2 + 7x - 4 - 2x^3 - 3x^2 + x - 6"
},
{
"text": "Now combine like terms: (5 times x cubed minus 2 times x cubed) plus (minus 2 times x squared minus 3 times x squared) plus (7 times x plus x) plus (-4 minus 6)",
"latex": "(5x^3 - 2x^3) + (-2x^2 - 3x^2) + (7x + x) + (-4 - 6)"
},
{
"text": "Simplify: three times x cubed minus five times x squared plus eight times x minus ten. That’s your final result.",
"latex": "3x^3 - 5x^2 + 8x - 10"
},
{
"text": "Subtracting polynomials is just like adding — but be careful with the signs. Distribute, then combine like terms.",
"latex": ""
}
],
"outro": {
"text": "To subtract polynomials, distribute the minus sign and combine like terms. With practice, it becomes second nature.",
"audio": "To subtract polynomials, distribute the minus sign and combine like terms. With practice, it becomes second nature."
}
}
}
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